Algorithms to Detect and Rectify Multiplicative and Ordinal Inconsistencies of Fuzzy Preference Relations

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Consistency, multiplicative and ordinal, of fuzzy preference relations (FPRs) is investigated. The geometric consistency index (GCI) approximated thresholds are extended to measure the degree of consistency for an FPR. For inconsistent FPRs, two algorithms are devised (1) to find the multiplicative inconsistent elements, and (2) to detect the ordinal inconsistent elements. An integrated algorithm is proposed to improve simultaneously the ordinal and multiplicative consistencies. Some examples, comparative analysis, and simulation experiments are provided to demonstrate the effectiveness of the proposed methods

An overview on managing additive consistency of reciprocal preference relations for consistency-driven decision making and Fusion: Taxonomy and future directions

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.The reciprocal preference relation (RPR) is a powerful tool to represent decision makers’ preferences in decision making problems. In recent years, various types of RPRs have been reported and investigated, some of them being the ‘classical’ RPRs, interval-valued RPRs and hesitant RPRs. Additive consistency is one of the most commonly used property to measure the consistency of RPRs, with many methods developed to manage additive consistency of RPRs. To provide a clear perspective on additive consistency issues of RPRs, this paper reviews the consistency measurements of the different types of RPRs. Then, consistency-driven decision making and information fusion methods are also reviewed and classified into four main types: consistency improving methods; consistency-based methods to manage incomplete RPRs; consistency control in consensus decision making methods; and consistency-driven linguistic decision making methods. Finally, with respect to insights gained from prior researches, further directions for the research are proposed

A Local Adjustment Method to Improve Multiplicative Consistency of Fuzzy Reciprocal Preference Relations

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Preferences that verify the transitivity property are usually referred to as rational or consistent preferences. Existent methods to improve the consistency of inconsistent fuzzy reciprocal preference relations (FPRs) fail to retain the original preference values because they always derive a new FPR. This article presents a new inconsistency identification and modification (IIM) method to detect and rectify only the most inconsistent elements of an inconsistent FPR. As such, the proposed IIM can be considered a local adjustment method to improve multiplicative consistency (MC) of FPRs. The case of inconsistent FPRs with missing values, i.e., incomplete FPRs, is addressed with the estimation of the missing preferences with a constrained nonlinear optimization model by the application of the IIM method. The implementation process of the proposed algorithms is illustrated with numerical examples. Simulation experiments and comparisons with existent methods are also included to show that the new method requires fewer iterations than existent methods to improve the MC of FPRs and achieves better MC level, while preserving the original preference information as much as possible than the existent methods. Thus, the results presented in this article demonstrate the correctness, effectiveness, and robustness of the proposed method

Fuzzy Rankings for Preferences Modeling in Group Decision Making

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Although fuzzy preference relations (FPRs) are among the most commonly used preference models in group decision making (GDM), they are not free from drawbacks. First of all, especially when dealing with many alternatives, the definition of FPRs becomes complex and time consuming. Moreover, they allow to focus on only two options at a time. This facilitates the expression of preferences but let experts lose the global perception of the problem with the risk of introducing inconsistencies that impact negatively on the whole decision process. For these reasons, different preference models are often adopted in real GDM settings and, if necessary, transformation functions are applied to obtain equivalent FPRs. In this paper, we propose fuzzy rankings, a new approximate preference model that offers a higher level of user‐friendliness with respect to FPRs while trying to maintain an adequate level of expressiveness. Fuzzy rankings allow experts to focus on two alternatives at a time without losing the global picture so reducing inconsistencies. Conversion algorithms from fuzzy rankings to FPRs and backward are defined as well as similarity measures, useful when evaluating the concordance between experts’ opinion. A comparison of the proposed model with related works is reported as well as several explicative examples

Pairwise comparison matrix in multiple criteria decision making

The measurement scales, consistency index, inconsistency issues, missing judgment estimation and priority derivation methods have been extensively studied in the pairwise comparison matrix (PCM). Various approaches have been proposed to handle these problems, and made great contributions to the decision making. This paper reviews the literature of the main developments of the PCM. There are plenty of literature related to these issues, thus we mainly focus on the literature published in 37 peer reviewed international journals from 2010 to 2015 (searched via ISI Web of science). We attempt to analyze and classify these literatures so as to find the current hot research topics and research techniques in the PCM, and point out the future directions on the PCM. It is hoped that this paper will provide a comprehensive literature review on PCM, and act as informative summary of the main developments of the PCM for the researchers for their future research. First published online: 02 Sep 201

Are incomplete and self-confident preference relations better in multicriteria decision making? A simulation-based investigation

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Incomplete preference relations and self-confident preference relations have been widely used in multicriteria decision-making problems. However, there is no strong evidence, in the current literature, to validate their use in decision-making. This paper reports on the design of two bounded rationality principle based simulation methods, and detailed experimental results, that aim at providing evidence to answer the following two questions: (1) what are the conditions under which incomplete preference relations are better than complete preference relations?; and (2) can self-confident preference relations improve the quality of decisions? The experimental results show that when the decision-maker is of medium rational degree, incomplete preference relations with a degree of incompleteness between 20% and 40% outperform complete preference relations; otherwise, the opposite happens. Furthermore, in most cases the quality of the decision making improves when using self-confident preference relations instead of incomplete preference relations. The paper ends with the presentation of a sensitivity analysis that contributes to the robustness of the experimental conclusions

