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Nowadays, healthcare waste management has become one of the significant environmental, health, and social problems. Due to population and urbanization growth and an increase in healthcare waste disposals according to the growing number of diseases and pandemics like COVID-19, disposal of healthcare waste has become a critical issue. Authorities in big cities require reliable decision support systems to empower them to make strategic decisions to provide safe disposal methods with a prospective vision. Since inappropriate healthcare waste management systems would definitely bring up dangerous environmental, social, health, and economic issues for every city. Therefore, this paper attempts to address the landfill location selection problem for healthcare waste using a novel decision support system. Novel decision support model integrates K-means algorithms with Stratified Best-Worst Method (SBWM) and a novel hybrid MARCOS-CoCoSo under grey interval numbers. The proposed decision support system considers waste generate rate in medical centers, future unforeseen but potential events, and uncertainty in experts’ opinion to optimally locate required landfills for safe and economical disposal of dangerous healthcare waste. To investigate the feasibility and applicability of the proposed methodology, a real case study is performed for Mazandaran province in Iran. Our proposed methodology could efficiently deal with 79 medical centers within 4 clusters addressing 9 criteria to prioritize candidate locations. Moreover, the sensitivity analysis of weight coefficients is carried out to evaluate the results. Finally, the efficiency of the methodology is compared with several well-known methods and its high efficiency is demonstrated. Results recommend adherence to local rules and regulations, and future expansion potential as the top two criteria with impor- tance values of 0.173 and 0.164, respectively. Later, best location alternatives are determined for each cluster of medical centers. . . . . . Keywords Healthcare Waste Management K-mean Algorithm Stratified BWM MARCOS Grey Numbers CoCoSo 1 Introduction why it should be carefully designed, established and moni- tored in order to efficiently isolate the waste from the sur- Healthcare landfills mainly consist of hazardous waste and rounding environment. The location of healthcare facilities serve to prevent contamination between the waste and the or Healthcare Landfill Selection (HLS) is regarded as an un- surrounding environment, particularly groundwater. That is exceptional ill-structured decision-making problem since it contains issues related to various fields of study and there are different and occasionally contradictory stakeholders to This article belongs to the Topical Collection: Big Data-Driven Large- take into account. In other words, it is critical to provide a Scale Group Decision Making Under Uncertainty multidisciplinary technique that is able to take into account all these factors and meet the expectations of actors affected * Ali Ebadi Torkayesh by the location [47, 80]. ali.torkayesh@socecon.rwth-aachen.de Landfilling has been known as the most efficient way of Erfan Babaee Tirkolaee disposing in various countries compared to other waste dis- erfan.babaee@istinye.edu.tr posal ways, which is still being utilized even in developed countries [49]. Since Healthcare Waste Management Department of Industrial Engineering, Istinye University, Istanbul, Turkey (HWM) involves harmful elements; thus, it has been catego- rized under infectious and hazardous activities by a large num- School of Business and Economics, RWTH Aachen University, 52072 Aachen, Germany ber of environmental associations and scholars worldwide. A Cluster-based Stratified Hybrid Decision Support Model under Uncertainty: Sustainable Healthcare Landfill... 13615 With the onset of the recent COVID-19 pandemic, its impor- proximity to them and their waste generation rate. Next, envi- tance has become increasingly clear [63, 64]. There are several ronmental decision-making problems such as HLS problems modern engineered landfills, i.e., sanitary landfills, to reduce are very sensitive to changes, scenarios and future events that the risk evaluation of landfill hazards to conserve the public may impact the importance of decision criteria. Such events and health and environment [7]. Usually, the landfills are located scenarios can make the decision-making result obsolete under at a distance away from the healthcare facilities. The most different circumstances only after a few months. Thus, to ad- significant idea of the landfill is containment and storage of dress the HLS problem in the best way, we consider possible the waste transferred and disposed in it [54]. On the other impacts of future events within the decision-making environ- hand, sustainable development is another non-ignorable con- ment. For this purpose, this study develops a hybrid DSS that cept in which the triple bottom line perspectives of economic, takes the impacts of future events into account to address the environmental and societal sustainability are addressed. HLS problem. In the weight determination part of the DSS, Therefore, it is necessary to find a sustainable location to Stratified Best-Worst Method (SBWM) is utilized to identify locate a landfill facility for daily and recurring processes of optimal weight values of criteria considering most potential storage, treatment, and disposal [64]. future events and their impacts. This is the first study to develop Based on the above-mentioned factors, it is obvious the a DSS including stratification theory for the HLS problem complexity of the decision-making problem examined and through the SBWM. This study introduces a hybrid MCDM the requirement to organize it with an efficient Decision framework in the proposed DSS where two well-known Support System (DSS) according to multi-dimensional criteria Combined Compromise Solution (CoCoSo) and should be considered. Accordingly, the major goal of the cur- Measurement Alternatives and Ranking according to the rent study is to design a DSS in order to support decision- Compromise Solution (MARCOS) are integrated to develop makers in the sustainable HLS problem with the application the MARCOS-CoCoSo method. Furthermore, this study is of big data in the decision-making process. the first in its kind to develop a hybrid MCDM method using Finally, this research tries to find appropriate answers for MARCOS and CoCoSo as the MARCOS-CoCoSo under grey the following questions: interval numbers (MARCOS-CoCoSo-G). The biggest motiva- tion behind developing the hybrid MARCOS-CoCoSo method 1) Why HLS problem is important? is to minimize the biasedness and subjectivity of any of these 2) How location alternatives should be selected for medical methods in the prioritization of candidate locations. To be more centers? In terms of the correct and optimal selection of specific, CoCoSo and MARCOS are two novel MCDM rank- location alternatives, how medical centers should be ing methods that are developed recently. Both methods have assigned to the right, closest and most efficient landfill? shown high efficiency in addressing highly complex decision- making, evaluation, and assessment problems in the previous 3) What are the effective and important decision criteria for the HLS problem? studies. On the other hand, both methods consist of a combined 4) Are there any future events that may affect the HLS prob- structure of different compromise solutions and utility functions lem? If yes, what are these future events? How can a which enhance the reliability of the results. Finally, this is the decision-making problem consider their impacts? first study to develop a DSS using the K-means algorithm, 5) How can location alternatives for the HLS problem be SBWM, and MARCOS-CoCoSo-G to tackle a big data HLS prioritized based on experts’ opinions? How should we problem considering the impacts of uncertain future events and consider uncertainty in real-life experts’ opinions? uncertain