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Highlights • The results of aggregation by weighted arithmetic mean are normalization-dependent. • Weighted arithmetic mean aggregation fails to reflect preference information well. • Serious problems caused by the arithmetic mean aggregation shown on examples. • Theorems claiming the superiority of geometric mean aggregation in AHP presented. • Weighted geometric mean recommended for aggregation of local priorities in AHP. Abstract The main focus of this paper is the aggregation of local priorities into global priorities in the Analytic Hierarchy Process (AHP) method. We study two most frequently used aggregation approaches - the weighted arithmetic and weighted geometric means - and identify their strengths and weaknesses. We investigate the focus of the aggregation, the assumptions made on the way, and the effect of different normalizations of local priorities on the resulting global priorities and their ratios. We clearly show the superiority of the weighted geometric mean aggregation over the weighted arithmetic mean aggregation in AHP for the purpose of deriving global priorities of alternatives. We also contribute to the literature on rank reversal in AHP. In particular, we show that a change of the normalization condition for the local priorities of alternatives may result in different ranking when the weighted arithmetic mean aggregation is used for deriving global priorities of alternatives, and we demonstrate that the ranking obtained by the weighted geometric mean aggregation is not normalization dependent. Moreover, we prove that the ratios of global priorities of alternatives obtained by the weighted geometric mean aggregation are invariant under the normalization of local priorities of alternatives and weights of criteria. We also propose three alternative approaches to aggregating preference information contained in local pairwise comparison matrices of alternatives into a global consistent pairwise comparison matrix of alternatives and prove their equivalence. [ABSTRACT FROM AUTHOR]

The choice of heating system is significant for city planners and building owners alike, and many important areas, such as the well-being of residents, climate change impact and resource efficiency, may influence the choice. Understanding how to balance these areas is crucial for effective decision-making that can contribute to sustainable development and the green energy transition. However, these decisions represent complex problems where disparate knowledge areas must be considered simultaneously. When faced with this type of decision-making problem, employing different multi-criteria decision-making methods is common. However, such methods only provide a snapshot of which alternative is preferred and because of this, their results may become obsolete due to changes in the performance of alternatives or the value perceptions of the decision-makers. To overcome this challenge and to improve the longevity and reliability of multi-criteria decision-making results, the authors of this study explored a novel approach to producing semi-dynamic results through scenarios, which were used to consider possible future changes to the alternatives' performance and the decision-makers' value perceptions. The application of scenarios in the multi-criteria decision-making method enabled nuanced information to be produced on how the performance of different heating alternatives may change under different plausible futures. This approach was demonstrated by applying it to the case of residential heating in Denmark, where results showed that while final rankings varied across both scenarios and ranking methods, solar heating was the preferred alternative, while the oil boiler alternative performed the worst. Overall, this study highlights the importance of considering likely future changes to both the performance of alternatives and the value perceptions of decision-makers when making decisions with long lifetimes and suggests an approach for doing this. • Heating system choices affect well-being, climate impact and resource efficiency. • Multi-criteria decision-making methods help balance complex trade-offs. • Scenarios enable semi-dynamic results that account for future changes. • Solar heating is preferred and oil boilers perform worst in Danish residential case. • Future-proofing decisions is important and feasible with scenario approaches. [ABSTRACT FROM AUTHOR]

The selection of appropriate materials for sustainable development of products is a very intricate process. Sustainable material selection problems with various non commensurable and incompatible decision factors can be efficiently handled using multi-criteria decision making (MCDM) methods. However, these methods suffer from a general and famous problem, namely rank reversal. In this phenomenon the ordering of alternatives inverts when an alternative is added or eliminated from the list of alternatives. In this paper, we reveal that COPRAS (Complex Proportional Assessment), TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) and VIKOR (VlseKriterijumska Optimizacija I Kompromisno Resenje, Serbian term) as three of the most popular techniques in material selection area may produce rank reversal when an option is removed from or added to a decision process. Moreover, we provide a comparative analysis about the rank reversal problem in the aforementioned MCDM methods. To the best of our knowledge, this work is the first to study rank reversal phenomenon for general material selection problem using more than 100 scientific references. Finally, we suggest a new MCDM-based method for helping decision maker (DM) to select the best sustainable material against the rank reversal pitfall. We exemplify our reasoning with thirteen real-world cases adopted from literature. [ABSTRACT FROM AUTHOR]

