Fuzzy Pairwise Comparison Matrices Research Articles

Numerical fact-finding of different functions impact on the fuzzy preference programming optimality

The fuzzy analytic hierarchy process (FAHP) is a widely implemented approach for determining the weights of criteria and alternatives from pairwise comparison matrices. FAHP methodology uses triangular fuzzy as a tool for the decision-maker to arrange judgments expressed as the pairwise comparison matrix elements. FAHP is then modeled into a nonlinear constrained optimization problem to increase the decision maker’s satisfaction. However, in some cases, this model would yield multiple optimal solutions. Logarithmic fuzzy preference programming (LFPP) is offered to overcome this unfavorable situation. Nevertheless, LFPP includes a parameter in its model for which no specific method is available to determine. Meanwhile, the differences in parameter values will affect the solution. In the worst case, the weights obtained will be inaccurate. As a result, the decision taken based on the weights will be biased and unreliable. This issue is particularly important when it requires high accuracy. It includes the decisions on the portfolio investment, economic, human capital measurements, and shipping registry. Another crucial thing is that the use of the natural logarithm function in the LFPP method has the potential for an overflow effect at the computational stage when it is implemented to derive the weights. Therefore, in the application context, it is significant to improve the shortcomings of the LFPP method in terms of parameter involvement and the use of the logarithmic function. For this purpose, this paper proposes a non-parameter transcendental fuzzy preference programming (TFPP) model for deriving the optimal weights from fuzzy pairwise comparison matrices. The TFPP is obtained by investigating different functions’ effects on fuzzy preference programming (FPP). The proposed method has a more general form. One of the specific forms of the TFPP is chosen in a computational implementation. The numerical results confirm that the TFPP optimization model is reliable in obtaining the optimum global weights. The comparison with the LFPP method also shows that the TFPP is more efficient.

A healthcare service quality assessment model using a fuzzy best–worst method with application to hospitals with in-patient services

Hospitals and healthcare centers face many service problems during the pandemic. Problems that may arise in providing high-quality services lead to increased dissatisfaction. The Covid-19 crisis saw an unprecedented rise in the number of visits and hospitalizations in healthcare centers, which led to drastic fluctuations in the quality of services provided by these centers. This study aims to assess the quality of services in hospitals through a fuzzy Best–Worst Method (BWM). This method makes fewer computations and more consistent comparisons than Analytic Hierarchy Process (AHP), the most common method used among Multi-Criteria Decision Making (MCDM) methods. Our proposed fuzzy BWM is an efficient, reliable, easy-to-apply quality assessment technique. To show the applicability of the proposed method, we have investigated the service quality of four hospitals. Accordingly, the factors and sub-factors of the quality of health and medical services were obtained through an in-depth review of the literature. The matrices of pairwise comparisons were then completed based on experts’ opinions, and the weights were extracted from the fuzzy pairwise comparison matrices after solving the model. The results show even the hospitals with the highest score are far from what patients and experts perceive as the quality of service. Based on our results, caring, accuracy, skill, and timeliness are the most important criteria in evaluating healthcare service quality in Iran during the pandemic.

Selection of Supply Chain Sustainability Management System by Fuzzy Additive Preference Programming Method

A selection of suitable sustainability management systems (SMS) is a major part of supply chain strategies to create a competitive advantage, reduce total costs, and manage long-term sustainability. A framework and method for prioritizing supply chain SMSs are presented in this research. Analytic hierarchy process (AHP) is the most common method for alternative selection in multi-criteria decision-making (MCDM). However, complex information is mixed with ambiguity and uncertainty, which makes decision makers unable to use precise or crisp numbers, so fuzzy numbers are presented to remedy this difficulty. Therefore, this research proposes a fuzzy additive preference programming (FAPP) to select the optimum SMS for a supply chain. FAPP method can produce the unique normalized optimal priority vector of fuzzy pairwise comparison matrices for SMS selection effectively with linear constraints. The additive linear constraints can eliminate the weaknesses of existing methods and equalize the upper and lower triangular fuzzy judgments. In addition, the proposed method can identify abnormal pairs of fuzzy judgments that cause inconsistency. The proposed methodology can prioritize the key criteria which lead to the selection of the most appropriate SMS. An example of SMS selection in a rubber factory demonstrates the feasibility and validity of the proposed method.