opinions of experts. This study is broken down into 4 sections. Section 2 con- To answer these questions, this study proposes a cluster- textualizes the research within the existing literature about the based stratified hybrid DSS considering uncertainty. The first application of MCDM approaches in HLS. Section 3 repre- contribution of this study is related to using the K-means al- sents the proposed hybrid MCDM method. The case study gorithm for HLS along with uncertain Multi-Criteria problem is illustrated in Section 4, and finally, Section 5 con- Decision-Making (MCDM). The K-means algorithm is one cludes the research with a discussion on the main findings, of the popular clustering algorithms among data mining algo- limitations, and future research opportunities. rithms. Due to its high reliability and straightforward struc- ture, K-means algorithm is used to analyze big data of medical centers to group them with medical centers which have high 2 Background and related work similar characteristics. The reason to use K-means algorithm to group medical centers relies on the fact that managers In this section, the most relevant studies performed on the would be able to understand how medical centers with similar application of MCDM techniques for HLS and in conjunction characteristics are located in the province. Therefore, the prop- with the use of Big Data Analytics (BDA) in healthcare waste er location of a landfill can be determined accurately based on systems. 13616 E. B. Tirkolaee and A. E. Torkayesh MCDM methods have been considered as one of the po- Consistency Method (FUCOM) and Combined Distance- tential comprehensive tools to deal with complex environmen- based Assessment (CODAS) method, to classify 5 sug- tal and healthcare problems such as healthcare landfill location gested landfill sites with respect to the criteria of environ- selection ([14, 80]). During the recent decade, landfill location mental protection and public health. Another hybrid selection problem has attracted noticeable attention from re- MCDM approach was designed by Rahimi et al. [49]to searchers. Dehe and Bamford [11] proposed two MCDM tackle the sustainable landfill site selection for MSW. methods for a healthcare infrastructure location problem in They utilized GIS techniques, group fuzzy Best-Worst the National Health Service (NHS) organization, United Method (BWM) and group fuzzy Multi-Objective Kingdom. Evidential Reasoning (ER) was first employed to Optimization by Ratio Analysis (MULTIMOORA) solve the model and then Analytical Hierarchy Process (AHP) method in order to generate suitability maps, obtain was implemented to evaluate the results obtained by ER. criteria weights and evaluate the alternative sites, respec- Finally, the same solutions were achieved for the case study tively. Yazdani et al. [71] suggested a rough-based BWM problem. According to Eiselt and Marianov [19], AHP has the method for HWM disposal location in Madrid, Spain. The highest application to treat Municipal Solid Waste (MSW) interval rough numbers were used to process imprecise data facility location problems. A comprehensive structured survey for a private hospital. was conducted by Thakur and Ramesh [62] in order to review Recently, Manupati et al. [35] applied the fuzzy VIKOR the main research works performed on HWM between 2005 method for selecting the best HWM disposal procedures and 2014. They discussed the trends, main topics, challenges, during and after the COVID-19 pandemic in Tamil Nadu, and future research directions in the field of study, such as India. They considered 10 criteria and 9 alternatives and landfill location analysis. A hybrid MCDM method, accord- compared the output with the results obtained with fuzzy ing to Interpretive Structural Modelling (ISM), fuzzy AHP TOPSIS. Finally, incineration was demonstrated as the and fuzzy Techniques for Order Preference and Similarity to best disposal technique. Torkayesh et al. [65] introduced Ideal Solution (TOPSIS), was developed by Chauhan and the SBWM for sustainable waste disposal technology se- Singh [8] to tackle the sustainable healthcare waste disposal lection. They incorporated uncertainty and doubts into facility location problem in a region of Uttarakhand, India. decision-making processes for two major cities in Iran. They considered 8 different criteria based on sustainable de- In another research, Torkayesh et al. [66] proposed a velopment, which were extracted from the literature. Lee hybrid BWM-grey MARCOS model based on GIS to et al. [30] applied AHP to evaluate HWM treatment tech- cope with the landfill location section for HWM during nologies in the NHS organization, United Kingdom. To the COVID-19 pandemic. They addressed the sustainabil- find the optimal disposal technology, they considered 4 ity criteria and could implement their method in criteria of “Legal & Compliance”, “Guidelines”, Hamedan, Iran. Eventually, a set of sensitivity analyses “Carbon & Environmental” and “Economics” and 3 alter- were carried out to test the reliability and robustness of natives. A Multi-Criteria-Spatial Decision Support System the results. (MC-SDSS) was developed by Dell’Ovo et al. [12]tofind Table 1 summarizes recent studies conducted on landfill the best locations for healthcare facilities in Milan, Italy. location selection which developed their methodologies based They took into account 3 criteria from the literature and on the MCDM methods. assessed them by Multi-Criteria Decision Analysis Since the last decade, BDA has been recently become an (MCDA) and then employed Geographic Information important topic in healthcare systems due to its high and effi- System (GIS) to add spatial components. There are some cient applications [24, 29, 41, 42, 50]. There are some useful other hybridized solutions based on GIS and MCDM review studies addressing the significance, adoption, chal- methods which have been suggested to examine the lenges, and implications of BDA in healthcare, such as HLS problem. For example, Vucijak et al. [69]claimed Mehta and Pandit [37], Chen et al. [10] and Shafqat et al. that the application of MCDM approaches with GIS tools [60]. Sahni et al. [52] underlined the use of BDA to address in environmental topics has risen significantly over the the application of HWM in the agriculture and disaster man- last years. agement sector. Their proposed model based on predictions Mardani et al. [36] surveyed three decades of research on demonstrated that waste can be utilized either in the same healthcare and medical problems addressing recent develop- industry or even in some other industry. ments of MCDM methods. They evaluated 202 research Although BDAs are very well-known in different fields studies and concluded that AHP and fuzzy AHP are the [53], such algorithms have not been frequently used in the most frequently employed techniques by scholars. A case field of waste management. In one of the recent studies which study was investigated by Badi and Kridish [4] in Libya have used BDA, Eghtesadifard et al., (2020) developed a nov- in order to treat the landfill site selection problem. They el DSS using GIS, K-means algorithm and integrated MCDM proposed a hybrid MCDM method, based on Full model to address municipal landfill location selection problem A Cluster-based Stratified Hybrid Decision Support Model under Uncertainty: Sustainable Healthcare Landfill... 