Journal ArticleDOI
Reduction of fuzzy strict order relations
Mihir K. Chakraborty,Mili Das +1 more
TLDR
Fuzzy strict order relations and the notion of their reduction are defined and a necessary and sufficient condition is obtained for the transitive closure of the reduction to coincide with the strict order itself.About:
This article is published in Fuzzy Sets and Systems.The article was published on 1985-02-01. It has received 13 citations till now. The article focuses on the topics: Transitive closure & Fuzzy number.read more
Citations
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Book ChapterDOI
Fuzzy Sets: History and Basic Notions
TL;DR: This Chapter also contains a discussion on operational semantics of the generally too abstract notion of membership function and a survey of variants of fuzzy sets and related matters.
Journal ArticleDOI
Fuzzy sets and sheaves. Part II
TL;DR: It is shown that large parts of fuzzy set theory are actually subfields of sheaf theory, resp.
Journal ArticleDOI
Fuzzy congruences on semigroups
TL;DR: The lattice of fuzzy equivalence (congruence) relations on a semigroup gives certain lattice theoretic properties and the fuzzy congruence relation generated by a given fuzzy relation on aSemigroup is studied.
Journal ArticleDOI
Fuzzy sets and sheaves. Part II:: Sheaf-theoretic foundations of fuzzy set theory with applications to algebra and topology
TL;DR: It is shown that large parts of fuzzy set theory are actually subfields of sheaf theory, resp.
Journal ArticleDOI
Aggregation of preferences: the fuzzy case
TL;DR: A fuzzy behavior of preference is defined which allows us to build up two determinant fuzzy coalitions which will be the base of the planner's requirement and the link between pessimistic results and optimistic ones, and May's theorem of majority choice is defined.
References
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Journal ArticleDOI
Similarity relations and fuzzy orderings
TL;DR: An extended version of Szpilrajn's theorem is proved and various properties of similarity relations and fuzzy orderings are investigated and, as an illustration, a fuzzy preordering is investigated which is reflexive and antisymmetric.
Journal ArticleDOI
Structure of fuzzy binary relations
TL;DR: The structure of fuzzy binary relations of indifference and preference is studied and the general notion of a relative ‘degree of fuzziness’ is defined in connection with a study of the quantitative description of preservation properties under fuzzy mappings.
Journal ArticleDOI
On fuzzy equivalence I
Mihir K. Chakraborty,Mili Das +1 more
TL;DR: F fuzzy reflexive, symmetric and transitive relations on fuzzy subsets are studied and the possible fuzzy partitioning of a fuzzy subset is investigated.
Journal ArticleDOI
Studies in fuzzy relations over fuzzy subsets
Mihir K. Chakraborty,Mili Das +1 more
TL;DR: In this paper a generalisation of fuzzy relations is introduced - fuzzy relations are defined on fuzzy subsets and properties like ordered reflexivity, symmetry, transitity, transitive closures of such generalised relations and operations on them are discussed.