189,818 research outputs found
Left and right compatibility of strict orders with fuzzy tolerance and fuzzy equivalence relations
The notion of extensionality of a fuzzy relation w.r.t. a fuzzy equivalence was first introduced by Hohle and Blanchard. Belohlavek introduced a similar definition of compatibility of a fuzzy relation w.r.t. a fuzzy equality. In [14] we generalized this notion to left compatibility, right compatibility and compatibility of arbitrary fuzzy relations and we characterized them in terms of left and right traces introduced by Fodor. In this note, we will again investigate these notions, but this time we focus on the compatibility of strict orders with fuzzy tolerance and fuzzy equivalence relations
Fuzzy Cores and Fuzzy Balancedness
We study the relation between the fuzzy core and balancedness for fuzzy games. For regular games, this relation has been studied by Bondareva (1963) and Shapley (1967). First, we gain insight in this relation when we analyse situations where the fuzzy game is continuous. Our main result shows that any fuzzy game has a non-empty core if and only if it satisfies all (fuzzy) balanced inequalities. We also consider deposit games to illustrate the use of the main result.Cooperative fuzzy games;fuzzy balancedness;fuzzy core
Hopf Maps, Lowest Landau Level, and Fuzzy Spheres
This paper is a review of monopoles, lowest Landau level, fuzzy spheres, and
their mutual relations. The Hopf maps of division algebras provide a prototype
relation between monopoles and fuzzy spheres. Generalization of complex numbers
to Clifford algebra is exactly analogous to generalization of fuzzy two-spheres
to higher dimensional fuzzy spheres. Higher dimensional fuzzy spheres have an
interesting hierarchical structure made of "compounds" of lower dimensional
spheres. We give a physical interpretation for such particular structure of
fuzzy spheres by utilizing Landau models in generic even dimensions. With
Grassmann algebra, we also introduce a graded version of the Hopf map, and
discuss its relation to fuzzy supersphere in context of supersymmetric Landau
model.Comment: v2: note and references added; v3: references adde
Homomorphisms between fuzzy information systems revisited
Recently, Wang et al. discussed the properties of fuzzy information systems
under homomorphisms in the paper [C. Wang, D. Chen, L. Zhu, Homomorphisms
between fuzzy information systems, Applied Mathematics Letters 22 (2009)
1045-1050], where homomorphisms are based upon the concepts of consistent
functions and fuzzy relation mappings. In this paper, we classify consistent
functions as predecessor-consistent and successor-consistent, and then proceed
to present more properties of consistent functions. In addition, we improve
some characterizations of fuzzy relation mappings provided by Wang et al.Comment: 10 page
On the priority vector associated with a fuzzy preference relation and a multiplicative preference relation.
We propose two straightforward methods for deriving the priority vector associated with a fuzzy preference relation. Then, using transformations between multiplicative preference relations and fuzzy preference relations, we study the relationships between the priority vectors associated with these two types of preference relations.pairwise comparison matrix; fuzzy preference relation; priority vector
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