13617 Table 1 Summary of recent MCDM-based studies Reference Methodology Combined methods Uncertainty type Case study Kharat et al. [28] AHP-TOPSIS – Type-1 fuzzy set India Güler and Yomralıoğlu [23] AHP GIS – Turkey Yildirim et al. [76]TOPSIS GIS – Turkey Alkaradaghi et al. [2] AHP GIS – Iraq Chabuk et al. [9] AHP GIS – Iraq Karasan et al. [25]AHP – Pythagorean fuzzy set Turkey Kamdar et al. [27] AHP GIS – Thailand Moghaddam et al. [40] MCDM concept GIS – Iran Rahimi et al. [49] BWM-MULTIMOORA GIS Type-1 fuzzy set Iran Tercan et al. [61] AHP GIS – Turkey Zarin et al. [77] AHP GIS Type-1 fuzzy set Pakistan Ali et al. [3] AHP-TOPSIS GIS Type-1 fuzzy set India Mahmood et al. [32] AHP GIS – Iraq Torkayesh et al. [66] BWM-MARCOS GIS Grey interval-numbers Iran in Iran. The MCDM model was constructed based on 3Methodology Decision-Making Trial and Evaluation Laboratory (DEMATEL), Analytical Network Process (ANP), multi- This section presents definitions, requirements, and important objective optimization method by ratio analysis (MOORA), preliminaries of the proposed decision support model for lo- Weighted Aggregated Sum Product Assessment (WASPAS), cating landfills to address healthcare waste management. and Complex Proportional Assessment (CORAS) methods. In the most recent example, Qureshi et al., [48] developed a novel method based on fuzzy AHP, Support Vector 3.1 K-means algorithm Machine (SVM) algorithm, and Markov Chain to address mu- nicipal landfill location selection based on the prediction of K-means algorithm has been among the most well-known and urban physical growth in Iran. frequently developed algorithms in data mining and machine To the best of our knowledge, there are a limited number of learning fields [1, 6]. K-means clustering is an unsupervised research works in the literature that have been exclusively algorithm that enables clustering a big dataset into k number of addressing the application of BDA, specifically clustering clusters based on the closest distance. In other words, the K- algorithms in HLS. The present work is among the first means algorithm is developed based on the principle of mini- studies which provides a useful framework based on the mization of intra-cluster variance and maximization of the application of BDA to treat the sustainable HLS problem. distance between each pair of clusters [18, 33, 34]. Using Therefore, the main contributions of the research are ex- the K-means algorithm, the number of clusters is selected first. plained as follows: Then, for each datum in the dataset, represented as a point, the distance between these points and the central cluster point is i. Proposing a novel DSS based on a complex integration of determined. To calculate the distance of these points and clus- data mining and MCDM methods. ter points, Euclidean distances are used. In each iteration, the ii. Proposing K-means clustering algorithm along with average distance of data points in each cluster is computed and Stratified interval-valued MCDM to address HLS the central gravity of each cluster is computed. The K-means problem. algorithm can be mathematically represented as follows. iii. Addressing the HLS problem considering stratification For a given set of data points (x , x , …, x ), the K-means 1 2 n theory to consider the impact of future events using algorithm attempt to cluster n data points (observations) into K SBWM. clusters S ={S , S , …, S } with an aim to minimize the 1 2 n iv. Proposing a novel hybrid decision model using cluster sum of squares or variance. MARCOS and CoCoSo which ended up to the K K MARCOS-CoCoSo method. arg min ∑ ∑jj jj x−μ ¼ arg min ∑ jS j VarðÞ S ; ð1Þ i i S i¼1 x∈S S i¼1 v. Implementing the developed MARCOS-CoCoSo under grey interval numbers (MARCOS-CoCoSo-G). 13618 E. B. Tirkolaee and A. E. Torkayesh where μ denotes the mean of data points in S.Eq. (1)can Step 6- Optimal weight of criteria in each state is calcu- i i W j * * * be rewritten to formulate an equivalent model to minimize the B lated as W ; W ; …; W . For each pair of W and 1 2 n pairwise squared deviations of data points as Eq. (2). W W , the optimal weight must meet the requirement of 1 W ¼ a and W ¼ a . To ensure these constraints, j Bj W jW arg min ∑ ∑ jj jj x−y : ð2Þ 2jS j the maximum absolute differences of W −a j and S i¼1 i x;y∈S i j Bj W −a j are minimized for criteria. Therefore, W jW BWM can be formulated by taking into account the non-negativity characteristic and the sum condition of 3.2 Stratified BWM the weights. Weight determination in MCDM methods is of high signifi- W W B j cance as weight vector and its values have a critical role in minimize max −a ; −a Bj jW W W j W generating results of a decision model. In the middle of 2010s, Rezaei et al., [51] offered a weight determination model for MCDM problems which was based on mathematical optimi- subject to zation formulation. BWM has attracted the attention of scholars in various fields due to its reliable procedure through ∑ W ¼ 1; ð3Þ optimization models [5, 66]. Considering the high integration of uncertain sets into the MCDM model, several versions of W ≥0 for all j: BWM have been developed in recent years [38]. Fuzzy BWM This model can be reformulated below: [22], and Bayesian BWM [39] are two important extensions of BWM which allow decision-makers to express their opin- minimizeξ ions through uncertain and possibilistic scales. Recently, Torkayesh et al., [65] proposed a novel version of BWM subject to under the concept of stratification to include possible impacts of future unforeseen events on the weight determination pro- −a ≤ξ for all j; Bj cess. The SBWM model is defined based on the following algorithm. −a for all j; jW ð4Þ ∑ W ¼ 1 for all j; Step 1- Required decision criteria {c , c , …, c }are 1 2 n identified and defined according to the literature review W ≥0 for all j; and experts’ opinions. Step 2- Potential and possible future events with a high where W shows the weight of criterion j, W represents the j W impact on the weight of decision criteria are identified weight of the worst criterion, W denotes the weight of the and defined. The likelihood of occurrence of the defined best criterion, a represents the pairwise value of comparing Bj events is assigned by experts. the best criterion to criterion j,and a indicates the pairwise jW Step 3- Probabilities for transitioning between the states value of comparing each criterion to the worst criterion. are calculated based on the likelihood of occurrence of events. Step 7- Consistency ratio of the obtained optimal weight Step 4- Under each defined state, the best criterion (the of criteria in each state is calculated based on Eq. (5). most preferred) and the worst criterion (the least pre- ferred) are chosen based on experts’ opinions. Step 5- Best-to-other (B-t-O) and others-to-worst (O-t- W) vectors are obtained through a pairwise comparison Consistency Ratio ¼ ð5Þ Consistency index using a scale of 1–9. In this scale, 9 stands for the highest preference and 1 shows the lowest preference for a crite- rion. B-t-O vector is represented by A =(a , a , …, B B1 B2 a )where a displays the preference of the best criterion Bn Bj Step 8- Final optimal weight of each criterion considering over criterion j. Similarly, O-t-W vector is shown as impacts of all states is obtained through the multiplication A =(a , a , …, a ) where a represents W 1W 2W nB jw of transition probability and weight coefficients in each the preference of criterion j over the worst criterion state. W and a =1. WW A Cluster-based Stratified Hybrid Decision Support Model under Uncertainty: Sustainable Healthcare Landfill... 13619 n m D a a b b a a 1 i i i i i i 3.3 Preliminaries of grey numbers (4) D ¼ ⋃ ⋃ min c ; d ; c ; d g; max ; 2 j j j j i¼1 j¼1 b b i i d ; c ; d g,while c ≠ 0, d ≠ 0and (j =1,2,…,m), j j j j j n m A grey number is an unknown and uncertain number whose (5) D *D ¼ ⋃ ⋃ min a c ; a d ; b c ; b d g; max 1 2 i j i j i j i j i¼1 j¼1 exact value is shown within a range (interval). Preliminaries, a c ; a d ; b c ; b d ; i j i j i j i j definitions, requirements, and functions for grey numbers are (6) μD ¼ ⋃½ μa ; μb ; 1 i i i¼ n 1 completely described below. μ μ μ μ μ (7) D ¼ ⋃½ minðÞ a ; b ; maxðÞ a ; b : 1 i i i i i¼1 Definition 1- Let D be a grey value. If ∀d∈D and Definition 5- The length of a grey value like D =[a, b]is e e d ¼½ a; b , then d is represented as an interval grey num- calculated as: L(D)=[b − a]. e Definition 6- For two grey numbers D =[a, b]and D = 1 2 ber. a and b are the upper and lower values of d such that [c, d]while a < b and c < d, the possibility degree P a, b ∈ R. Max 0;L −MaxðÞ 0;b−c ðÞ e e Definition 2-[31,79]. Suppose that d ¼½ a; b and d ¼ 1 2 fg G ≤G ¼ ,where L = L(G )+ L(G ). 