We introduce the concepts of interval-valued fuzzy mα-open sets and interval-valued fuzzy mα-continuous mappings. And we study some characterizations and properties of such concepts.

In this paper, we introduce the notions of fuzzy γ-I-open sets and fuzzy γ-I-continuous functions to obtain a decomposition of fuzzy semi-I-continuity. We also investigated the fundamental properties of such functions.

We discuss fuzzy simplicial sets, and their relationship to something like metric spaces. Namely, we present an adjunction between the categories: a metric realization functor and fuzzy singular complex functor. The following document is a rough draft and may have (substantial) errors. 1. Fuzzy simplicial sets Let I denote the Grothendieck site whose objects are initial open intervals contained...

In many scientific and engineering applications, the fuzzy set concept plays an important role. The fuzziness appears when we need to perform, on manifold, calculations with imprecision variables. The fuzzy set theory was introduced initially by Zadeh [1] in 1965. In the theory and applications of fuzzy sets, convexity is a most useful concept. In fact, in the basic and classical paper [1], Zad...

in this paper, rstly we have introduced to entropy of sequences of fuzzy sets and given sometheorems about it. secondly, the waves p and t which appears in electrocardiograms weretransferred to fuzzy sets, by using denition of entropy for sequences of fuzzy sets, and somenumerical values were obtained for sequences of waves p and t. thus any person can makea medical predictions for some cardiac...

This paper introduces a new approach to topology, based on category theory and universal algebra, and called categorically-algebraic (catalg) topology. It incorporates the most important settings of lattice-valued topology, including poslat topology of S.~E.~Rodabaugh, $(L,M)$-fuzzy topology of T.~Kubiak and A.~v{S}ostak, and $M$-fuzzy topology on $L$-fuzzy sets of C.~Guido. Moreover, its respe...

In last years, a variety of papers on fuzzy sets and other fuzzy topics was concerned with set-algebraic operations for and properties of fuzzy sets. However, only few remarks are devoted to fuzzy cardinals. In classical set theory the cardinality of a set is a measure of its size or "power". In the fuzzy case one has to differentiate: there are measures of fuzziness and measures of power. Here...

Consider sets X and Y each with associated membership functions. Further suppose that there is a map f : X → Y . A membership may be induced onY from the membership ofX calculated using the extension principle, and the two memberships on Y may be combined to give an overall membership. The point with the highest membership in X can be determined directly or by back mapping the value with the hi...

Using mid-infrared and radio criteria, we select a sample of candidate z ∼ 2 obscured quasars. Optical spectroscopy confirms about half of these as type-2 quasars, and modelling the population suggests 50-80% of the quasars are obscured. We find some flat radio spectrum type-2 quasars, and tentative evidence for obscuration unrelated to the torus. Using a similar sample, we also find evidence f...