Bayesian revision of the individual pair-wise comparison matrices under consensus in AHP–GDM

Analytic hierarchy process (AHP) has been widely used in group decision making (GDM). There are two traditional aggregation methods for the synthesis of group priorities in AHP–GDM: aggregation of the individual judgments (AIJ) and aggregation of the individual priorities (AIP). However, AIJ and AIP may be less reliable because of inconsistency of the individual pair-wise comparison matrices (PCMs) and deviation among decision makers. Based on multiplicative AHP model with lognormal errors, we propose a Bayesian revision method for improving the individual PCMs under the assumption that the consensus exists among decision makers, which is considered an aid to AIJ and AIP. In order to effectively deal with decision making involving multiple actors when using AHP as the methodological support, we revise the individual PCMs using the Bayesian revision method before using AIJ and AIP for the synthesis of group priorities. The Bayesian revision method not only makes full use of the prior distribution for parameters and sample information while complying with the Pareto principal of social choice theory, but also provides the reliable individual Bayesian PCMs for AIJ and AIP. Finally two numerical examples are examined to illustrate the applications and advantages of the Bayesian revision method.     

A Model for Decision Making with Missing,Imprecise, and Uncertain Evaluations of Multiple Criteria

In real‐life multicriteria decision making (MCDM) problems, the evaluations against some criteria are often missing, inaccurate, and even uncertain, but the existing theories and models cannot handle such evaluations well. To address the issue, this paper extends the Dempster–Shafer (DS)/analytic hierarchy process (DS/AHP) approach of MCDM to handle three types of ambiguous evaluations: missing, interval‐valued, and ambiguous lottery evaluations. In our extension, the aggregation of criteria's evaluation takes the following six steps: (i) calculate the expected evaluation interval and the ambiguity degree of each group of decision alternatives regarding each criterion, (ii) from them to obtain the preference degree of each group of decision alternatives, (iii) apply the DS/AHP method to obtain the mass function distribution of each group of decision alternatives, (iv) use the Dempster's rule of combination to get the overall mass function of each group of decision alternatives with respect to all criteria, (v) according to the overall mass function to count the belief function and the plausibility function of each decision alternative, and (vi) set the overall preference ordering of decision alternatives by our regret‐avoid ambiguous principle and then find the optimal solution. Finally, we give an example of real estate investment to illustrate how our approach is employed to deal with real‐life MCDM problems.     

A method of aggregation in DS/AHP for group decision-making with the non-equivalent importance of individuals in the group

Group decision-making (GDM) is an active area of research within multi-criteria decision-making (MCDM). This paper develops the nascent DS/AHP method of MCDM as an effective tool in GDM. Attention here is given to the aggregation of evidence from individual members of a decision-making group who are considered non-equivalent in their importance within the group. A discount rate value is defined for each member of the group depending on their perceived individual levels of importance. This discount rate attenuates the evidence from an individual by re-assigning more value to their concomitant level of ignorance. The adjusted evidence from each group member is then combined to derive the group's collective decision. A small real world GDM problem concerning the choice of university course textbooks is utilised throughout the analysis presented.     

A new method selection approach for fuzzy group multicriteria decision making

Fuzzy multicriteria decision making (MCDM) has been widely used in ranking a finite number of decision alternatives characterized by fuzzy assessments with respect to multiple criteria. In group decision settings, different fuzzy group MCDM methods often produce inconsistent ranking outcomes for the same problem. To address the ranking inconsistency problem in fuzzy group MCDM, this paper develops a new method selection approach for selecting a fuzzy group MCDM method that produces the most preferred group ranking outcome for a given problem. Based on two group averaging methods, three aggregation procedures and three defuzzification methods, 18 fuzzy group MCDM methods are developed as an illustration to solve the general fuzzy MCDM problem that requires cardinal ranking of the decision alternatives. The approach selects the group ranking outcome of a fuzzy MCDM method which has the highest consistency degree with its corresponding ranking outcomes of individual decision makers. An empirical study on the green bus fuel technology selection problem is used to illustrate how the approach works. The approach is applicable to large-scale group multicriteria decision problems where inconsistent ranking outcomes often exist between different fuzzy MCDM methods.     