In the present study, a novel approach based on multi-criteria analysis was proposed to prioritize PM mitigation strategies from economic, environmental and social aspects. Multi-criteria decision making (MCDM) methods are suitable tools for prioritizing strategies on various topics. However, it has been observed that adding/removing strategies has led to a change in preference which is called rank reversal. The present study was aimed with three objectives: (i) evaluating the rank reversal phenomenon in MCDM methods frequently used in environmental topics, (ii) introducing a novel approach based on wins in league (WIL) in order to reduce the rank reversal in MCDM methods and (iii) a new application of this method in prioritizing PM mitigation strategies in arid urban areas. Qualitative results showed that in studies in the field of environment, the rank reversal has occurred frequently in classical MCDM methods but its occurrence was prevented in the proposed method. Quantitative evaluation also showed that the probability of rank reversal occurrence in Technique For Order Performance By Similarity To Ideal Solution (TOPSIS), Additive Ratio ASsessment (ARAS), Weighted Aggregated Sum Product Assessment (WASPAS), Evaluation Based On Distance From Average Solution (EDAS), Combinative Distance-Based Assessment (CODAS) and Measurement Alternatives and Ranking According to Compromise Solution (MARCOS) methods was 36.4%, 32.8%, 21.2%, 31.6%, 36.1% and 29.9%, respectively. However, the probability of rank reversal occurrence in the proposed approach was almost 90% less than classical MCDM methods. Evaluation of PM mitigation strategies in arid urban areas has also shown that urban green belt plan is the most appropriate strategy. • Rank reversal (RR) in TOPSIS, ARAS, WASPAS, EDAS, CODAS and MARCOS was evaluated. • A guideline for choosing proper MCDM method in environmental science was introduced. • New proposed approach based on wins in league greatly reduced the RR occurrence. • 10 strategies from 6 attribute was analyzed by MCDM methods to reduce PM mitigation. • Urban green belt was the best strategy for urban areas near dust sources. [ABSTRACT FROM AUTHOR]

• A new Multi-Criteria Decision-Making Method, ABAC, is proposed. • ABAC is simple, more scalable and free from rank reversal problem. • ABAC is illustrated and validated using cloud service selection. • Various case studies using ABAC in different domains are provided. Decision-making appears as a complex and challenging task when it requires finding the most suitable alternative among the numerous alternatives in the presence of multiple, usually conflicting criteria. At the same time, stakeholders expect a simple, transparent, and traceable decision-making method. Multi-Criteria Decision-Making (MCDM) methods rank the alternatives considering multiple criteria. The rank reversal problem is an important issue in most existing conventional MCDM methods. This paper proposes a new alternative by alternative comparison-based MCDM Method (ABAC) that addresses the rank reversal problem. We prove that ABAC is free from the rank reversal problem. To illustrate and validate ABAC, we have taken the cloud service selection problem as an application. Further, to show the effectiveness of ABAC, we have provided several case studies covering various domains. We perform several experiments by simulating the ABAC method. We have compared ABAC and existing MCDM methods. The experimental results support that the ABAC method is a rank reversal free MCDM method. We also carry out sensitivity analysis for ABAC. Salient features of ABAC over existing MCDM methods are (i) it is simple; (ii) it is rank reversal free; (iii) it is more scalable. [ABSTRACT FROM AUTHOR]

The aim of this paper is to improve the applicability of the fuzzy-AHP method by using the rotational priority investigation (RPI) method. Despite its popularity and convenience, the AHP and fuzzy-AHP method is criticized by many scholars because of intransitivity and the rank reversal phenomenon. Experts may question the rational choice theory and cross priorities may indicate conflicting interactions. Also, the extraction of a number of alternatives may cause a different order of priorities. The rotational priority investigation method is proposed to investigate sub-group priorities and their corresponding rankings. Every rotation refers to the investigation of sub-group priorities after extraction of an alternative. The final result is based on the normalized average priority among the several rotations. An empirical study is presented by using the RPI method in the fuzzy AHP for the marine engine selection problem in the shipping industry. [ABSTRACT FROM AUTHOR]