1 2 * 1 2 ½ c; d are two grey numbers, and μ >0, μ ∈ R. The For the position relation between two grey values, arithmetic operations are denoted as follows: (1) if P{D ≥ D } < 0, 5 then D < D , expressing that D 1 2 1 2 1 e e d þ d ¼½ a þ c; b þ d 1 2 is smaller than D , −d ¼½ −b;−a ; 1 (2) if P{D ≥ D } = 0, 5 then D = D , expressing that D 1 2 1 2 1 e e is equal to D , d −d ¼½ a−d; b−c ; 2 1 2 (3) if P{D ≥ D } > 0, 5 then D > D , expressing that D e 1 2 1 2 1 μd ¼½ μa; μb : is more significant than D . Generally, grey numbers are continuous in an interval, 3.4 Grey MARCOS (G-MARCOS) while those values from a finite number or a set of numbers are known as discrete grey numbers. An integrated method for MARCOS is one of the recently developed ranking MCDM both continuous and discrete grey numbers has led to a novel description of grey numbers [75, 79]. techniques [59]. Stević et al. [59] tested the MARCOS method on a sustainable supplier selection problem in the healthcare Definition 3- Assume that D is a grey number. If D ¼ ⋃ i¼1 sector. Since its initial days of development, MARCOS has ½a ; b ,then we call D as an Extended Grey Number (EGN). i i been used in various fields. Stević and Brković [58] integrated Now, we suppose that D is a union of a set of closed or open the full consistency method (FUCOM) and MARCOS to eval- intervals, while n is an integer and 0 < n < ∞,while a , b ∈ i i uate the human resource department in the transportation in- R,and b < a ≤ b < a [75]. i − 1 i i i +1 dustry. Stanković et al. [56] suggested a new version of MARCOS under fuzzy logic to examine road traffic risk Theorem 1- If D is an EGN, then, the following conditions analysis with uncertain information. Simić et al. [55]in- come true: 1) D =[a , b ]is a continues EGN if and only if 1 n troduced the MARCOS method under picture fuzzy logic a ≤ b (∀i >1) or n =1. i i − 1 to assess risks related to railway infrastructures. Grey 2) D ={a , a , …, a } is a discrete EGN if and only if a = 1 2 n i numbers constitute another well-known uncertain set that b ; are frequently integrated with MCDM models. Torkayesh 3) D represents a mixed EGN if only part of its intervals et al. [66] proposed an integrated decision model using integrates to crisp numbers and the others keep as geographic information system, BWM, and MARCOS intervals. method under grey interval numbers to select a suitable location for the construction of a landfill. In the same Definition 4- For two EGNs D ¼ ⋃ ½a ; b and D ¼ year, Pamucar et al. [44] suggested a combined MCDM 1 i i 2 i¼1 framework basedonSWARA andMARCOSmethods ⋃ c ; d ,let a ≤ b (i =1, 2, …, n), c ≤ d (j =1, 2, j j i i i i under grey interval numbers for the evaluation of service j¼1 quality in Spanish airports. Ecer and Pamucar [16]pro- …, m), μ ≥ 0and μ ∈ R. Therefore, the arithmetic operations posed a new version of MARCOS under an intuitionistic are [79]: fuzzy environment to evaluate the performance of insur- n m ance companies on healthcare services during the (1) D þ D ¼ ⋃ ⋃ a þ c ; b þ d ; 1 2 i j i j n i¼1 j¼1 COVID-19 pandemic. Ecer [15] suggested a combined (2) −D ¼ ⋃½ −b ; −a ; ; 1 i i n m i¼1 decision model consisting of six MCDM models includ- (3) D −D ¼ ⋃ ⋃ a −d ; b −c ; 1 2 i j i j i¼1 j¼1 ing MARCOS, ARAS, COPRAS, CoCoSo, MAIRCA, 13620 E. B. Tirkolaee and A. E. Torkayesh and SECA to evaluate 10 batteries of electric vehicles Step 5- Sum of the elements of the weighted normalized based on different socio-economic factors. matrix is determined as follows. MARCOS-G performs based on the following steps. 1. Step 1- According to the performance of alternatives against several criteria, the initial decision matrix is con- S ¼ S ; S ¼ ∑ ⋃ V ; V ; ð12Þ i 1ij 2ij 1ij 2ij i¼1 structed accordingly. 2. Step 2- Ideal (AI) and anti-ideal (AAI) solutions are de- where S denotes the sum of the weighted normalized grey termined based on the initial decision matrix. values of each alternative i. Step 6- Utility degrees of each alternative i in relation to 2 3 the anti-ideal and ideal solution are computed based on ⋃½ a ; b ⋃½ a ; b ⋯⋃½ a ; b 11 11 12 12 1m 1m Eqs. (13)–(14): 6 7 ⋃½ a ; b ⋃½ a ; b ⋯⋃½ a ; b 21 21 22 22 2m 2m 6 7 X ¼ ; ð6Þ 4 5 ⋮⋮ ⋯ ⋮ ⋃½ a ; b ⋃½ a ; b ⋯⋃½ a ; b n1 n1 n2 n2 nm nm where a represents the lower bound value, and b the − − − H ¼ H ; H ¼ ; ð13Þ ij ij i 1ij 2ij aai upper bound value for alternative i and criterion j,for i =1, 2, …, m, j =1, 2, …, n. i H þ ¼ H þ ; H þ ¼ : ð14Þ i 1ij 2ij With regard to the nature of criteria, AAI and AI can be S ai determined according to Eqs. (7)–(8): AAI ¼ min x if j∈B;max x if j∈C; ð7Þ ij ij i i Step 7- The utility function of each alternative i concern- AI ¼ max x if j∈B;min x if j∈C; ð8Þ ij ij ing the anti-ideal and ideal solutions is determined based i i on Eqs. (15)–(16): where B stands for benefit criteria, and C shows cost criteria. H þ Step 3- The components of the normalized matrix N = − − − fHðÞ¼ fH ;fH ¼ ; ð15Þ i 1ij 2ij þ − H þ H [n ] are computed using Eqs. (9)–(10): ij m ∗ n fHðÞ þ ¼ fH þ ;fH þ ¼ ; ð16Þ i 1ij 2ij H þ þ H i i ⋃½ a ; b ia ia − where fHðÞ denotes the utility function with respect to e ¼ ⋃ c ; d ¼ if j∈C; ð9Þ ij ij ij ⋃ a ; b þ ij ij the anti-ideal solution, while fHðÞ shows the utility function with respect to the ideal solution. ⋃ a ; b ij ij e ¼ ⋃ c ; d ¼ if j∈B; ð10Þ ij ij ij ⋃½ a ; b ia ia Step 8- Total utility function of alternatives is obtained by Eq. (17). where e represents normalized grey value of alternative i ij against criterion j. Step 4- The weighted matrix V =[v ] is determined ij m ∗ n fHðÞ¼ fH ;fHðÞ j i 1ij 2i by multiplying the normalized matrix with the weight H þ H i i coefficients of criteria according to Eq. (11): ¼ : ð17Þ þ − 1−fHðÞ 1−fHðÞ 1 þ þ fHðÞ þ fHðÞ i i V ¼ ⋃ V ; V ¼ w e ; ð11Þ ij 1ij 2ij ij ij where V represents weighted normalized grey value of ij Step 9- Grey length values of utility functions are em- alternative i against criterion j. ployed to find the final ranking order of alternatives. A Cluster-based Stratified Hybrid Decision Support Model under Uncertainty: Sustainable Healthcare Landfill... 13621 3.5 Grey CoCoSo (CoCoSo-G) Yazdani et al. [72] introduced a novel ranking MCDM tech- δ ¼ ∑ w l ; ð17Þ i j ij j¼1 nique based on combined compromise functions. Due to the utilization of three compromise score functions to compute the where δ indicates the sum of the weighted normalized grey final compromise score of alternatives in CoCoSo, it has values of each alternative i. shown high reliability in generating results for complex decision-making problems. This characteristic of CoCoSo Step 4- Power weight of comparability sequences of al- made it a very popular tool to address complex problems in ternatives is calculated as Eq. (18): various fields. Right after its development, Yazdani et al. [73] extended the traditional CoCoSo method under grey interval numbers to address a supplier selection problem in construc- tion management. Ecer and Pamucar [17] integrated BWM P ¼ ∑ ⋃ c ; d ; ð18Þ i ij ij and improved CoCoSo with Bonferroni functions to address j¼1 a sustainable supplier selection problem. Peng and Huang [45] where P denotes the sum of the power of weighted nor- combined CRITIC and CoCoSo under fuzzy logic to evaluate i malized grey values of each alternative i. financial risks. Torkayesh et al. [67] offered an integrated MCDM model using BWM, LBWA, and CoCoSo techniques Step 5- Three aggregation scores are determined based to analyze healthcare sectors in Eastern Europe with respect to on Eqs. (19)–(21): healthcare fundamentals and infrastructures. Deveci et al. [13] developed an improved version of CoCoSo using the fuzzy power heronian function to rank autonomous vehicles in traf- fic management. Recently, Yazdani et al. [74] suggested a P þ δ i i new decision support model to address a sustainable supplier Q ¼ t ; t ¼ ; ð19Þ 1ij 2ij i1 m ∑ðÞ P þ δ selection problem using the integrated CRITIC-CoCoSo tool i i i¼1 under interval-valued Neutrosophic set. The CoCoSo-G method and its execution steps are given δ P below: i i Q ¼ n ; n ¼ þ ; ð20Þ 1ij 2ij i2 min δ min P i i i i Step 1- Using Eq. (6), the