Group decision making with a fuzzy linguistic majority
Fuzzy Sets and Systems
A rational consensus model in group decision making using linguistic assessments
Fuzzy Sets and Systems
An investigation into relations between some transitivity-related concepts
Fuzzy Sets and Systems
Transitivity of fuzzy preference relations—an empirical study
Fuzzy Sets and Systems
A method for improving the consistency of judgements
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
General transitivity conditions for fuzzy reciprocal preference matrices
Fuzzy Sets and Systems - Special issue: Preference modelling and applications
Inconsistent and contradictory judgements in pairwise comparison method in the AHP
Computers and Operations Research
Incomplete linguistic preference relations and their fusion
Information Fusion
On the cycle-transitive comparison of artificially coupled random variables
International Journal of Approximate Reasoning
A consistency-based procedure to estimate missing pairwise preference values
International Journal of Intelligent Systems
Consistent models of transitivity for reciprocal preferences on a finite ordinal scale
Information Sciences: an International Journal
Group decision making with incomplete fuzzy linguistic preference relations
International Journal of Intelligent Systems
International Journal of Approximate Reasoning
IEEE Transactions on Fuzzy Systems
A method for repairing the inconsistency of fuzzy preference relations
Fuzzy Sets and Systems
Transitivity frameworks for reciprocal relations: cycle-transitivity versus FG-transitivity
Fuzzy Sets and Systems
A note on group decision-making procedure based on incomplete reciprocal relations
Soft Computing - A Fusion of Foundations, Methodologies and Applications
Group Decision-Making Model With Incomplete Fuzzy Preference Relations Based on Additive Consistency
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
A consensus model for multiperson decision making with different preference structures
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
A Consensus Model for Group Decision Making With Incomplete Fuzzy Preference Relations
IEEE Transactions on Fuzzy Systems
IEEE Transactions on Fuzzy Systems
Distance-based consensus models for fuzzy and multiplicative preference relations
Information Sciences: an International Journal
Incomplete interval fuzzy preference relations and their applications
Computers and Industrial Engineering
Information Sciences: an International Journal
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In this paper, we first analyze the rationality of weak transitivity of a fuzzy preference relation defined by Tanino [Fuzzy preference orderings in group decision making, Fuzzy Sets and Systems 12 (1984) 117-131]. We then propose a revised definition of weak transitivity (we call it ordinal consistency). We propose the ordinal consistency index (OCI) to measure the degree of ordinal consistency of a fuzzy preference relation, which is to count the unreasonable 3-cycles in a directed graph that represents the fuzzy preference relation. Afterwards, a procedure to compute the order consistency index and to locate each cycle, as well as to find the inconsistent judgments in the fuzzy preference relation is proposed. In order to repair the inconsistency of a fuzzy preference relation, an algorithm is developed to find and remove 3-cycles in the graph. The algorithm eliminates 3-cycles in a graph more effectively and the proposed method for improving consistency method aims to preserve the initial preference information of the decision maker. Furthermore, the method can be used not only for a strict fuzzy preference relation, but also for non-strict fuzzy preference relation. Finally, we provide some examples to show the effectiveness and validity of the proposed method.