Healthcare is considered one basic necessity to sustaining life; thereby, assessing the character of a healthy and resilient supply chain can help a nation develop ideas to combat the healthcare crisis. COVID-19 has led to a long-term strain on the healthcare supply chain (HCSC) and has resulted in a lack of basic healthcare necessities. It has become apparent that supply chain disruptions and increased usage has led to a lack of medical supplies needed to provide the proper care to patients. Multicriteria decision-making (MCDM) will help to indicate what characteristics contribute to resilient healthcare supply chains. To assess the characteristic of a resilient supply chain, significant healthcare supply chains will help indicate significant characteristics. A case study on the medical supplies' supply chains is presented. A rank reversal proximity index MCDM method ranks criteria to assist with decision making. The proximity index will reduce the chances of the rank reversal phenomenon that results in incorrect rankings from occurring. Results show that redundancy, collaboration, and robustness are key indicators of a resilient supply chain while, supply chain design , communication capabilities , and supply chain risk management become comparatively less important during the COVID-19 pandemic. Furthermore, an unsupervised machine learning tecnique named "cluster analysis" is conducted to group the resilience indicators of the respective supply chain. Through this study, the best way to combat disruptions in the healthcare supply chain due to large-scale pandemics is to share information quickly, reduce reliance on the design of the supply chain, and track the usage of necessary medical supplies. Alternatively, we validated our study by comparing a Preference Selection Index (PSI) to the proposed method. [ABSTRACT FROM AUTHOR]

Highlights: [•] We demonstrated the occurrence of rank reversal in different ranking models in DEA. [•] Certain ranking methods are surveyed in DEA focusing on rank preservation and rank reversal phenomena. [•] We discussed three other models in which the phenomenon does not occur when a copy of a DMU is added to the PPS. [ABSTRACT FROM AUTHOR]

Abstract: Company ranking is a complex process in which multiple financial ratios are required to be considered simultaneously. Furthermore, the selection process of an appropriate credit applicant company has become more complex as the experts in the financial organizations have to assess a wide range of alternatives based on a set of conflicting financial criteria. This paper studies the application of a new approach, i.e., Design of Experiment and TOPSIS method (DoE–TOPSIS) together to make company raking as frequently encountered in the real-time financial environment. The developed model is tested by case studies and satisfactory results are obtained. In the case studies, the results obtained by using the combined DoE–TOPSIS method are almost corroborated by those derived from conventional multi attribute decision making (MADM) methods which prove the applicability, potentiality, simplicity and flexibility of this method in making company ranking. [Copyright &y& Elsevier]

Abstract: Rank reversal is a phenomenon that occurs when a decision maker, in the process of selecting an alternative from a set of choices, is confronted with new alternatives that were not thought about when the selection process was initiated. It depends on the relationship between this new alternative and the old ones under each criterion. In this paper, we study the rank reversal phenomenon in the TOPSIS method and we propose modifications in the algorithm of Hwang and Yoon in order to solve the problem. Moreover, we present a general demonstration of the proposed modifications in the algorithm, as well as a numerical example to show these modifications. [Copyright &y& Elsevier]

Abstract: Rank preservation and reversal, so fundamental in decision making, have been an unresolved issue in the field of economics and utility theory and came into focus when the Analytic Hierarchy Process was developed because it uses paired comparisons that inevitably make the priorities of the alternatives interdependent. This paper summarizes the important issues that can play a role in rank preservation and reversal with counterexamples to show that preserving rank in all situations is wrong. [Copyright &y& Elsevier]