initial decision matrix is also λδ þðÞ 1−λ ðÞ P considered in CoCoSo-G. i i Q ¼ m ; m ¼ ; ð21Þ 1ij 2ij i3 Step 2- Initial decision matrix is normalized using Eqs. λ max δ þðÞ 1−λ max P i i (18)–(19) based on the nature of criteria. i i For benefit criteria: where 0 ≤ λ ≤ 1 which is normally as λ = 0.5 or can be chosen by experts. ⋃ a ; b − min ⋃ a ; b ij ij ij ij Step 6- Final compromise score of each alternative is l ¼ ⋃ c ; d ¼ ; ð15Þ ij ij ij calculated using three aggregation scores according to max ⋃ a ; b − min ⋃ a ; b ij ij ij ij i i Eq. (22): and for cost criteria: max ⋃ a ; b −⋃ a ; b ij ij ij ij 1 1 l ¼ ⋃ c ; d ¼ : ð16Þ Q ¼ðÞ Q Q Q þðÞ Q þ Q þ Q : ð22Þ ij ij ij i i1 i2 i3 i1 i2 i3 max ⋃ a ; b − min ⋃ a ; b 3 ij ij ij ij i i where l represents the normalized grey value of alternative ij i over criterion j. Step 7- To prioritize the alternatives, the length of the grey values of Q is obtained. Step 3- Sum of the weighted grey decision matrix is calculated according to Eq. (17): 13622 E. B. Tirkolaee and A. E. Torkayesh 3.6 Cluster-based SBWM-MARCOS-CoCoSo-G Healthcare landfill location selection with sustainability perspective. This section presents a novel decision-making model, called cluster-based SBWM-MARCOS-CoCoSo-G which is used to Definition of scope, criteria, and potential future address a landfill location selection for healthcare waste with a events. sustainability perspective. The main contribution of this meth- od relies on integrating the SBWM model with an uncertain ranking hybrid MCDM model. To solve a complex decision- Data collection for clustering medical centers using making problem with big data structure, the K-means algo- K-means algorithm. rithm is used to enhance the capability of the decision-making by clustering hospitals and medical centers with respect to Identification of possible candidate loction their characteristics. Integration of the K-means algorithm alternatives in each cluster. with a stratified hybrid decision model under grey numbers is conducted for the first time in this study. Moreover, this research is the first to develop a hybrid ranking MCDM model Calculation of probabilities of states based on by combining CoCoSo and MARCOS methods under grey likelihood of occurrence of events. interval numbers. Although there exist other well-known un- certainty sets such as fuzzy logic and Neutrosophic sets, the current study aims to apply grey interval numbers according to Applying SBWM for calculation of optimal weight coefficients of criteria. the following reasons. Interval grey numbers can express the diversified and usable information based on decision-makers’ thoughts and logic. On the other hand, interval grey numbers Applying Grey MARCOS-CoCoSo to prioritize can easily consider uncertainty, impreciseness, vagueness, locations in each cluster. and inconsistency of the information in better-diversified environment. Although fuzzy logic and Neutrosophic sets also empower us to express uncertain information but are Applying BORDA method to determine overall not as well as interval grey numbers in terms of express- ranking order. ing diversified uncertain information. Finally, this is the first study in the literature of waste facility location prob- lems to select landfill locations using a cluster-based strat- Sensitivity and comparative analysis. ified hybrid decision-making model with a prospective vision. Fig. 1 Diagram of the proposed methodology In this section, the complete procedure of the cluster-based SBWM-MARCOS-CoCoSo-G is given based on the prelim- Step 5. Ranking order of location alternatives in each inaries reviewed in previous subsections. A graphical presen- cluster is obtained using MARCOS-G with the integra- tation of the proposed methodology is illustrated in Fig. 1. tion of the weight in SBWM. Step 6. To identify the final ranking order of location Step 1. Primary clustering attributes are defined, and alternatives in each cluster, Borda voting method is used clusters are made using the K-means algorithm. to integrate the ranking order of CoCoSo-G and According to the constructed clusters of hospitals and MARCOS-G into a unified ranking order. medical centers, potential location alternatives are identified. Step 2. Required criteria and potential future events are defined. Under each state, the weight coefficients of the criteria are computed. Then, transitioning probability is used along with weight coefficients of the criteria in each 4 Problem definition state to calculate the optimal weight coefficient of the criteria. For developing countries, landfilling is still considered as one Step 3. Initial decision matrix is constructed considering of the waste disposal methods for urban and rural waste. location alternatives in each cluster. Although landfilling may seem like a semi-sanitary disposal Step 4. Ranking order of location alternatives in each method with a simple structure, it needs deep investigation to cluster is obtained using CoCoSo-G with the integration construct landfills with respect to different factors. On the of weights of the SBWM. other hand, waste separation is another important issue that A Cluster-based Stratified Hybrid Decision Support Model under Uncertainty: Sustainable Healthcare Landfill... 13623 should be addressed before landfilling operations. Healthcare stands for the total number of hospitals and infirmaries in a waste is different from other types of waste such as organic city. waste; therefore, it takes specific requirements for landfilling healthcare waste. This happens due to dangerous and infec- 4.2 Results of clustering tious materials that may be included within the waste of healthcare centers such as hospitals. Increasing demand for Due to the high amount of medical waste generated in 79 healthcare services and the high consumption rate of medical major hospitals and infirmaries in the province, there are pos- materials have intensified attention to address healthcare sible future investments by public and private environmental waste in the most appropriate way. Since inappropriate treat- sectors to build four landfills in different parts considering ment of healthcare waste could cause too many environmental accessibility and expansion ability. For this purpose, the K- and social damages for people living around the landfills. means clustering algorithm is applied to categorize 79 medical Considering all these conditions, selecting a location for centers into four groups based on three main parameters as landfilling becomes a highly complex and multi-dimensional medical waste generation rate before COVID-19, medical decision-making problem. Addressing such problems requires waste generation rate after COVID-19, and proximity of hos- reliable decision support models to enable real-life authorities pitals to each other in different districts or cities. All the re- in related organizations to select the most suitable locations quired input data were collected from the healthcare depart- for constructing new landfills. An important step to address ment of Mazandaran University of Medical Sciences (2021) landfill location selection for healthcare waste is to find the for a day. Based on the K-means algorithm defined in the most important and effective criteria that have a significant previous section, 79 medical centers are categorized into four role in terms of technical, environmental, social, and econom- groups as illustrated in Fig. 3. Cluster 1 (first from left) in- ic aspects. As discussed earlier, several indicators and decision cludes 16 medical centers, cluster 2 (on the right of cluster 1) criteria are defined considering the visions of stakeholders and includes 17 medical centers, cluster 3 covers up to 20 medical associated experts. Identified criteria are categorized into three centers, and cluster 4 (first from right) includes 26 medical sustainability pillars of social, environmental, and economic centers. criteria. Table 2 presents a detailed overview of the main In order to determine possible location alternatives accord- criteria, sub-criteria, their type, description, and