Interval-Valued Fuzzy Multi-Criteria Decision-Making by Combining Analytic Hierarchy Process with Utility Representation Function

To encompass uncertainty and vagueness of information, the analytic hierarchy process (AHP) was often extended into fuzzy multi-criteria decision-making (FMCDM) under an uncertain environment. However, the extension of AHP was rarely constructed on interval-valued fuzzy numbers. Recently, interval-valued fuzzy numbers were utilized for decision-making to obtain more messages than others. For AHP extended under a fuzzy environment into fuzzy AHP, fuzzy computations are critical to derive priorities of pairwise comparison matrices. Although AHP’s approximate computations including the normalization of row arithmetic averages may be adopted to the fuzzy environment, the fuzzy extension of AHP is still complicated for division and multiplication of fuzzy numbers, especially interval-valued fuzzy numbers. To resolve complicated ties, a utility representation function of interval-valued fuzzy numbers in fuzzy AHP is used for yielding vectors consisting of priority representations of fuzzy pairwise comparison matrices on evaluation criteria based on objective, alternatives based on evaluation criteria, and more hierarchies. Then, sum product of multiplying the priority representation vectors is derived to form the utility representations of alternative performance indices, and alternative performance indices are represented by their corresponding utility representations. Therefore, FMCDM problems are easily solved by fuzzy AHP, i.e., combining AHP with the utility representation function under an interval-valued fuzzy environment.

FAHP FOR SELECTING TRANSPORT MODES OF TAIWAN OFF-SHORE ISLANDS’ MILITARY LOGISTICS

Three off-shore islands of Taiwan: Penghu, Kinmen and Matsu are critical in tactical position for Taiwan military, but lack of scarcity resource. Therefore, logistics is very important especially for the off-shore islands. Practically, most of the goods and materials are transported to the islands in the way of shipping and air transportation by Taiwan. However, the severe weather of the islands makes the transportation difficult or even to delay, which is a serious problem for the military logistics of the islands. To raise transportation performance, a proper evaluation method is necessary for military logistics to select the best transport mode based on reducing cost and emphasizing efficiency. Generally, analytic hierarchy process (AHP) may be a method in the selection of transport modes for Taiwan off-shore islands’ military logistics. However, some computation procedures in AHP are hard or complicated especially for processing numerous interviewees’ messages. To resolve the above tie, we utilize fuzzy analytic hierarchy process(FAHP) in selecting transport modes for Taiwan off-shore islands’ military logistics in this paper. After integrating interviewees’(i.e., querying soldiers’) opinions into fuzzy pair-wise comparison matrices, FAHP, being different from AHP, simply and efficiently yields priorities of the fuzzy pair-wise comparison matrices to find the best transport mode of Taiwan off-shore islands’ military logistics.

An Ordinal Consistency Indicator for Pairwise Comparison Matrix

The pairwise comparison (PC) matrix is often used to manifest human judgments, and it has been successfully applied in the analytic hierarchy process (AHP). As a PC matrix is formed by making paired reciprocal comparisons, symmetry is a striking characteristic of a PC matrix. It is this simple but powerful means of resolving multicriteria decision-making problems that is the basis of AHP; however, in practical applications, human judgments may be inconsistent. Although Saaty’s rule for the consistency test is commonly accepted, there is evidence that those so-called “acceptable” PC matrices may not be ordinally consistent, which is a necessary condition for a PC matrix to be accepted. We propose an ordinal consistency indicator called SDR (standard deviation of ranks), derive the upper bound of the SDR, suggest a threshold for a decision-maker to assess whether the ordinal consistency of a PC matrix is acceptable, and reveal a surprising fact that the degree of ordinal inconsistency of a small PC matrix may be more serious than a large one. We made a comparative analysis with some other indicators. Experimental results showed that the ordinal inconsistency measured by the SDR is invariant under heterogeneous judgment measurements with a varied spectrum of scales, and that the SDR is superior to the two compared indicators. Note that the SDR not only works for a multiplicative PC matrix but can also be used for additive and fuzzy PC matrices.

