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On Convexity of Fuzzy Sets and Fuzzy Relations
Information Sciences, 1992A fuzzy set \(A\) on the vector space \(X\) (i.e. \(A\) is a mapping from \(X\) to the unit interval) is called convex if all \(\alpha\)-cuts of \(A\) are convex. The question that paper deals with is: For which operations applied to convex fuzzy sets or convex fuzzy relations is the resulting fuzzy set or relation again convex?
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IEEE Transactions on Systems, Man and Cybernetics, Part B (Cybernetics), 1999
This study concentrates on fuzzy relational calculus regarded as a basis of data compression. In this setting, images are represented as fuzzy relations. We investigate fuzzy relational equations as a basis of image compression. It is shown that both compression and decompression (reconstruction) phases are closely linked with the way in which fuzzy ...
Kaoru Hirota, Witold Pedrycz
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This study concentrates on fuzzy relational calculus regarded as a basis of data compression. In this setting, images are represented as fuzzy relations. We investigate fuzzy relational equations as a basis of image compression. It is shown that both compression and decompression (reconstruction) phases are closely linked with the way in which fuzzy ...
Kaoru Hirota, Witold Pedrycz
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Fuzzy Sets and Systems, 2013
In this paper, first we give the definitions of various indicators of fuzzy relations and their basic properties. Then we investigate the relationships between these indicators, particularly between those of T-transitivity, negative S-transitivity, T-S-semitransitivity and T-S-Ferrers property.
Xuzhu Wang +3 more
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In this paper, first we give the definitions of various indicators of fuzzy relations and their basic properties. Then we investigate the relationships between these indicators, particularly between those of T-transitivity, negative S-transitivity, T-S-semitransitivity and T-S-Ferrers property.
Xuzhu Wang +3 more
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Information Sciences, 2010
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Humberto Bustince Sola +5 more
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Humberto Bustince Sola +5 more
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On fuzzy difunctional relations
Information Sciences, 1996zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Habib Ounalli, Ali Jaoua
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New Mathematics and Natural Computation, 2018
Fuzzy relations are fundamental in applications of fuzzy set theory and fuzzy logic. The entire literature on fuzzy relations as applied to fuzzy graph theory are based on Rosenfeld’s relations. Rosenfeld used minimum and maximum as the norm and conorm in his study of compositions of fuzzy relations.
John N. Mordeson +2 more
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Fuzzy relations are fundamental in applications of fuzzy set theory and fuzzy logic. The entire literature on fuzzy relations as applied to fuzzy graph theory are based on Rosenfeld’s relations. Rosenfeld used minimum and maximum as the norm and conorm in his study of compositions of fuzzy relations.
John N. Mordeson +2 more
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Proceedings of the 35th Annual Southeast Regional Conference on - ACM-SE 35, 1997
We present a fuzzy version of the crisp spatial logic developed by Randell et al., which takes the single relation connected-with as primitive. Membership functions are defined for each spatial relation defined in the crisp theory. Furthermore, principles are presented for defining linguistic variables whose linguistic values are spatial relations. The
Albert C. Esterline +2 more
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We present a fuzzy version of the crisp spatial logic developed by Randell et al., which takes the single relation connected-with as primitive. Membership functions are defined for each spatial relation defined in the crisp theory. Furthermore, principles are presented for defining linguistic variables whose linguistic values are spatial relations. The
Albert C. Esterline +2 more
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Fuzzy relational algebra for possibility-distribution-fuzzy-relational model of fuzzy data
Journal of Intelligent Information Systems, 1994In the real world, there exist a lot of fuzzy data which cannot or need not be precisely defined. We distinguish two types of fuzziness: one in an attribute value itself and the other in an association of them. For such fuzzy data, we propose a possibility-distribution-fuzzy-relational model, in which fuzzy data are represented by fuzzy relations whose
Motohide Umano, Satoru Fukami
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Fuzzy Relation Equations with Fuzzy Quantifiers
2017In this paper, we follow the previous works on fuzzy relation compositions based on fuzzy quantifiers and we introduce systems of fuzzy relation equations stemming from compositions based on fuzzy quantifiers. We address the question, whether such systems under some specific conditions may become solvable, and we provide a positive answer. Based on the
Nhung Cao, Martin Stepnicka
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Fuzzy congruence relation generated by a fuzzy relation in vector spaces
Journal of Intelligent & Fuzzy Systems, 2018In this paper, we introduce the concepts of fuzzy congruence relation and fuzzy coset relation on vector spaces and find some their properties. We define some operations on fuzzy coset relations and show that the set of all fuzzy coset relations on a vector space is a vector space, too.
S. Khosravi Shoar +2 more
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