Preference relations, transitivity and the reciprocal property
نویسندگان
چکیده
منابع مشابه
Cyclic Evaluation of Transitivity of Reciprocal Relations
A general framework for studying the transitivity of reciprocal relations is presented. The key feature is the cyclic evaluation of transitivity: triangles (i.e. any three points) are visited in a cyclic manner. An upper bound function acting upon the ordered weights encountered provides an upper bound for the ‘sum minus 1’ of these weights. Commutative quasi-copulas allow to translate a genera...
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The aim of this work is to study an essential property in the framework of fuzzy preference structures, which is the transitivity. In particular, we discuss the relationship between the transitivity of a fuzzy large preference relation R and the transitivity of the fuzzy strict preference relation P obtained from R when every pair of elements can be compared. We consider some of the most import...
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Intuitionistic preference relations are becoming increasingly important in the field of group decision making since they present a flexible and simple way to the experts to provide their preference relations, while at the same time allowing them to accommodate a certain degree of hesitation inherent to all decision making processes. In this contribution, we prove the mathematical equivalence be...
متن کاملA generalization of stochastic and fuzzy transitivity for reciprocal fuzzy relations
b) moderate stochastic transitivity: For a reciprocal fuzzy relation Q : x2 + [O, 11 on a finite set of alternatives X , we introduce the concept of U-transitivity which is based upon the ordering of the matrix elements qij, qjk and qki of Q for all triples of indices i, j and k. We show that U-transitivity generalizes both stochastic and fuzzy transitivity. The U-transitivity of the secalled u...
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A binary relation R on a set S is transitive iff for all a, b, c ∈ S, if aRb and bRc, then aRc. This almost never applies to the relations logicians tend to think of as consequence relations; where such relations are relations on a set at all, they are rarely transitive. Yet it is common to hear consequence relations described as ‘transitive’, and to see rules imposed to ensure ‘transitivity’ o...
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ژورنال
عنوان ژورنال: Mathematical Modelling
سال: 1987
ISSN: 0270-0255
DOI: 10.1016/0270-0255(87)90560-4