references. ing to the clustered medical centers, an expert is invited from the healthcare department of Mazandaran University of Medical Sciences who is also in contact with environmental 4.1 Case study organizations and waste management department of the prov- ince. According to the experts in healthcare waste manage- Mazandaran is one of the most densely populated provinces in ment, candidate locations are identified and illustrated in Iran which is located on the southern coast of the Caspian Sea. Fig. 4. It is geographically divided into two zones: the coastal plains, Figure 4 presents information about medical centers and and the mountainous areas. There are 79 major hospitals and clusters that they are associated with. More importantly, infirmaries in Mazandaran. Accordingly, waste management Fig. 4 demonstrates 12 candidate locations in each cluster. is one of the most significant concerns of the managers in this Each cluster is assigned with three possible and candidate province. Moreover, the recent pandemic has made unexpect- locations that have potential characteristics to be used as ed challenges and waste management has encountered a high- landfills. level of uncertainty. According to the current status of Mazandaran University of Medical Sciences (2021) to cope 4.3 Results of SBWM with the challenges and burden of the pandemic, managers believe that they should consider alternative facilities to dis- Weight determination of effective and critical decision criteria pose the COVID-19 related medical waste quickly and timely. to select the best candidate locations in each cluster is of high The purpose is to prevent from running out of available ca- significance. However, as discussed earlier, healthcare waste pacity to treat the medical waste. Hence, it is so critical to management and landfill location selection have become com- utilize MCDM techniques under uncertainty to define and plex and period-based decision-making. This indicates that prioritize some alternatives as candidate locations for waste authorities require more reliable decision-making models that disposal. In this study, a set of alternatives is considered for can consider the impact of changes of future events in the each cluster and the aim is to rank the best ones. weight determination process. For this purpose, again the ex- Figure 2 illustrates Mazandaran province and the number pert is invited to provide important insights on possible future of medical centers in each city. Each number on the red points events that can have deep effects on locating landfills. The expert states two important events that may occur in the future https://en.mazums.ac.ir/ and have a serious influence on solutions. Event 1 is related to 13624 E. B. Tirkolaee and A. E. Torkayesh Table 2 Criteria for healthcare landfill location selection Main criteria Sub-criteria Type Description References Social Adherence to local rules Beneficial This criterion measures how each alternative is aligned with local rules as well [26, 70, 71] and regulations (C1) as governmental and organizational regulations. Satisfaction level (C2) Beneficial This criterion measures the satisfaction level of occupants of residential areas [25, 66, 71] around the landfill alternative. Economic Land price (C3) Cost This criterion represents the average land price. [25, 46] Transportation and Cost This criterion measures operational costs including transportation and [25, 70] maintenance cost (C4) maintenance. Future expansion potential Beneficial This criterion represents the possibility of future expansion in the capacity of a [66, 71] (C5) landfill alternative. Environmental Emissions (C6) Cost This criterion represents water, soil, and air emissions. [65, 70] Distance to residential areas Beneficial This criterion measures the average distance of landfill alternatives from [49, 66, 77] (C7) residential areas. Distance to waste sorting Cost This criterion denotes the distance of landfill alternatives from sorting and [27, 49] facilities (C8) segregation facilities. Geological characteristics Beneficial Geological characteristics are used to measure environmental and geological [2, 3, (C9) characteristics around landfill alternatives. 25, 71, 77] the development of special collection technologies for medical 3) S3: Event 2 happens. waste. Event 2 is related to the possible enactment of laws on 4) S4: Both events happen at the same time. making restrictions on the structural condition of landfills for their expansion ability and sustainability. According to the The next step is to determine the likelihood of occurrence identified events, two potential future events generate four of states which are required to determine transition probabil- different states. These states are defined as below: ities. According to the experts, the likelihood of Event 1 is 55%, and the likelihood of Event 2 is 75%. Also, it is estimat- 1) S1: None of the events happen and the system stays in its ed that with a likelihood of 10% none of the events happen in current situation. the future. In this case, we take into account the probability of 2) S2: Event 1 happens. the state occurrence according to the lowest provided Fig. 2 Distribution of 79 medical centers in Mazandaran province A Cluster-based Stratified Hybrid Decision Support Model under Uncertainty: Sustainable Healthcare Landfill... 13625 Fig. 3 Generated clusters and hospitals likelihood. For example, the probability of State 1 (S1) is The probabilities for transitioning the states are demon- represented by P while the probabilities of Event 2 are de- strated in Fig. 5. noted as 5.5 P , and 7.5P .Let’s assume that all events are After determining probabilities of transitioning among 1 1 independent; therefore, the probability of State 4 (S4) can be states, the weight determination process starts with applying determined based on the multiplication of two events that are BWM under stratification theory. For this purpose, the best involved. Thus, the probability of S4 is 37.5 P . The sum of criterion (BC) and the worst criterion (WC) are selected in these probabilities must be equal to one. Hence. P can be each state. Later, best-to-others (BTC) and others-to-worst determined as follows: (OTW) vectors are constructed in each state. Detailed infor- mation of the SBWM model is presented in Table 3 where BC 14P þ 37:5P ¼ 1; 1 1 and WC, as well as weight vectors, are provided under each state. P ¼ 0:0613: Fig. 4 Candidate locations in each cluster 13626 E. B. Tirkolaee and A. E. Torkayesh Table 3 SBWM results States S1 S2 S3 S4 Best criterion C3 – C4 – C5 – C1 – Worst criterion – C2 – C2 – C2 – C2 C1 36 37 28 19 C2 81 71 91 81 C3 18 39 68 36 C4 53 19 79 25 C5 46 44 13 27 C6 45 56 35 65 C7 34 57 35 56 C8 55 57 54 54 C9 56 34 35 47 Table 5 presents the performance score of candidate loca- tion alternatives in each cluster based on the expert’s opinion. This multi-cluster matrix is used to generate a normalized decision matrix and weight normalized decision matrix for each cluster. Finally, compromise solutions and utility func- Fig. 5 Transitioning probabilities tions are obtained in order to prioritize candidate locations in each cluster. Table 6 represents information regarding calcu- To find the optimal weights of criteria, transitioning prob- lations of the MARCOS-G method for each cluster. In the abilities are used. In this regard, weight coefficients of the same way, Table 7 represents information about the results defined criteria are multiplied to transitioning probabilities in of the CoCoSo-G method for each cluster. order to determine the optimal weight coefficients according- Finally, Table 8 illustrates the grey length of solutions of ly. Table 4 presents information on optimal weight coeffi- both MARCOS-G and CoCoSo-G along with the ranking cients of the defined criteria. Adherence to local rules and order of alternatives in each cluster. Now using the Borda regulations (C1) is assigned with the highest importance while method, we can obtain insights from Table 8. In Cluster #1, the satisfaction level of people around