Revisiting the supplier selection problem: An integrated approach for group decision support

Decision support for supplier selection is a highly researched theme in procurement management literature. However applications of group decision support theories are yet to be explored extensively in this domain. This study proposes an approach for group decision support for the supplier selection problem by integrating fuzzy Analytic Hierarchy Process (AHP) for group decision making and fuzzy goal programming for discriminant analysis. In the first step, the fuzzy AHP theory with the Geometric Mean Method has been used to prioritize and aggregate the preferences of a group of decision makers. Then consensus has been developed between these aggregated priorities using the Ordinal Consensus Improvement Approach. Subsequently, the consensual priorities of this group of decision makers have been integrated with fuzzy goal programming theory for discriminant analysis to provide predictive decision support. Finally it has been shown through a case study how the integrated approach using fuzzy AHP for group decision making and fuzzy goal programming with soft constraints has been more effective as compared to an existing approach for group decision making using only AHP.     

Group multi-criteria decision making based upon interval-valued fuzzy numbers: An extension of the MULTIMOORA method

Multi criteria decision making (MCDM) often involves uncertainty which can be tackled by employing the fuzzy set theory. Type-2 fuzzy sets offer certain additional means for the latter purpose. This paper therefore extends the MULTIMOORA method with type-2 fuzzy sets viz. generalized interval-valued trapezoidal fuzzy numbers. The proposed method thus provides the means for multi-criteria decision making related to uncertain assessments. Utilization of aggregation operators also enables to facilitate group multi-criteria decision making. A numerical example of personnel selection demonstrates the possibilities of application of the proposed method in the field of human resource management and performance management in general.     

An expert system for multi-criteria decision making using Dempster Shafer theory

This paper outlines a new software system we have developed that utilises the newly developed method (DS/AHP) which combines aspects of the Analytic Hierarchy Process (AHP) with Dempster–Shafer Theory for the purpose of multi-criteria decision making (MCDM). The method allows a decision maker considerably greater level of control (compared with conventional AHP methods) on the judgements made in identifying levels of favouritism towards groups of decision alternatives. More specifically, the DS/AHP analysis allows for additional analysis, including levels of uncertainty and conflict in the decisions made, for example. In this paper an expert system is introduced which enables the application of DS/AHP to MCDM. The expert system illustrates further the usability of DS/AHP, also including new aspects of analysis and representation offered through using this method. The principal application used to illustrate this expert system is that of identifying those residential properties to visit (view), from those advertised for ales through a real estate brokerage firm.     

Multi-criteria decision-making for coronavirus disease 2019 applications: a theoretical analysis review