Hierarchical fuzzy-AHP-based multi-criteria decision making approach for selection of underground metal mining method

In the last few decades, many underground mining methods were proposed for extractions of ores. The decision-making for selecting the most suitable mining method for a typical ore depost depnds on various intrinsic and extrinsic factors (intrinsic – dip, shape, thickness, depth, grade distribution, RMR (rock mass rating) and RSS (rock substance strength) of ore, hanging wall, footwall, and extrinsic – recovery, dilution, safety, productivity, flexibility, capital). The present study aims to develop a hierarchical Fuzzy-AHP (FAHP) model for choosing the most suitable underground mining method for an ore deposit. The structure of the proposed hierarchical FAHP model consists of five levels. The level-1 of the hierarchy defines two variables (intrinsic factors and extrinsic factors). These are further classified into quantitative or qualitative nature of variable (listed in level-2). The criteria, sub-criteria, and mining method variables are listed respectively in Level 3, Level 4, and Level 5. For each level of the hierarchy, a fuzzy pair-wise comparison matrices are developed using the corresponding levels’ listed variables. These matrices at each level are subsequently used to determine the local and global weights of each variable. The global weights are used for prioritizing the different mining methods. The proposed hierarchical FAHP model was validated by considering the field data of two different ore deposits in India. The results showed that the most appropriate mining method predicted from the decision-making model and the adopted mining method for extracting the ore deposit are same in two case studied mines.

A Note on “A New Method for Triangular Fuzzy Compare Wise Judgment Matrix Process Based on Consistency Analysis”

In the paper “A new method for triangular fuzzy compare wise judgment matrix process based on consistency analysis” (Meng and Chen in Int J Fuzzy Syst 19(1):27–46, 2017), the authors defined consistency of triangular fuzzy pairwise comparison matrices (TFPCMs), and presented theorems and propositions used to derive a computation formula of ]0, 1[-valued fuzzy priority weights for consistent TFPCMs. This note shows that under such a consistency definition, there is not any consistent $$n \times n$$ TFPCM ( $$n \ge 3$$ ) with fuzzy judgments. Two counterexamples are provided to illustrate that the presented theorems and propositions are not true, and the given computation formula of fuzzy priority weights is incorrect and thus it should be replaced with a new formula.

Coherent weights for pairwise comparison matrices and a mixed-integer linear programming problem

Pairwise comparison matrices (PCMs) have been a long standing technique for comparing alternatives/criteria and their role has been pivotal in the development of modern decision making methods. In order to obtain general results, suitable for several kinds of PCMs proposed in the literature, we focus on PCMs defined over a general unifying framework, that is an Abelian linearly ordered group. The paper deals with a crucial step in multi-criteria decision analysis, that is to obtain coherent weights for alternatives/criteria that are compared by means of a PCM. Firstly, we provide a condition ensuring coherent weights. Then, we provide and solve a mixed-integer linear programming problem in order to obtain the closest PCM, to a given PCM, having coherent weights. Isomorphisms and the mixed-integer linear programming problem allow us to solve an infinity of optimization problems, among them optimization problems concerning additive, multiplicative and fuzzy PCMs.

A New Fuzzy Risk Management Model for Production Supply Chain Economic and Social Sustainability

The issues of operational, organisational and process risk assessment in supply chains (SCs) are the most usually analysed, while other risk groups (like economic and social risks) are not taken into account, even though they have a critical effect on the competitive advantage and SCs sustainability over long time periods. The determination of risk value that may arise due to the materialisation of each defined risk factor (RF) is based on the assessment of the severity of RF consequences and frequency of RF occurrence. These judgments are obtained by decision makers and modelled by using fuzzy set theory. The relative importance of RFs are stated by fuzzy pair-wise comparison matrices in compliance with fuzzy analytical hierarchy process (FAHP). The risk level of SCs could be obtained in an exact way by applying fuzzy logic. The proposed model, to be presented in this paper, provides a possibility to easily and simply determine risk level from the automotive industry SC and to propose appropriate management initiatives that should lead to a reduction or elimination of RF influence.