landfills is considered both methods select A1 as the best option to be considered for as the least important criterion. Based on the results, the healthcare landfills. In Cluster #2, both methods are consistent criteria are ranked based on their importance as follows: C1 in selecting A5 as the best candidate location. In Cluster #3, > C5 > C4 > C9 > C3 > C7 > C6 > C8 > C2. According methods are inconsistent in selecting the best option for land- to this ranking, social satisfaction level (C2) is the least im- fill location where MARCOS-G selects A8 as the best option portant criterion. Table 4 Optimal weight coefficients 4.4 Results of MARCOS-CoCoSo-G States S1 S2 S3 S4 Optimal weight This section presents the results of the proposed hybrid rank- ing MCDM method which is called MARCOS-CoCoSo-G for C1 0.127 0.126 0.188 0.258 0.173 evaluation of landfill location candidates in Fig. 4.The C2 0.027 0.025 0.023 0.023 0.024 MARCOS-CoCoSo-G is applied to prioritize these location C3 0.298 0.126 0.063 0.111 0.105 alternatives in each cluster in order to find the most suitable C4 0.076 0.277 0.054 0.167 0.146 location candidate for possible future landfill construction in C5 0.096 0.094 0.222 0.167 0.164 each cluster. The most important step in applying MARCOS- C6 0.096 0.075 0.125 0.056 0.097 CoCoSo-G is to construct an initial decision matrix based on C7 0.127 0.075 0.125 0.067 0.100 experience and background of the expert using interval num- C8 0.076 0.075 0.075 0.067 0.074 bers which takes a value between 0 and 100. Since there exist C9 0.076 0.126 0.125 0.084 0.117 several qualitative criteria in this study, 0–100 scale is used to ξ* 0.084 0.101 0.153 0.076 – express opinions with more convenience. A Cluster-based Stratified Hybrid Decision Support Model under Uncertainty: Sustainable Healthcare Landfill... 13627 Table 5 Initial decision matrix with grey interval numbers Cluster Loc. C1C2 C3C4 C5 C6C7 C8C9 #1 A1 [70,90] [90,95] [55,60] [30,50] [70,80] [55,60] [20,30] [20,35] [80,90] A2 [60,75] [80,90] [50,60] [60,70] [65,75] [25,40] [60,80] [70,80] [55,60] A3 [40,45] [80,90] [60,65] [40,45] [25,45] [35,55] [35,55] [55,65] [50,55] #2 A4 [80,85] [45,75] [60,70] [65,70] [30,40] [65,70] [25,40] [50,60] [35,55] A5 [35,55] [55,60] [25,40] [35,50] [15,30] [40,50] [30,50] [45,60] [60,70] A6 [80,90] [40,60] [20,30] [45,60] [75,85] [55,60] [35,60] [50,55] [35,40] #3 A7 [30,35] [50,75] [65,80] [35,45] [25,30] [60,80] [40,60] [40,50] [45,50] A8 [55,65] [50,55] [25,30] [50,70] [60,80] [20,30] [75,85] [30,40] [65,85] A9 [50,60] [85,90] [45,55] [40,55] [65,85] [35,40] [65,70] [70,80] [40,60] #4 A10 [55,60] [35,60] [30,50] [40,60] [35,55] [45,55] [15,30] [25,30] [50,55] A11 [50,75] [75,85] [35,50] [40,60] [55,60] [15,25] [35,45] [40,50] [40,50] A12 [65,75] [70,80] [35,50] [40,60] [45,60] [35,50] [30,40] [75,90] [70,75] while CoCoSo-G selects A7 as the best option. In the last complexity of the K-means algorithm is highly dependent on cluster, again both methods are consistent in selecting A11 the input data size. Therefore, for case studies with bigger data as the best location for landfill. structures on a national or global level, the solution time of the K- With regard to the obtained results, it should be noted that means can strongly affect the total time complexity of the sug- decision-making under different criteria and uncertainty leads gested methodology. to a reliable solution that can be implemented. Here, managers According to the obtained results, one of the most impor- may consider a number of highly-prioritized candidate loca- tant practical implications on locating a landfill in the tions in each cluster according to the required capacity for Mazandaran Province is related to local rules and regulations. treating waste. Therefore, the next important step is the estab- This means that all strategical and long-term decisions regard- lishment of the required facilities. ing landfills for HWM must pay high attention to adherence of One of the main advantages of the proposed cluster-based new projects to the current local policies and guidelines. SBWM-MARCOS-CoCoSo-G along with its reliability and pre- Another important practical point has to do with the possible cise is related to its low time complexity. It is important to point laws and regulations on the structural conditions of landfill out that time of complexity of soft computing-based MCDM and other related infrastructures. Therefore, any efforts to lo- methods increases as the number of decision criteria and alterna- cate landfills for HWM should take all current regulations, tives. Time complexity of the SBWM is very sensitive to the acts, and incentives in order to install landfills in the most number of events and generated states. Moreover, the time optimal locations. Results of the ranking part show how well Table 6 MARCOS-G results − þ − þ Cluster Alternative S H H fHðÞ fHðÞ f(H ) i i i i i i #1 A1 0.978 1.247 0.786 1.001 0.978 1.247 0.435 0.707 0.349 0.568 0.424 1.033 A2 1.169 1.417 0.939 1.138 1.169 1.418 0.457 0.672 0.367 0.540 0.539 1.093 A3 0.918 1.152 0.737 0.925 0.918 1.152 0.442 0.696 0.355 0.559 0.405 0.933 #2 A4 1.153 1.352 1.013 1.188 1.153 1.352 0.454 0.624 0.399 0.548 0.584 1.047 A5 0.713 1.022 0.626 0.898 0.713 1.022 0.371 0.764 0.326 0.671 0.281 1.067 A6 0.937 1.167 0.823 1.025 0.937 1.167 0.427 0.663 0.375 0.583 0.439 0.986 #3 A7 1.059 1.346 0.727 0.923 1.059 1.346 0.467 0.754 0.320 0.517 0.419 1.003 A8 0.938 1.221 0.644 0.838 0.938 1.222 0.455 0.772 0.312 0.530 0.360 0.944 A9 1.111 1.365 0.762 0.936 1.112 1.365 0.483 0.728 0.331 0.500 0.458 0.969 #4 A10 0.959 1.296 0.720 0.973 0.959 1.296 0.423 0.772 0.317 0.579 0.372 1.122 A11 0.911 1.243 0.684 0.933 0.911 1.243 0.419 0.780 0.314 0.585 0.349 1.092 A12 1.185 1.549 0.889 1.162 1.186 1.549 0.437 0.747 0.328 0.560 0.478 1.277 13628 E. B. Tirkolaee and A. E. Torkayesh Table 7 CoCoSo-G results Cluster Alternative δ P Q Q Q Q i i i1 i2 i3 i #1 A1 0.196 0.512 5.716 8.600 0.216 0.544 2.273 4.522 0.628 0.967 1.715 3.346 A2 0.393 0.773 5.493 8.645 0.215 0.562 3.221 5.859 0.625 1.000 2.110 3.961 A3 0.467 0.757 4.491 8.072 0.181 0.527 3.378 5.651 0.526 0.937 2.047 3.780 #2 A4 0.196 0.512 6.556 8.684 0.246 0.552 2.847 5.054 0.714 0.972 2.062 3.587 A5 0.393 0.773 3.549 8.261 0.143 0.542 2.998 6.261 0.417 0.955 1.750 4.066 A6 0.467 0.757 5.512 8.512 0.217 0.556 3.931 6.253 0.632 0.980 2.408 4.101 #3 A7 0.196 0.512 3.590 7.897 0.140 0.507 2.000 4.807 0.404 0.897 1.332 3.368 A8 0.393 0.773 4.651 8.443 0.187 0.555 3.294 6.285 0.538 0.983 2.031 4.116 A9 0.467 0.757 7.292 8.602 0.288 0.564 4.409 6.250 0.828 0.998 2.858 4.126 #4 A10 0.393 0.773 4.680 8.670 0.180 0.598 3.803 7.277 0.521 0.970 2.211 4.564 A11 0.196 0.512 2.594 8.467 0.099 0.569 2.000 5.872 0.286 0.922 1.180 3.909 A12 0.467 0.757 7.463 8.967 0.282 0.616 5.255 7.311 0.814 0.998 3.181 4.625 the proposed methodology tackled decision-making on land- vector, weight vector in State 1, weight vector in State 2, weight fills locations based on characteristics of 79 medical centers. vector in State 3, and weight vector in State 4. The goal of Based on the optimal selection of the location candidates, sensitivity analysis is to show how well SBWM can consolidate medical centers would minimize their external costs related all events and their impacts and propose a solution accordingly. to the disposal of healthcare waste by selecting right location Table 9 presents information about weight vectors and their for the establishment of landfills. corresponding grey length and ranking order using MARCOS-G for candidate locations in each cluster. Benchmarking Cluster #1, we observe that as the focus is only Event 1 is the best option 4.5 Sensitivity analysis: Impact of weight coefficients (A1) is no longer best in other states. State 1 considers A3 as best, State 2 considers A1, and in the worst-case State 3 selects A1 as The aim of this study by using SBWM within the proposed the worst option for landfill. This shows that focusing only on DSS is to ensure how considering multiple future events and one specific event and considering its impact cannot provide us a their impacts can affect the solutions of the DSS. In other reliable environment to make decisions. All possible events words, this is to show how only considering a specific event should be considered to obtain a consensus solution. can lead to misleading solutions. In this regard, this part con- In thesameway,Table 10 presents a similar test for ducts a sensitivity analysis test to observe the behavior of the CoCoSo-G under several weight vectors and their DSS under five different weight vectors as optimal weight Table 8 Final results of Cluster Alternative MARCOS-G CoCoSo-G Borda MARCOS-CoCoSo Grey length Rank Grey length Rank Score Rank #1 A1 0.590 1 0.488 1 4 1 A2 0.506 3 0.467 2 1 2 A3 0.565 2 0.458 3 1 2 #2 A4 0.442 3 0.425 2 1 2 A5 0.736 1 0.570 1 4 1 A6 0.555 2 0.413 3 1 2 #3 A7 0.583 2 0.604 1 3 1 A8 0.619 1 0.506 2 3 1 A9 0.527 3 0.307 3 0 2 #4 A10 0.669 2 0.516 2 2 2 A11 0.680 1 0.698 1 4 1 A12 0.625 3 0.312 3 0 3 A Cluster-based Stratified Hybrid Decision Support Model under Uncertainty: Sustainable Healthcare Landfill... 