Some issues on consistency of fuzzy preference relations

By Enrique Herrera-Viedma, Francisco Herrera, Francisco Chiclana, María Luque. European Journal of Operational Research, 2004

1,009 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Management Science and Operations Research, Signal Processing

View Paper: https://www.semanticscholar.org/paper/ba8b8dd3f15f15dcb8b5b5ff1342086076c7fb1d

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Citations in the corpus

Supplier selection using AHP methodology extended by D numbers (2014, methodology): “A fuzzy preference relation R on a set of alternatives A = {A1,A2, - . . . ,An} is represented by a fuzzy set on the product set A A, and is characterized by a membership function (Herrera-Viedma et al., 2004; Xu, 2007) lR : A A!”
A web based consensus support system for group decision making problems and incomplete preferences (2010, background): “Consistency measures The consistency of a preference relation is related to the concept of transitivity [10,15,20,32,50].”
Cardinal Consistency of Reciprocal Preference Relations: A Characterization of Multiplicative Transitivity (2009, methodology): “associated with the transitivity property [9], [10], [31], [50].”
Managing the consensus in group decision making in an unbalanced fuzzy linguistic context with incomplete information (2010, methodology): “Many properties have been suggested to model transitivity of a fuzzy preference relation [32].”
Consensus models for AHP group decision making under row geometric mean prioritization method (2010, methodology): “For group decision making using preference relations, the consistencymeasure itself includes two subproblems [31]:”
Intuitionistic preference relations and their application in group decision making (2007, background): “(2) Fuzzy preference relation [13,14,30,33,37,41,42,49,51,52,56,59,60]: A fuzzy preference relation R on the set X is represented by a complementary matrix R 1⁄4 ðrijÞn n X X with rij P 0; rij þ rji 1⁄4 1; rii 1⁄4 0:5 for all i; j 1⁄4 1; 2; .”
Group Decision-Making Model With Incomplete Fuzzy Preference Relations Based on Additive Consistency (2007, methodology): “One of these properties is the “additive transitivity”, which, as shown in [17], can be seen as the parallel concept of Saaty’s consistency property in the case of the multiplicative preference relation.”
Some induced ordered weighted averaging operators and their use for solving group decision-making problems based on fuzzy preference relations (2007, background): “If the set of fuzzy preference relations are additive consistent [10], i.”
A review of soft consensus models in a fuzzy environment (2014, methodology): “Fortunately, the lack of consistency can be quantiﬁed and monitored [13,64,65], and it has been used as a parameter to validate the ﬁnal solution obtained after consensus reaching process [13,16,62,63].”
Consistency Measures for Hesitant Fuzzy Linguistic Preference Relations (2014, background): “The consistency measures on NPRs have been studied extensively [10]–[12].”
Fuzzy Group Decision Making With Incomplete Information Guided by Social Influence (2018, background): “Many consistency measures have been defined so far for this purpose [40], although the most widely used are based on the concept of additive transitivity property.”
Applying fuzzy linguistic preference relations to the improvement of consistency of fuzzy AHP (2008, methodology): “Herrera-Viedma et al. [24] proposed a new concept of consistency based on the additive transitivity property of fuzzy preference relations (Fuzzy LinPreRa) to avoid misleading conclusions.”
Computing the Numerical Scale of the Linguistic Term Set for the 2-Tuple Fuzzy Linguistic Representation Model (2009, background): “[25], [26], and Tanino [40] and analyze the physical implication of this consistency index in detail.”