Fuzzy multi-criteria decision analysis for environmentally conscious solid waste treatment and disposal technology selection

Municipal solid waste management (MSWM) is a major challenge for developing countries due to an enormous and rapid increase in waste generation rates, environmental issues and financial constraints for proper management. Poorly managed municipal solid waste (MSW) causes severe detrimental consequences to society like financial and aesthetic degradation, contamination of natural resources, environmental pollution and is a serious health hazard. The selection of appropriate MSW treatment and disposal technology is a multi-criteria decision-making process. This paper presents an evaluation method that can aid decision-makers to prioritise and select appropriate MSW treatment and disposal methods even under uncertain conditions. It adopts a systematic three-stage evaluation method. The first stage utilizes the Fuzzy Delphi method to obtain the critical factors for the evaluation of technology alternatives. In the second stage, the Fuzzy Analytic Hierarchy Process is applied to obtain the weights and importance degree of each criterion as the measurable indices of the technologies by fuzzy pairwise comparison matrices. Finally, the Fuzzy TOPSIS technique is used for the selection of appropriate treatment and disposal technology alternative. The applicability of the proposed approach is demonstrated with an illustrative example and the results are analyzed. The fuzzy multiple-criteria approach applied in the study accommodates both quantitative and qualitative data, and thus, makes the uncertain decision-making process more objective and analytical. The study highlights the importance of ‘‘appropriate scale” and how the priority order of technologies changes under various domains of experts. The results reveal that the developed model can successfully help the decision-makers to determine the priority sequence of the MSW treatment and disposal scenarios taking into account the interest of relevant stakeholders. In view of the real-world scenario, it is proven to be efficient, practical, and case-independent for effectively managing MSW and supporting the existing MSWM systems in both developed and developing countries.

Drawing a Strategy Canvas Using the Fuzzy Best–Worst Method

Blue ocean strategy is a new approach to strategy-making and innovation with the aim of sustained performance and growth of the company. In this approach, an analytical and decision-making tool known as Strategy Canvas is introduced in order to create blue oceans and to innovate value. Strategy Canvas provides a basic framework for taking into account all competitive and key factors in the current industry. In this study, the proposed fuzzy best–worst method is employed as a multi-criteria decision-making method to map Strategy Canvas of a manufacturing company in Iran. The proposed method is concerned with the proposition of a new approach to eliciting the weight vector from the fuzzy pairwise comparison matrices. For this purpose, a nonlinear optimization model was proposed. After solving the model, crisp weights were extracted from the fuzzy pairwise comparison matrices. The proposed method was an execution of the best–worst method in a fuzzy environment. This method is able to carry out fewer and more consistent comparisons. This method is also capable of substituting the fuzzy AHP method.

Measuring inconsistency and deriving priorities from fuzzy pairwise comparison matrices using the knowledge-based consistency index

The fuzzy analytic hierarchy process (AHP) is a widely applied multiple-criteria decision-making (MCDM) technique, making it possible to tackle vagueness and uncertainty arising from decision makers, especially in a pairwise comparison process. Indeed, as the human brain reasons with uncertain rather than precise information, pairwise comparisons may involve some degree of inconsistency, which must be correctly managed to guarantee a coherent result/ranking. Several consistency indexes for fuzzy pairwise comparison matrices (FPCMs) have been proposed in the literature. However, some scholars argue that most of these fail to be axiomatically grounded, which may lead to misleading results. To overcome this lack of an axiomatically grounded index, a new index is proposed in this paper, referred to as the knowledge-based consistency index (KCI). A comparative study of the proposed index with an existing one is carried out, and the results show that KCI contributes to substantially reducing the computation time. In addition, the different fuzzy weights derived from the initial FPCM (for KCI computation purposes) can also be employed to find a crisp set of weights that corresponds to an optimal solution to the MCDM problem according to the decision maker’s viewpoint and expertise.

A hybrid hierarchical fault diagnosis method under the condition of incomplete decision information system

Processing attribute reduction plays a key role in the fault diagnosis of incomplete decision information system (IDIS), and it improves the efficiency and accuracy of fault diagnosis. Tolerance relation-based attribute reduction is widely used in the IDIS. However, the fuzziness of relation-based classification always exists in the practical attribute reduction problems of fault diagnosis as the incompleteness and uncertainty of data information, and the traditional tolerance relation-based attribute reduction methods are not suitable for fault diagnosis of IDIS. Therefore, this paper proposes a hybrid hierarchical fault diagnosis method with the combination of tolerance relation-based attribute reduction method and integrated logarithmic fuzzy preference programming (LFPP) based methodology. The method utilizes both qualitative and quantitative data information and constructs the hierarchical structure of fault diagnosis in IDIS. The integrated LFPP based methodology obtains the unique normalized optimal significance priorities vector for attribute fuzzy pairwise comparison matrices simultaneously and directly as the sorting part of proposed method. The tolerance relation-based attribute reduction method decomposes the fault attributes reduction problem into multiple sub-problems, which is the decomposing part of proposed method. Hence, the proposed hybrid method can handle the fuzziness of relation-based classification and mitigate complexity attribute reduction for fault diagnosis of IDIS. Finally, an engineering case for strategy reduction of fault diagnosis is provided to demonstrate the feasibility of the proposed method and obtain the reduction diagnosis strategies. Another test case is given for verifying the validity of the reduction results and for comparison between the proposed method and other different methods, which shows that the method is indeed efficient and has greater advantages at producing higher accuracy, reducing difficulty and mitigating complexity in fault diagnosis.