The influence of the ongoing COVID-19 pandemic that is being felt in all spheres of our lives and has a remarkable effect on global health care delivery occurs amongst the ongoing global health crisis of patients and the required services. From the time of the first detection of infection amongst the public, researchers investigated various applications in the fight against the COVID-19 outbreak and outlined the crucial roles of different research areas in this unprecedented battle. In the context of existing studies in the literature surrounding COVID-19, related to medical treatment decisions, the dimensions of context addressed in previous multidisciplinary studies reveal the lack of appropriate decision mechanisms during the COVID-19 outbreak. Multiple criteria decision making (MCDM) has been applied widely in our daily lives in various ways with numerous successful stories to help analyse complex decisions and provide an accurate decision process. The rise of MCDM in combating COVID-19 from a theoretical perspective view needs further investigation to meet the important characteristic points that match integrating MCDM and COVID-19. To this end, a comprehensive review and an analysis of these multidisciplinary fields, carried out by different MCDM theories concerning COVID19 in complex case studies, are provided. Research directions on exploring the potentials of MCDM and enhancing its capabilities and power through two directions (i.e. development and evaluation) in COVID-19 are thoroughly discussed. In addition, Bibliometrics has been analysed, visualization and interpretation based on the evaluation and development category using R-tool involves; annual scientific production, country scientific production, Wordcloud, factor analysis in bibliographic, and country collaboration map. Furthermore, 8 characteristic points that go through the analysis based on new tables of information are highlighted and discussed to cover several important facts and percentages associated with standardising the evaluation criteria, MCDM theory in ranking alternatives and weighting criteria, operators used with the MCDM methods, normalisation types for the data used, MCDM theory contexts, selected experts ways, validation scheme for effective MCDM theory and the challenges of MCDM theory used in COVID-19 studies. Accordingly, a recommended MCDM theory solution is presented through three distinct phases as a future direction in COVID19 studies. Key phases of this methodology include the Fuzzy Delphi method for unifying criteria and establishing importance level, Fuzzy weighted Zero Inconsistency for weighting to mitigate the shortcomings of the previous weighting techniques and the MCDM approach by the name Fuzzy Decision by Opinion Score method for prioritising alternatives and providing a unique ranking solution. This study will provide MCDM researchers and the wider community an overview of the current status of MCDM evaluation and development methods and motivate researchers in harnessing MCDM potentials in tackling an accurate decision for different fields against COVID-19.

     

Logistics tool selection with two-phase fuzzy multi criteria decision making: A case study for personal digital assistant selection

Efficient logistics and supply chain management are enabled through the use of efficient information technologies (IT). The mobile logistics tools represent the IT interface in the supply chain. This paper aims to aid decision makers to identify the most appropriate mobile logistics tools and to achieve this aim, several evaluation criteria are identified to evaluate logistics tools, and a fuzzy axiomatic design (FAD) based group decision-making method is adopted to perform the evaluation in two phases. In the first phase of pre-assessment, alternatives that cannot meet basic requirements and the defined threshold are eliminated. In the second phase of selection, the remaining alternatives are more meticulously evaluated. Criteria weights are determined using fuzzy analytic hierarchy process (AHP) and another fuzzy multi-criteria decision-making (MCDM) technique, namely fuzzy technique for order preference by similarity to ideal solution (TOPSIS), is applied in the second phase to compare the outcome of FAD. A case study is provided in order to demonstrate the potential of the proposed methodology. Personal digital assistants (PDAs) with integrated barcode scanner that are available in the Turkish market are evaluated.     

Linguistic Discriminative Aggregation in Multicriteria Decision Making

Several new aggregation operators are proposed in the context of multicriteria decision making (MCDM) in the linguistic domain. The proposed operators first infer the discrimination index, based on the extent of variability in the various linguistic evaluations against a criterion. This value is then utilized in the actual aggregation step to discriminate among the alternatives. Besides, the proposed operators also take into account the a priori weights associated with the criteria. The proposed concepts are illustrated through an example in group MCDM.     

A preference aggregation method through the estimation of utility intervals

In this paper, a preference aggregation method is developed for ranking alternative courses of actions by combining preference rankings of alternatives given on individual criteria or by individual decision makers. In the method, preference rankings are viewed as constraints on alternative utilities, which are normalized, and linear programming models are constructed to estimate utility intervals, which are weighted and averaged to generate an aggregated utility interval. A simple yet pragmatic interval ranking method is used to compare and/or rank alternatives. The final ranking is generated as the most likely ranking with certain degrees of belief. Three numerical examples are examined to illustrate the potential applications of the proposed method.Scope and purposeThe aggregation of preference rankings has wide applications in group decision making, social choice, committee election and voting systems. The purpose of this paper is to develop a preference aggregation method through the estimation of utility intervals, in which preference rankings are associated with utility intervals that are estimated using linear programming models and aggregated using the simple additive weighting method.     