Consistency-driven methodology to manage incomplete linguistic preference relation: A perspective based on personalized individual semantics

The file attached to this record is the author's final peer reviewed version.In linguistic decision making problems there may be cased when decision makers will not be able to provide complete linguistic preference relations. However, when estimating unknown linguistic preference values in incomplete preference relations, the existing research approaches ignore the fact that words mean different things for different people, i.e. decision makers have personalized individual semantics (PISs) regarding words. To manage incomplete linguistic preference relations with PISs, in this paper we propose a consistency-driven methodology both to estimate the incomplete linguistic preference values and to obtain the personalized numerical meanings of linguistic values of the different decision makers. The proposed incomplete linguistic preference estimation method combines the characteristic of the personalized representation of decision makers and guarantees the optimum consistency of incomplete linguistic preference relations in the implementation process. Numerical examples and a comparative analysis are included to justify the feasibility of the PISs based incomplete linguistic preference estimation method

Developing A Group Decision Support System (gdss) For Decision Making Under Uncertainty

Multi-Criteria Decision Making (MCDM) problems are often associated with tradeoffs between performances of the available alternative solutions under decision making criteria. These problems become more complex when performances are associated with uncertainty. This study proposes a stochastic MCDM procedure that can handle uncertainty in MCDM problems. The proposed method coverts a stochastic MCDM problem into many deterministic ones through a Monte-Carlo (MC) selection. Each deterministic problem is then solved using a range of MCDM methods and the ranking order of the alternatives is established for each deterministic MCDM. The final ranking of the alternatives can be determined based on winning probabilities and ranking distribution of the alternatives. Ranking probability distributions can help the decision-maker understand the risk associated with the overall ranking of the options. Therefore, the final selection of the best alternative can be affected by the risk tolerance of the decisionmakers. A Group Decision Support System (GDSS) is developed here with a user-friendly interface to facilitate the application of the proposed MC-MCDM approach in real-world multiparticipant decision making for an average user. The GDSS uses a range of decision making methods to increase the robustness of the decision analysis outputs and to help understand the sensitivity of the results to level of cooperation among the decision-makers. The decision analysis methods included in the GDSS are: 1) conventional MCDM methods (Maximin, Lexicographic, TOPSIS, SAW and Dominance), appropriate when there is a high cooperation level among the decision-makers; 2) social choice rules or voting methods (Condorcet Choice, Borda scoring, Plurality, Anti-Plurality, Median Voting, Hare System of voting, Majoritarian iii Compromise ,and Condorcet Practical), appropriate for cases with medium cooperation level among the decision-makers; and 3) Fallback Bargaining methods (Unanimity, Q-Approval and Fallback Bargaining with Impasse), appropriate for cases with non-cooperative decision-makers. To underline the utility of the proposed method and the developed GDSS in providing valuable insights into real-world hydro-environmental group decision making, the GDSS is applied to a benchmark example, namely the California‘s Sacramento-San Joaquin Delta decision making problem. The implications of GDSS‘ outputs (winning probabilities and ranking distributions) are discussed. Findings are compared with those of previous studies, which used other methods to solve this problem, to highlight the sensitivity of the results to the choice of decision analysis methods and/or different cooperation levels among the decision-maker

Introducing disruption on stagnated Group Decision Making processes using Fuzzy Ontologies

In Group Decision Making processes, experts debate about how to rank a set of alternatives. It is usual that, at a certain point of the discussion, the debate gets stuck. In this paper, a novel Group Decision Making method for environments with a high number of alternatives is presented. Fuzzy Ontologies are used in order to represent the alternatives and their characteristics. Moreover, a novel stagnation analysis is used in order to determine if the debate gets stuck. If it does, the method modifies the alternatives set in order to introduce new options and remove the least popular ones. This way, the debate can revive since that the new alternatives provide different points of view. The presented method helps experts to conduct long and thorough debates in order for them to be able to make effective and reliable decisions.MCIN/AEI PID2019-103880RB-I00FEDER/Junta de Andalucia-Consejeria de Transformacion Economica, Industria, Conocimiento y Universidades B-TIC-590-UGR20Andalusian government P20_00673Ministry of Education and King Abdulaziz University, DSR, Jeddah, Saudi Arabia IFPHI-049-135-2020Universidad de Granada/CBU

Multi-criteria decision-making in whole process design

PhD ThesisIn recent years, the chemical and pharmaceutical industries have faced increased development times and costs with fewer novel chemicals being discovered. This has resulted in many companies focusing on innovative research and development as they consider this key to business success. In particular, a number of leading industrial organisations have adopted the principles of Whole Process Design (WPD). WPD considers the optimisation of the entire product development process, from raw materials to end product, rather than focusing on each individual unit operation. The complexity involved in the implementation of WPD requires rationalised decision-making, often with limited or uncertain information. This thesis assesses the most widely applied methods in Multi-Criteria Decision Analysis (MCDA) in conjunction with the results of two interviews and two questionnaires that identified the industrial requirements for decision-making during WPD. From the findings of this work, a novel decision-making methodology was proposed, the outcome of which allows a decision-maker to visually interpret their decision results with associated levels of uncertainty. To validate the proposed methodology, a software framework was developed that incorporates two other decision-making approaches, the Analytical Hierarchy Process (AHP) and ELimination Et Choix Traduisant la REalité trois (ELECTRE III). The framework was then applied to a number of industrial case studies to validate the application of the proposed methodology.Engineering and Physical Sciences Research Council (EPSRC) and Chemistry Innovatio