Triangular bounded consistency of fuzzy preference relations

There are typically two types of consistency of fuzzy preference relations (FPR), namely additive and multiplicative consistency. They are defined based on the assumption that decision makers are rational and can provide strictly consistent FPRs. To take into consideration the bounded rationality of decision makers, the current study relaxes this assumption and proposes a new measure called triangular bounded consistency for judging the consistency of FPRs. To define triangular bounded consistency, a directed triangle is used to represent three FPRs among any three alternatives, with each directed edge representing an FPR. The condition of restricted max–max transitivity (RMMT) in the directed triangle is quantitatively examined. Under the assumption that the bounded rationality of a decision maker is characterized by their historical FPRs, which are represented by directed triangles that satisfy RMMT, triangular bounded consistency is determined using the historical FPRs. We then illustrate how triangular bounded consistency can be used to verify the consistency of FPRs that are newly provided by decision makers and how to estimate some missing FPRs that are not provided by decision makers. Finally, to demonstrate the application of triangular bounded consistency of FPRs in multi-attribute decision analysis, we investigate a problem that involves selecting areas to market products for a company

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

Managing Consistency and Consensus in Group Decision-Making with Incomplete Fuzzy Preference Relations

Group decision-making is a field of decision theory that has many strengths and benefits. It can solve and simplify the most complex and hard decision problems. In addition, it helps decision-makers know more about the problem under study and their preferences. Group decision-making is much harder and complex than individual decision-making since group members may have different preferences regarding the alternatives, making it difficult to reach a consensus. In this thesis, we deal with three interrelated problems that decision-makers encounter during the process of arriving at a final decision. Our work addresses decision-making using preference relations. The first problem deals with incomplete reciprocal preference relations, where some of the preference degrees are missing. Ideally, the group members are able to provide preferences for all the alternatives, but sometimes they might not be able to discriminate between some of the alternatives, leading to missing values. Two methods are proposed to handle this problem. The first is based on a system of equations and the second relies on goal programming to estimate the missing information. The former is suitable to complete any incomplete preference relation with at leas

An integrated approach of fuzzy linguistic preference based AHP and fuzzy COPRAS for machine tool evaluation

Globalization of business and competitiveness in manufacturing has forced companies to improve their manufacturing facilities to respond to market requirements. Machine tool evaluation involves an essential decision using imprecise and vague information, and plays a major role to improve the productivity and flexibility in manufacturing. The aim of this study is to present an integrated approach for decision-making in machine tool selection. This paper is focused on the integration of a consistent fuzzy AHP (Analytic Hierarchy Process) and a fuzzy COmplex PRoportional ASsessment (COPRAS) for multi-attribute decision-making in selecting the most suitable machine tool. In this method, the fuzzy linguistic reference relation is integrated into AHP to handle the imprecise and vague information, and to simplify the data collection for the pair-wise comparison matrix of the AHP which determines the weights of attributes. The output of the fuzzy AHP is imported into the fuzzy COPRAS method for ranking alternatives through the closeness coefficient. Presentation of the proposed model application is provided by a numerical example based on the collection of data by questionnaire and from the literature. The results highlight the integration of the improved fuzzy AHP and the fuzzy COPRAS as a precise tool and provide effective multi-attribute decision-making for evaluating the machine tool in the uncertain environment

The triangle assessment method: a new procedure for eliciting expert judgement

The Analytic Hierarchy Process (AHP) is one of the most widely used Multi-Criteria Decision-Making methods worldwide. As such, it is subject to criticisms that highlight some potential weaknesses. In this study, we present a new Multi-Criteria Decision-Making method denominated the “Triangular Assessment Method” (referred to by its Spanish abbreviation, MTC©). The MTC© aims to make use of the potential of AHP while avoiding some of its drawbacks. The main characteristics and advantages of the MTC© can be summarised as follows: (i) evaluation of criteria, and of the alternative options for each criterion, in trios instead of pairs; (ii) elimination of discrete scales and values involved in judgements; (iii) a substantial reduction in the number of evaluations (trios) relative to the corresponding number of pairs which would have to be considered when applying the AHP method; (iv) consistent decision-making; (v) introduction of closed cyclical series for comparing criteria and alternatives; and (vi) the introduction of opinion vectors and opinion surfaces. This new method is recommended for supporting decision-making with large numbers of subjective criteria and/or alternatives and also for group decisions where the consensus must be evaluated. The MTC© provides a different promising perspective in decision-making and could lead to new research lines in the field of information systems.This work was supported by the Galician Regional Government [“Programa de Consolidación e Estructuración de Unidades de Investigación Competitivas, modalidade de Grupos de Referencia Competitiva” for the period 2006–2017] and by the European Union [ERDF program]. Likewise, the authors thank Daniele de Rigo, Dora Henriques and Cesar Pérez-Cruzado, because his comments improved notably this manuscript.info:eu-repo/semantics/publishedVersio

A proactive approach to quantitative assessment of disruption risks of petroleum refinery operation

Petroleum refinery consists of numerous process units in operation, which are subjected to diverse accident risks in day-to-day operations under extreme operating conditions. Due to the complexity of petroleum refinery operations, any failure can lead to major accident and a huge financial loss for a petroleum refining company. However, petroleum refinery operations can be disrupted by various risk elements from the organization, technical, operational and external latent conditions. Risk elements are often inherent in operations, which can be based on uncertain knowledge, oversight and lack of perception of interactive events that can lead to disruption. In order to circumvent events that can cause disruption in a petroleum refinery, the criticality of the risk elements and their attributes that are associated with Petroleum Refinery Process Units (PRPU) operations need to be investigated. Therefore, there is a need to identify and assess the most critical risk elements and attributes that can interact to cause the disruption of operational reliability and availability of a petroleum refinery process unit. Hence, this article proposes a robust fuzzy linguistic assessment methodology for identification and assessment of PRPU risk elements and their attributes. The methodology deals with the main challenges of utilising expert's subjective judgements, in terms of the assessment of PRPU risk elements under uncertain situations. The result of the evaluation and ranking of PRPU risk elements and their attributes can provide salient risk information to duty holders and decision makers in the petroleum refinery in order to prioritise resources for risk management of the most critical attributes of the risk elements. © 2020 Elsevier Lt

Introduction to the Analytic Hierarchy Process

The Analytic Hierarchy Process (AHP) has been one of the foremost mathematical methods for decision making with multiple criteria and has been widely studied in the operations research literature as well as applied to solve countless real-world problems. This book is meant to introduce and strengthen the readers’ knowledge of the AHP, no matter how familiar they may be with the topic. This book provides a concise, yet self-contained, introduction to the AHP that uses a novel and more pedagogical approach. It begins with an introduction to the principles of the AHP, covering the critical points of the method, as well as some of its applications. Next, the book explores further aspects of the method, including the derivation of the priority vector, the estimation of inconsistency, and the use of AHP for group decisions. Each of these is introduced by relaxing initial assumptions. Furthermore, this booklet covers extensions of AHP, which are typically neglected in elementary expositions of the methods. Such extensions concern different numerical representations of preferences and the interval and fuzzy representations of preferences to account for uncertainty. During the whole exposition, an eye is kept on the most recent developments of the method.Peer reviewe