Multi-Criteria Decision Making for PLM Maturity Analysis based on an Integrated Fuzzy AHP and VIKOR Methodology

A wide range of product lifecycle management (PLM) maturity models are proposed to assess the relative position of companies on their road to complete PLM implementation. However, it is a tough job for the company to dynamically evaluate the gradual process of PLM maturity by using existing values and accurately make decisions of improving PLM maturity by selecting the optimum alternative. A fuzzy PLM components maturity model (PCMA) is presented to build the internal logical relationship between maturity levels and existing values that can automatically predict the unknown PLM maturity levels. A fuzzy AHP–VIKOR methodology is used to make a decision among option PLM strategies. The weights of the criteria are determined by fuzzy pairwise comparison matrices (PCM). The weights of alternatives with respect to criteria are calculated by fuzzy VIKOR. The fuzzy AHP–VIKOR is a compromise solution and has the ability of transfer subjective and implicit linguistics into objective and transparent data. A numerical example illustrates and clarifies the running steps of the proposed methodology.

A system approach to decision support on basis of hierarchical and network models

A methodology and a system approach to decision support based on hierarchical and network models are proposed, which include methods for estimating and improving the consistency of pairwise comparison matrices (PCM), calculating fuzzy local weights for model elements based on fuzzy PCM, calculating confidence intervals for local weights, finding aggregated weights and aggregated belief functions for model elements, estimating the sensitivity of the results, tools for analyzing the effectiveness of the methods and an expert evaluation modeling system. A decision support system is built on basis of the proposed methodology. The proposed methodology makes it possible to increase the reliability of solutions of practical weakly structured decision-making problems by using more efficient methods at each of the stages of solving the problem. Reliability of results of application of the methodology while solving a practical decision-making problem can be assessed by means of sensitivity analysis using the stability indices of the computed local and global rankings of the decision alternatives.

Fuzzy AHP approach to passenger aircraft type selection

In order to choose an aircraft to operate a defined set of routes, an airline needs to consider passenger's interests in addition to its own interests. The goal of the paper is to propose a methodology which will help choose aircraft type(s) that meets the market conditions and airline's requirements best for known route network and known forecasted air travel demand by routes. Although this is a multi-criteria problem, planners usually have to make decisions under uncertainty, incorporating vagueness of human thinking. Therefore, we proposed the Fuzzy Analytic Hierarchy Process (FAHP) based approach. To derive crisp priorities from fuzzy pairwise comparison matrices, a logarithmic fuzzy preference programming (LFPP) method is employed, as well as an improved LFPP method. With regard to different criteria that involve quantitative and qualitative aspects, three criteria and ten sub-criteria are selected. Experts from different airlines and universities responded to an interview, contributing to the design of pairwise comparison matrices for the criteria and sub-criteria. The regional airline case study is used to show the applicability of the methodology proposed.

An integrated logarithmic fuzzy preference programming based methodology for optimum maintenance strategies selection

Selecting optimum maintenance strategies plays a key role in saving cost, and improving the system reliability and availability. Analytic hierarchical process (AHP) is widely used for maintenance strategies selection in the Multiple Criteria Decision-Making (MCDM) field. But the traditional or hybrid AHP methods either produce multiple, even conflict priority results, or have complicated algorithm structures which are unstable to obtain the optimum solution. Therefore, this paper proposes an integrated Logarithmic Fuzzy Preference Programming (LFPP) based methodology in AHP to solve the optimum maintenance strategies selection problem. The multiplicative constraints and deviation variables are applied instead of additive ones to utilize both qualitative and quantitative data, and process the upper and lower triangular fuzzy judgments to obtain the same priorities. The proposed methodology can produce the unique normalized optimal priority vector for fuzzy pairwise comparison matrices, and it is capable of processing all comparison matrices to obtain the global priorities simultaneously and directly in the form of super-matrix according to the different requirements and judgments of decision-makers. Finally, an example is provided to demonstrate the feasibility and validity of the proposed methodology.

