and Applied Analysis 3 Definition 1.4 see 18, 20–23 . 1 The intersection of all fuzzy α-closed resp., semiclosed, preclosed, γ-closed, semi-preclosed, β-closed sets containing a fuzzy set A is called a fuzzy α-closure resp., semiclosure, preclosure, γ-closure, semi-preclosure, β-closure of A. 2 The union of all fuzzy α-open resp., semiopen, preopen, γ-open, semi-preopen, β-open sets contained i...

In this paper, we used the supra fuzzy topology which generated from a fuzzy bitopological space [1] to introduce and study the concepts of continuity (resp. openness, closeness) of mapping, separation axioms and compactness for a fuzzy bitopological spaces. Our definition preserve much of the correspondence between concepts of fuzzy bitopological spaces and the associated fuzzy topological spa...

We prove that an hypersemigroup H is regular if and only, for any fuzzy subset f of H, we have f f ◦ 1 ◦ f and it is intra-regular if and only if, for any fuzzy subset f of H, we have f 1 ◦ f ◦ f ◦ 1. An hypersemigroup H is left (resp. right) quasi-regular if and only if, for any fuzzy subset f of S we have f 1 ◦ f ◦ 1 ◦ f (resp. f f ◦ 1 ◦ f ◦ 1) and it is semisimple if and only if, for any fuz...

measured HDRC Lars III C14 luminance output recovered resp. fitted resp. output recovered resp. fitted resp. recovered resp. [cd/m] 10 bit [cd/m] [cd/m] 16 bit [cd/m] [cd/m] [cd/m] 5.3 404 4.78 4.57 200 9.04 8.69 5.38 9.3 424 7.95 8.12 366 9.35 11.52 9.05 70.9 497 46.70 62.65 3,278 62.46 61.33 66.07 741.2 582 403.22 695.22 18,722 643.96 663.00 704.43 8,796 673 8,616.82 8,924.89 32,126 4,196.72 ...

a module m is called epi-retractable if every submodule of m is a homomorphic image of m. dually, a module m is called co-epi-retractable if it contains a copy of each of its factor modules. in special case, a ring r is called co-pli (resp. co-pri) if rr (resp. rr) is co-epi-retractable. it is proved that if r is a left principal right duo ring, then every left ideal of r is an epi-retractable ...

By a theorem of A. Björner [4], for every interval [u, v] in the Bruhat order of a Coxeter group W , there exists a stratified space whose strata are labeled by the elements of [u, v], adjacency is described by the Bruhat order, and each closed stratum (resp., the boundary of each stratum) has the homology of a ball (resp., of a sphere). Answering a question posed in [4], we suggest a natural g...

In rough set theory, the lower and upper approximation operators can be constructed via a variety of approaches. Various generalizations of rough approximation operators have been made over the years. This paper presents a framework for the study of rough sets and rough fuzzy sets on two universes of discourse. By means of a binary relation between two universes of discourse, a class of revised...

Suppose $textbf{M}_{n}$ is the vector space of all $n$-by-$n$ real matrices, and let $mathbb{R}^{n}$ be the set of all $n$-by-$1$ real vectors. A matrix $Rin textbf{M}_{n}$ is said to be $textit{row substochastic}$ if it has nonnegative entries and each row sum is at most $1$. For $x$, $y in mathbb{R}^{n}$, it is said that $x$ is $textit{sut-majorized}$ by $y$ (denoted by $ xprec_{sut} y$) if t...

By normalizing the values of its pixels with respect to the length of the gray scale used, a monochromatic image is interpreted as a fuzzy relation R. We find the GEFS (resp. SEFS) of R, that is the greatest (resp. smallest) eigen fuzzy set with respect to the max-min (resp. min-max) operator. The reconstruction of R is achieved via a genetic algorithm whose initial population of chromosomes is...

The purpose of this note is the study of L-multialgebras and fuzzy congruences of multialgebras. In this regards first the notion of a L-multialgebras are introduced and studied and then the notion of a P -fuzzy relations on multialgebra are given and is applied to introduce the notion of P -fuzzy congruence of multialgebras. Finally, the lattices of P -fuzzy (resp. strong) congruences of multi...