A Fuzzy Approach to Weight Vector from a Group of Pairwise Comparison Matrices Based on Inclusion Relation

2018 ◽  
Author(s):  
Tomoe Entani
Keyword(s):  
Pairwise Comparison ◽  
Weight Vector ◽  
Fuzzy Approach ◽  
Inclusion Relation

Algebraic structures for pairwise comparison matrices: Consistency, social choices and Arrow’s theorem

2021 ◽  
Vol 71 (5) ◽  
pp. 1047-1062
Author(s):  
Giuseppina Barbieri ◽  
Antonio Boccuto ◽  
Gaetano Vitale
Keyword(s):  
Algebraic Structure ◽  
Pairwise Comparison ◽  
Consistency Index ◽  
General Definition ◽  
Fuzzy Approach ◽  
Algebraic Structures ◽  
Arrow’S Theorem ◽  
Arrow's Theorem ◽  
Definition Of

Abstract We present the algebraic structures behind the approaches used to work with pairwise comparison matrices and, in general, the representation of preferences. We obtain a general definition of consistency and a universal decomposition in the space of PCMs, which allow us to define a consistency index. Also Arrow’s theorem, which is presented in a general form, is relevant. All the presented results can be seen in the main formulations of PCMs, i.e., multiplicative, additive and fuzzy approach, by the fact that each of them is a particular interpretation of the more general algebraic structure needed to deal with these theories.

scholarly journals A Fuzzy Approach for Ranking Discrete Multi-Attribute Alternatives under Uncertainty

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 945 ◽  
Author(s):  
Lihui Liu ◽  
Hepu Deng
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Pairwise Comparison ◽  
Fuzzy Approach ◽  
Attribute Importance ◽  
Decision Making Problem ◽  
Efficiency And Effectiveness ◽  
Multi Attribute Decision Making ◽  
Fuzzy Extent Analysis

This paper presents a fuzzy approach for ranking discrete alternatives in multi-attribute decision-making under uncertainty. Linguistic variables approximated by fuzzy numbers were applied for facilitating the making of pairwise comparison by the decision maker in determining the alternative performance and attribute importance using fuzzy extent analysis. The resultant fuzzy assessments were aggregated using the simple additive utility method for calculating the fuzzy utility of each alternative across all the attributes. An ideal solution-based procedure was developed for comparing and ranking these fuzzy utilities, leading to the determination of the overall ranking of all the discrete multi-attribute alternatives. An example is provided that shows the proposed approach is effective and efficient in solving the multi-attribute decision making problem under uncertainty, due to the simplicity and comprehensibility of the underlying concept and the efficiency and effectiveness of the computation involved.

Penilaian Kinerja Dosen Dengan Menggunakan Metode AHP Studi Kasus di STIE Ahmad Dahlan Jakarta

Liquidity ◽  
2018 ◽  
Vol 2 (1) ◽  
pp. 100-109
Author(s):  
Ellya Sestri
Keyword(s):  
Decision Making ◽  
Performance Appraisal ◽  
Technological Progress ◽  
Pairwise Comparison ◽  
Relative Importance ◽  
Faculty Performance ◽  
Business World ◽  
The Face ◽  
Hierarchy Process ◽  
Rule Out

An increasingly rapid technological progress in the era of globalization in the business world, so do not rule out the possibility that a decision-making is something that is very vital in determining the decisions to be taken in the face of competitive business world. Decision making can be influenced by several aspects, this can affect the speed of decision making by the decision maker in which decisions must be quick and accurate. Lecturer Performance Assessment Using the Analytical Hierarchy Process is a decision support system that aims to assess faculty performance according to certain criteria. This system of faculty performance appraisal criteria to map a hierarchy, where each hierarchy will be performed pairwise comparison, the pairwise comparisons between criteria, so to get a comparison of the relative importance of criteria with each other. The results of this comparison is then analyzed to obtain the priority of each criterion. Once completed and performed an assessment of alternative options to be compared and calculated to obtain the best alternatives according to established criteria.

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