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Covering-based rough fuzzy sets and binary relation
Journal of Intelligent & Fuzzy Systems, 2014Rough set theory is a powerful tool for dealing with uncertainty, granularity, and incompleteness of knowledge in information systems. In this paper we study covering-based rough fuzzy sets in which a fuzzy set can be approximated by the intersection of ...
A. M. Kozae, S. A. El-Sheikh, R. Mareay
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Subgroups of Binary Relations [PDF]
, 1974 A binary relation defined on a set containing n elements can be interpreted as an n × n incidence matrix. Such matrix may be taken either over the two element boolean algebra or over the field Z2 . The main purpose of this paper is to study the incidence subgroups and the collineation subgroups of semigroups of binary relations.
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On the Compatibility of a Ternary Relation with a Binary Fuzzy Relation
Int. J. Uncertain. Fuzziness Knowl. Based Syst., 2019Recently, De Baets et al. have characterized the fuzzy tolerance relations that a given strict order relation is compatible with. In general, the compatibility of a strict order relation with a binary fuzzy relation guarantees also the compatibility of ...
O. Barkat, L. Zedam, B. Baets
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Transformation of binary relations
Proceedings of the Sixth International Conference on Computer Supported Cooperative Work in Design (IEEE Cat. No.01EX472), 2002In the object-oriented paradigm, as complexity rises, the cost of developing and maintaining software systems grows exponentially. This complexity emerges from the continuous evolution of software systems to cope with changing requirements. This crucial problem can be dealt with by performing an active transformation of the elements (i.e.
E. Steegmans, J. Said
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2020
In the first sections of this chapter, we provide well-known fundamentals of linear spaces and topological spaces, binary relations and cones. We add some new results and details that are necessary for the understanding of the following chapters and for the proofs therein. Furthermore, our notation is introduced.
Petra Weidner, Christiane Tammer
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In the first sections of this chapter, we provide well-known fundamentals of linear spaces and topological spaces, binary relations and cones. We add some new results and details that are necessary for the understanding of the following chapters and for the proofs therein. Furthermore, our notation is introduced.
Petra Weidner, Christiane Tammer
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STRUCTURE OF FUZZY BINARY RELATIONS
Fuzzy Sets and Systems, 1981The structure of fuzzy binary relations of indifference and preference is studied. The full description of fuzzy equivalence relations in terms of fuzzy partitions is given. All possible logical relations between various transitivity properties of fuzzy preferences are established.
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1994
Binary relations play a central role in various fields of mathematics. Especially, equivalence relations and different kinds of ordering relations are employed in basic mathematical models. Typical areas are decision making and measurement theory. In addition, applications of binary relations appear naturally in social sciences.
János Fodor, Marc Roubens
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Binary relations play a central role in various fields of mathematics. Especially, equivalence relations and different kinds of ordering relations are employed in basic mathematical models. Typical areas are decision making and measurement theory. In addition, applications of binary relations appear naturally in social sciences.
János Fodor, Marc Roubens
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Fuzzy binary relation based elucidation of air quality over a highly polluted urban region of India
Earth Science Informatics, 2021G. Chattopadhyay +2 more
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Representation of binary systems by families of binary relations
Israel Journal of Mathematics, 1969It is proved that an arbitrary binary multiplicative system can be represented by a family of binary relations, using the so called generalized multiplication of relations. Transformations of such representations and existence of a ‘universal’ representation are studied.
D. Tamari +3 more
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2002
This chapter is devoted to binary fuzzy relations. For quite a variety of problems, binary relations turn out to be a simple but very powerful tool. Recall that a binary L-relation between (nonempty) sets X and Y is any mapping R: X × Y → L (L is the support set of the complete residuated lattice L; for x ∈ X and y ∈ Y, R(x,y) ∈ L is the truth degree ...
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This chapter is devoted to binary fuzzy relations. For quite a variety of problems, binary relations turn out to be a simple but very powerful tool. Recall that a binary L-relation between (nonempty) sets X and Y is any mapping R: X × Y → L (L is the support set of the complete residuated lattice L; for x ∈ X and y ∈ Y, R(x,y) ∈ L is the truth degree ...
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