Limited Rationality and Its Quantification Through the Interval Number Judgments With Permutations

The relative importance of alternatives expressed in terms of interval numbers in the fuzzy analytic hierarchy process aims to capture the uncertainty experienced by decision makers (DMs) when making a series of comparisons. Under the assumption of full rationality, the judgements of DMs in the typi...

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Bibliographic Details
Published in:IEEE transactions on cybernetics 2017-12, Vol.47 (12), p.4025-4037
Main Authors: Fang Liu, Pedrycz, Witold, Wei-Guo Zhang
Format: Article
Language:English
Subjects:
Algorithm design and analysis
Analytic hierarchy process
Approximate consistency
Approximation
Consistency
Cybernetics
Decision analysis
Decision making
exchange method
Fuzzy sets
interval multiplicative reciprocal preference relation
Judgments
limited rationality
Logic gates
Mathematical analysis
Permutations
permutations of alternatives
Rationality
Uncertainty
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Summary:The relative importance of alternatives expressed in terms of interval numbers in the fuzzy analytic hierarchy process aims to capture the uncertainty experienced by decision makers (DMs) when making a series of comparisons. Under the assumption of full rationality, the judgements of DMs in the typical analytic hierarchy process could be consistent. However, since the uncertainty in articulating the opinions of DMs is unavoidable, the interval number judgements are associated with the limited rationality. In this paper, we investigate the concept of limited rationality by introducing interval multiplicative reciprocal comparison matrices. By analyzing the consistency of interval multiplicative reciprocal comparison matrices, it is observed that the interval number judgements are inconsistent. By considering the permutations of alternatives, the concepts of approximation-consistency and acceptable approximation-consistency of interval multiplicative reciprocal comparison matrices are proposed. The exchange method is designed to generate all the permutations. A novel method of determining the interval weight vector is proposed under the consideration of randomness in comparing alternatives, and a vector of interval weights is determined. A new algorithm of solving decision making problems with interval multiplicative reciprocal preference relations is provided. Two numerical examples are carried out to illustrate the proposed approach and offer a comparison with the methods available in the literature.
ISSN:2168-2267
2168-2275
DOI:10.1109/TCYB.2016.2594491