13629 Table 9 Impact of weight coefficients on results of MARCOS-G Cluster Alternative Optimal S1 S2 S3 S4 Grey length Rank Grey length Rank Grey length Rank Grey length Rank Grey length Rank #1 A1 0.590 1 0.522 2 0.653 1 0.531 3 0.618 1 A2 0.506 3 0.519 3 0.479 3 0.533 2 0.487 3 A3 0.565 2 0.524 1 0.496 2 0.635 1 0.523 2 #2 A4 0.442 3 0.447 3 0.411 3 0.479 3 0.414 3 A5 0.736 1 0.764 1 0.728 1 0.730 1 0.754 1 A6 0.555 2 0.628 2 0.590 2 0.510 2 0.550 2 #3 A7 0.583 2 0.568 2 0.576 2 0.594 2 0.567 2 A8 0.619 1 0.576 1 0.636 1 0.612 1 0.609 1 A9 0.527 3 0.493 3 0.554 3 0.504 3 0.540 3 #4 A10 0.669 2 0.720 1 0.692 2 0.640 2 0.674 2 A11 0.680 1 0.694 2 0.703 1 0.658 1 0.685 1 A12 0.625 3 0.646 3 0.645 3 0.609 3 0.618 3 corresponding grey length and ranking order. For characteristics or algorithms can lead to different solutions. benchmarking the results, Cluster #1 is selected which indi- To validate the results of the proposed methodology, this sec- cates that as the system does not consider any possible future tion presents a comparative analysis test to analyze the results events, the worst location candidate in the optimal case be- of the problem using other MCDM approaches. For this pur- comes the best option in State 1. This is a good example of pose, grey Weighted Aggregated Sum-Product Assessment how stratification theory enables decision-makers to observe (WASPAS) method [78], Additive Ratio Assessment how misleading results they can obtain if they use a (ARAS) [68], grey Technique for Order of Preference by deterministic-based DSS which does not cover up any possi- Similarity to Ideal Solution [43], and grey Evaluation based bility of events. on Distance from Average Solution [57] are used to tackle the sustainable landfill location selection problem. Table 11 reports the results of different MCDM methods 4.6 Comparative analysis under grey interval numbers for the landfill location problem. Based on the findings, all MCDM methods were consensus One of the main deficiencies of the MCDM methods relies on with the proposed methodology in almost all of the cases in their structures where sometimes structures with specific Table 10 Impact of weight coefficients on results of CoCoSo-G Cluster Alternative Optimal S1 S2 S3 S4 Grey length Rank Grey length Rank Grey length Rank Grey length Rank Grey length Rank #1 A1 0.488 1 0.434 3 0.493 1 0.494 1 0.489 1 A2 0.467 2 0.488 1 0.471 3 0.465 2 0.452 2 A3 0.458 3 0.472 2 0.482 2 0.449 3 0.427 3 #2 A4 0.425 2 0.362 3 0.433 2 0.432 2 0.425 2 A5 0.570 1 0.636 1 0.569 1 0.567 1 0.543 1 A6 0.413 3 0.397 2 0.431 3 0.409 3 0.391 3 #3 A7 0.604 1 0.567 1 0.615 1 0.608 1 0.595 1 A8 0.506 2 0.520 2 0.511 2 0.504 2 0.491 2 A9 0.307 3 0.287 3 0.332 3 0.296 3 0.293 3 #4 A10 0.516 2 0.564 2 0.517 2 0.511 2 0.502 2 A11 0.698 1 0.661 1 0.700 1 0.703 1 0.701 1 A12 0.312 3 0.309 3 0.325 3 0.309 3 0.297 3 13630 E. B. Tirkolaee and A. E. Torkayesh selecting the best location alternative. However, there are CoCoSo-G method to address the sustainable landfill location slight differences in some of the clusters, specifically for al- selection problem. The developed DSS provides several con- ternatives that were selected as second and third options. tributions to the literature of decision-making methods as well According to the results of Table 11, the proposed methodol- as the HWM field. The DSS empowers real-life practices to ogy shows high reliability to tackle waste management prob- consider large information and data about the characteristics lems with big data where there exists a decision-making prob- of medical centers in order to cluster them into the most suit- lem under uncertain information and conditions. able groups for the location selection process. On the other To statistically analyze the results of the comparative analysis, hand, the DSS enables decision-makers to include impacts of the Pearson’s correlation coefficient isusedasastatisticaltest possible future events into the decision-making environment. which measures the relationship between two variables. Here, the For HWM which is a field full of dynamicity and uncer- Pearson’s correlation coefficient is applied to understand the re- tainties, this feature can contribute a lot to real-life practices. lationship between the ranking of the suggested methodology Finally, grey interval numbers are utilized to be implemented and other MCDM approaches. Table 12 represents the results for a novel hybrid decision model, MARCOS-CoCoSo, to of the correlation test between the proposed methodology and empower real-life decision-makers to express their uncertain other MCDM methods. It is demonstrated that our proposed information and judgments through an interval range. All in methodology has a complete correlation with the results of other all, the proposed DSS is novel in its kind which is used to MCDM methods. Although in some cases the correlation value address the sustainable HLS problem. drops to 0.5, our proposed methodology still chooses the best Although this work proposes a novel DSS to address the alternatives as same as other methods. sustainable HLS problem, there exist some limitations that can Finally, it is obvious that the proposed cluster-based SBWM- be tackled in future studies. Due to some disadvantages of the MARCOS-CoCoSo-G can be easily implemented on other K-means algorithm, one may consider using clustering algo- cases with different scales in order to proceed with decision- rithms such as Mean-Shift Clustering, Density-Based Spatial making under uncertainty in similar MCDM problems due to Clustering of Applications with Noise (DBSCAN), and its high efficiency in terms of considering impacts of future Expectation–Maximization (EM), clustering using Gaussian uncertain and unforeseen events on weight coefficients of de- Mixture Models (GMM). Another direction for future studies cision criteria, clustering alternatives or demand points based is to consider a systematic way to determine the likelihood of on various characteristics to facilitate evaluation process, and occurrence of events; thus, there will be no biasedness and efficient and precise evaluation of alternatives using hybrid subjectivity of experts in expressing the likelihood of occur- ranking MCDM model under uncertain environment. rence of events. MCDM methods are very sensitive to their parameters, inputs, and the way they calculate score functions. One study may develop a holistic MCDM approach by con- solidating more than two methods to provide a DSS with 5 Conclusions higher validation. Although grey interval numbers provide a reliable uncertainty model for decision-making models, other This study proposes a novel big data DSS using K-means uncertainty models such as fuzzy logic and its extensions, or clustering algorithm, SBWM, and a hybrid MARCOS- Table 11 Comparative analysis Clus. Alt. 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Applied Intelligence (Dordrecht, Netherlands) – Pubmed Central
Published: Mar 7, 2022
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