Abstract: Analytic hierarchy process (AHP) has been criticized for its possible rank reversal phenomenon caused by the addition or deletion of an alternative. This paper shows the fact that the rank reversal phenomenon occurs not only in the AHP but also in many other decision making approaches such as the Borda–Kendall (BK) method for aggregating ordinal preferences, the simple additive weighting (SAW) method, the technique for order preference by similarity to ideal solution (TOPSIS) method, and the cross-efficiency evaluation method in data envelopment analysis (DEA). Numerical examples are provided to illustrate the rank reversal phenomenon in these popular decision making approaches. [Copyright &y& Elsevier]

The world is moving towards a situation where resource scarcity leads to increased material cost, and the government is bound to dispose of heavy wastes generated by the growing population. Additive Manufacturing (AM) has bought a significant revolution in the current manufacturing processes. AM can fabricate complex and intricate shapes with ease. Material selection is an essential aspect in AM as a wide range of compatible materials available for AM. Appropriate material selection is necessary for cleaner production and sustainable development. Sustainable material selection considering various material properties and varied criteria can be effectively managed by Multi-Criteria Decision Making (MCDM) approach. However, several MCDM methods have a rank reversal problem, in which the rank of alternatives got changed when an alternative is added or removed from all considered alternatives. In this regard, this work presents a sustainable material selection of AM technologies. Sustainable material selection has been made for 3 a.m. technologies, namely Fused Deposition Modelling (FDM), Selective Laser Sintering (SLS), and Stereolithography (SLA). Four MCDM techniques have been used to analyze and compare AM materials, namely SAW (Simple Additive Weighting), MOORA (Multi-Objective Optimization based on Ratio Analysis), TOPSIS (Technique for order performance by similarity to ideal solution), and VIKOR (Vlsekriterijumska Optimizacija I Kompromisno Resenje). Rank reversal problems associated with MCDM methods are also highlighted in the material selection stage. The results reveal that 'TPU Elastomer', 'Accura HPC′, and 'Duraform EX′ are identified as the best material for FDM, SLA, and SLS based AM technologies. Further, practical and research implications have been derived based on the study to help industrial practitioners, researchers, and decision-makers for the selection of the best materials in the product development stage to support cleaner production. [Display omitted] • Aimed towards sustainable material selection for AM processes. • Identification of important criteria for sustainable material selection for AM processes. • Analyze and prioritize AM materials considering several MCDM methods. • Analyze rank reversal problem associated with MCDM methods. • Suggested implications on sustainable material selection for AM processes. [ABSTRACT FROM AUTHOR]

• Propose a post factum analysis framework for TOPSIS based decision making. • Analyze the dynamics of decision information change over recommendations. • Develop algorithms to explore different achievable targets set by decision maker. • Demonstrate the effectiveness of the proposal as a tool of robust decision analysis. TOPSIS (Technique of Order Preference by Similarity to Ideal Solution) is a popular decision-making technique used to rank a discrete set of alternatives based on the premise that a good alternative should simultaneously have the shortest distance from a positive ideal solution and the farthest distance from a negative ideal solution. Sometimes, ambiguity or impreciseness in the decision information may lead a decision maker to raise questions about the robustness of the recommendation of a TOPSIS based decision-making model. To address the concerns of the decision maker, this paper therefore proposes a sensitivity and stability analysis framework to address the robustness of the recommendations and the different achievable targets set by the decision maker. Specifically, we analyze the effect of a change in the rating of an alternative under a criterion and determine the appropriate conditions to predict how the closeness coefficients change. Through this analysis, we investigate the minimal performance change that is required in an alternative's rating under a criterion to achieve a particular target set by decision maker when the rest of the decision information set remains unaltered. An algorithm is provided to find the set of criteria whereby changing a criterion of a alternative, it can obtain another alternative's rank. We investigate the behaviour of the closeness coefficient of an alternative when a criterion rating changes, and provide two algorithms to identify the upper and lower-rank achievable alternatives. Subsequently, we describe the rank reversal of a pair of alternatives and introduce the concept of a rank sensitive interval. A numerical example on university ranking is provided to demonstrate the validity of the proposed model. [ABSTRACT FROM AUTHOR]