Microcomputer based multiple criteria decision support system for strategic planning

There are two major approaches currently used for developing Decision support Systems (DSS) for strategic planning, especially in the objective formulation stage. Several mathematical models have been developed to abstract the decision situation. However, they do not take into account either behavioral aspects of decision making or the presence of multiple and conflicting objectives. A second approach is to consider the several qualitative factors that go into decision making; such considerations are normally situation-dependent and hence it is difficult to provide a system for general managerial situations.The Multiple Criteria Decision Making (MCDM) approach combines the advantages of both the approaches and, therefore, is an excellent alternative for designing DSS. This paper develops an MCDM approach to strategic planning. The model is applied to such a problem in a simulated environment and the problem is solved interactively. Our experience shows that the proposed methodology is a viable approach for solving practical decision problems in strategic planning.     

群AHP法判断矩阵调整和群信息集结算法研究

对群层次分析法中不一致判断矩阵的调整和群信息的集结问题进行了研究,分别给出了多项推荐的判断矩阵调整算法和基于聚类的群信息集结算法来解决这2个问题,并以此为基础开发实现了一个基于Web的群层次分析法系统,以在企业的实施案例说明了系统的实用性和有效性。     

Finding the numerical compensation in multiple criteria decision-making problems under fuzzy environment

In this paper, we have developed a methodology to derive the level of compensation numerically in multiple criteria decision-making (MCDM) problems under fuzzy environment. The degree of compensation is dependent on the tranquility and anxiety level experienced by the decision-maker while taking the decision. Higher tranquility leads to the higher realisation of the compensation whereas the increased level of anxiety reduces the amount of compensation in the decision process. This work determines the level of tranquility (or anxiety) using the concept of fuzzy sets and its various level sets. The concepts of indexing of fuzzy numbers, the risk barriers and the tranquility level of the decision-maker are used to derive his/her risk prone or risk averse attitude of decision-maker in each criterion. The aggregation of the risk levels in each criterion gives us the amount of compensation in the entire MCDM problem. Inclusion of the compensation leads us to model the MCDM problem as binary integer programming problem (BIP). The solution to BIP gives us the compensatory decision to MCDM. The proposed methodology is illustrated through a numerical example.     

A Fuzzy AHP Approach to Evaluating Machine Tool Alternatives

Selecting process of a machine tool has been very important issue for companies for years, because the improper selection of a machine tool might cause of many problems affecting negatively on productivity, precision, flexibility and company’s responsive manufacturing capabilities. On the other hand, selecting the best machine tool from its increasing number of existing alternatives in market are multiple-criteria decision making (MCDM) problem in the presence of many quantitative and qualitative attributes. Therefore, in this paper, an analytic hierarchy process (AHP) is used for machine tool selection problem due to the fact that it has been widely used in evaluating various kinds of MCDM problems in both academic researches and practices. However, due to the vagueness and uncertainty on judgments of the decision-maker(s), the crisp pair wise comparison in the conventional AHP seems to insufficient and imprecise to capture the right judgments of decision-maker(s). That is why; fuzzy number logic is introduced in the pair wise comparison of AHP to make up for this deficiency in the conventional AHP. Shortly, in this study, an intelligent approach is proposed, where both techniques; fuzzy logic and AHP are come together, referred to as fuzzy AHP. First, the fuzzy AHP technique is used to weight the alternatives under multiple attributes; second Benefit/Cost (B/C) ratio analysis is carried out by using both the fuzzy AHP score and procurement cost, of each alternative. The alternative with highest B/C ratio is found out and called as the ultimate machine tool among others. In addition, a case study is also presented to make this approach more understandable for a decision-maker(s).     

Prioritized multi-criteria decision making based on preference relations

There may exist priority relationships among criteria in multi-criteria decision making (MCDM) problems. This kind of problems, which we focus on in this paper, are called prioritized MCDM ones. In order to aggregate the evaluation values of criteria for an alternative, we first develop some weighted prioritized aggregation operators based on triangular norms (t-norms) together with the weights of criteria by extending the prioritized aggregation operators proposed by Yager (Yager, R. R. (2004). Modeling prioritized multi-criteria decision making. IEEE Transactions on Systems, Man, and Cybernetics, 34, 2396–2404). After discussing the influence of the concentration degrees of the evaluation values with respect to each criterion to the priority relationships, we further develop a method for handling the prioritized MCDM problems. Through a simple example, we validate that this method can be used in more wide situations than the existing prioritized MCDM methods. At length, the relationships between the weights associated with criteria and the preference relations among alternatives are explored, and then two quadratic programming models for determining weights based on multiplicative and fuzzy preference relations are developed.     

