fuzzy relation inequalities based on max-f composition are discussed, where f is a binary aggregation on [0,1]. for a fixed fuzzy relation inequalities system $ a circ^{f}textbf{x}leqtextbf{b}$, we characterize all matrices $ a^{'} $ for which the solution set of the system $ a^{' } circ^{f}textbf{x}leqtextbf{b}$ is the same as the original solution set. similarly, for a fixed matrix ...

in this paper, we study an equivalence relation on the set of fuzzysubgroups of an arbitrary group g and give four equivalent conditions each ofwhich characterizes this relation. we demonstrate that with this equivalencerelation each equivalence class constitutes a lattice under the ordering of fuzzy setinclusion. moreover, we study the behavior of these equivalence classes under theaction of a...

For any channel $P_{Y|X}$ the strong data processing constant is defined as smallest number notation="LaTeX">$\eta _{KL}\in [{0,1}]$ such that notation="LaTeX">$I(U;Y)\le \eta _{KL} I(U;X)$ holds for Markov chain notation="LaTeX">$U-X-Y$ . It shown value of _{KL}$ given by best binary-input subc...

An algorithm for information organization based on rectangular decomposition of a binary relation is introduced, Rectangular decomposition allows a classification of databases presented as a binary relation. This problem, being NP-Complete problem, has been the subject of several previous works. However, we found out necessary the proposition of an approximate polynomial algorithm and to give a...

Bulatov (2008) gave a dichotomy for the counting constraint satisfaction problem #CSP. A problem from #CSP is characterised by a constraint language Γ, a fixed, finite set of relations over a finite domain D. An instance of the problem uses these relations to constrain an arbitrarily large finite set of variables. Bulatov showed that the problem of counting the satisfying assignments of instanc...