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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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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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Binary relations and hypergroupoids
2000The author associates a partial hyperoperation \(\langle\widetilde\circ_R\rangle\) to every binary relation \(R\) defined on a non-empty set \(H\) in the following way: \(x\widetilde\circ_R y=\{z\in H\mid xRz,\;zRy\}\). The hyperstructure \(\langle H,\widetilde\circ_R\rangle\) is a partial hypergroupoid and the necessary and sufficient condition so ...
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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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The Evolution of Compact Binary Star Systems
Living Reviews in Relativity, 2014Konstantin A Postnov
exaly