7,584 research outputs found
Aggregating fuzzy subgroups and T-vague groups
Fuzzy subgroups and T-vague groups are interesting fuzzy algebraic structures that have been widely studied. While fuzzy subgroups fuzzify the concept of crisp subgroup, T-vague groups can be identified with quotient groups of a group by a normal fuzzy subgroup and there is a close relation between both structures and T-indistinguishability operators (fuzzy equivalence relations).
In this paper the functions that aggregate fuzzy subgroups and T-vague groups will be studied. The functions aggregating T-indistinguishability operators have been characterized [9] and the main result of this paper is that the functions aggregating T-indistinguishability operators coincide with the ones that aggregate fuzzy subgroups and T-vague groups. In particular, quasi-arithmetic means and some OWA operators aggregate them if the t-norm is continuous Archimedean.Peer ReviewedPostprint (author's final draft
Solvable groups derived from fuzzy hypergroups
In this paper we introduce the smallest equivalence relation ξ ∗ on a finite fuzzy hypergroup S such that the quotient group S/ξ ∗ , the set of all equivalence classes, is a solvable group. The characterization of solvable groups via strongly regular relation is investigated and several results on the topic are presented
On the Geometry and Homology of Certain Simple Stratified Varieties
We study certain mild degenerations of algebraic varieties which appear in
the analysis of a large class of supersymmetric theories, including superstring
theory. We analyze Witten's sigma-model and find that the non-transversality of
the superpotential induces a singularization and stratification of the ground
state variety. This stratified variety (the union of the singular ground state
variety and its exo-curve strata) admit homology groups which, excepting the
middle dimension, satisfy the "Kahler package" of requirements, extend the
"flopped" pair of small resolutions to an "(exo)flopped" triple, and is
compatible with mirror symmetry and string theory. Finally, we revisit the
conifold transition as it applies to our formalism.Comment: LaTeX 2e, 18 pages, 4 figure
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