Using a multi-criteria decision making approach to evaluate mobile phone alternatives

The arrival of the mobile phone and its rapid and widespread growth may well be seen as one of the most significant developments in the fields of communication and information technology over the past two decades. The aim of this study is to propose a multi-criteria decision making (MCDM) approach to evaluate the mobile phone options in respect to the users' preferences order. Firstly, the most desirable features influencing the choice of a mobile phone are identified. This is realized through a survey conducted among the target group, the experiences of the telecommunication sector experts and the studies in the literature. Two MCDM methods are then used in the evaluation procedure. More precisely, Analytic Hierarchy Process (AHP) is applied to determine the relative weights of evaluation criteria and the extension of the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is applied to rank the mobile phone alternatives. A case study illustrates the effectiveness of the proposed approach.     

An incident information management framework based on data integration, data mining, and multi-criteria decision making

An effective incident information management system needs to deal with several challenges. It must support heterogeneous distributed incident data, allow decision makers (DMs) to detect anomalies and extract useful knowledge, assist DMs in evaluating the risks and selecting an appropriate alternative during an incident, and provide differentiated services to satisfy the requirements of different incident management phases. To address these challenges, this paper proposes an incident information management framework that consists of three major components. The first component is a high-level data integration module in which heterogeneous data sources are integrated and presented in a uniform format. The second component is a data mining module that uses data mining methods to identify useful patterns and presents a process to provide differentiated services for pre-incident and post-incident information management. The third component is a multi-criteria decision-making (MCDM) module that utilizes MCDM methods to assess the current situation, find the satisfactory solutions, and take appropriate responses in a timely manner. To validate the proposed framework, this paper conducts a case study on agrometeorological disasters that occurred in China between 1997 and 2001. The case study demonstrates that the combination of data mining and MCDM methods can provide objective and comprehensive assessments of incident risks.     

Discriminative aggregation operators for multi criteria decision making

A general aggregation formalism for multi criteria decision making (MCDM) applications is presented. Using this formalism, we derive the existing aggregation operators, and also develop some new ones. The proposed general formalism is further extended to develop discriminative class of aggregation operators for aiding MCDM. The proposed discriminative aggregation operators are based on the consideration of the variability in the various evaluations of a criterion. Four families of discriminative aggregation operators are developed using the extended formalism. These operators and applied in a managerial real world case-study.     

Comparative analysis of MCDM methods for the assessment of mortality in patients with acute coronary syndrome

Multi-criteria decision-making (MCDM) methods are commonly used in many fields of research, e.g., engineering and manufacturing systems, water resources studies , medicine, and etc. However, there is no effective approach of selecting a MCDM method to problem, which is solved. The formal requirements of each MCDM method are not sufficient because most methods would seem to be appropriate for most problems. Therefore, the main purpose of the paper is a comparison of accuracy selected MCDM methods. Proposed approach is presented on the example of mortality in patients with acute coronary syndrome. Additionally, the paper presents characteristic objects method (COMET) as a potential decision making method for use in medical problems, which accuracy is compared with TOPSIS and AHP. In the experimental study, the average and standard deviation of the root mean square error of evaluations are examined for groups of randomly selected patients, each described by age, blood pressure, and heart rate. Then, the correctness of choosing the patient in the best and worst condition is also examined among randomly selected pairs. As a result of the experimental study, rankings obtained by the COMET method are distinctly more accurate than those obtained by TOPSIS or AHP techniques. The COMET method, in the opposite of others method, is completely free of the rank reversal phenomenon, which is identified as a main source of problems with evaluations accuracy.