A hybrid life cycle assessment based fuzzy multi-criteria decision making approach for evaluation and selection of an appropriate municipal wastewater treatment technology

Multiple-criteria decision-making (MCDM) has become a main area of research for dealing with complex environmental decision-making problems. In this paper, a hybrid life cycle assessment (LCA) based fuzzy MCDM methodology is developed for the evaluation and selection of appropriate municipal wastewater treatment (WTT) technology based on expert opinion and questionnaires. Further, the study also aims to identify the key evaluation criteria in the process of selecting WTT from a sustainability perspective. The use of fuzzy MCDM in wastewater management has the advantage of rendering subjective and implicit decision-making more objective and analytical, with its ability to accommodate both qualitative and quantitative data. This study provides a systematic approach towards WWT technology selection, in which four-phase procedure is proposed. First, the appropriate technology evaluation and selection criteria were derived from the literature, LCA and experts’ opinion. Next, in the second stage, the fuzzy Delphi method was used to evaluate and screen the critical factors for the evaluation of technology alternatives by interviewing the experts. Twelve criteria including sustainability and those derived from LCA and life cycle costing were obtained consisting of both qualitative and quantitative criteria. In the third stage, the weights of the selection criteria as the measurable indices of the WWT technologies were determined by fuzzy pairwise comparison matrices of analytic hierarchy process. Finally, the fuzzy the technique for order of preference by similarity to ideal solution technique was used for ranking the alternatives. The six most commonly used WWT technologies, viz. sequencing batch reactors (SBR), membrane bioreactor (MBR), moving bed bio-film reactor (MBBR), soil biotechnology, facultative aerated lagoon and activated sludge process were evaluated. The present study is the first study of its kind to develop a hybrid LCA-based fuzzy MCDM methodology for the selection of best WWT alternatives. Results illustrated that advanced technologies, MBR, SBR and MBBR are the preferred options with MBR the most preferred one followed by SBR and MBBR. The developed technology assessment framework enables decision makers to understand the complete evaluation and selection process better and provide a more accurate, effective, and systematic decision support framework. The framework is superior to existing methods since it has the capability of representing vague qualitative data and presenting all possible results with different degrees of membership. The framework developed and applied in this work will help identify appropriate WWT technologies for various decision-making situations faced while managing wastewaters.

A state-of the-art survey & testbed of fuzzy AHP (FAHP) applications

As a practical popular methodology for dealing with fuzziness and uncertainty in Multiple Criteria Decision-Making (MCDM), Fuzzy AHP (FAHP) has been applied to a wide range of applications. As of the time of writing there is no state of the art survey of FAHP, we carry out a literature review of 190 application papers (i.e., applied research papers), published between 2004 and 2016, by classifying them on the basis of the area of application, the identified theme, the year of publication, and so forth. The identified themes and application areas have been chosen based upon the latest state-of-the-art survey of AHP conducted by [Vaidya, O., & Kumar, S. (2006). Analytic hierarchy process: An overview of applications. European Journal of operational research, 169(1), 1–29.]. To help readers extract quick and meaningful information, the reviewed papers are summarized in various tabular formats and charts. Unlike previous literature surveys, results and findings are made available through an online (and free) testbed, which can serve as a ready reference for those who wish to apply, modify or extend FAHP in various applications areas. This online testbed makes also available one or more fuzzy pairwise comparison matrices (FPCMs) from all the reviewed papers (255 matrices in total).In terms of results and findings, this survey shows that: (i) FAHP is used primarily in the Manufacturing, Industry and Government sectors; (ii) Asia is the torchbearer in this field, where FAHP is mostly applied in the theme areas of Selection and Evaluation; (iii) a significant amount of research papers (43% of the reviewed literature) combine FAHP with other tools, particularly with TOPSIS, QFD and ANP (AHP’s variant); (iv) Chang’s extent analysis method, which is used for FPCMs’ weight derivation in FAHP, is still the most popular method in spite of a number of criticisms in recent years (considered in 57% of the reviewed literature).