Generally, there are two main streams of theories for studying uncertainties. One is probability theory and the other is fuzzy set theory. One of the basic ideas of fuzzy set theory is how to define and interpret membership functions. In this paper, we will study tree-structured data mining model based on a new interpretation of fuzzy theory. In this new theory, fuzzy labels will be used for mo...

This paper generates a variety of general-systems theoretic concepts and a range of systems theories using a minimal set of primitives. The notion of a distinction is taken as primitive and the natural hierarchy of distinctions becomes the primitive structure. A number of system theories are then analysed in terms of these primitives: Zadeh’s fuzzy sets theory; Klir’s epistemological hierarchy ...

By “alternative set theories” we mean systems of set theory differing significantly from the dominant ZF (Zermelo-Frankel set theory) and its close relatives (though we will review these systems in the article). Among the systems we will review are typed theories of sets, Zermelo set theory and its variations, New Foundations and related systems, positive set theories, and constructive set theo...

using the notion of “belongingness ($epsilon$)” and “quasi-coincidence (q)” of fuzzy points with fuzzy sets, we introduce the concept of an ($ alpha, beta$)- fuzzyhv-ideal of an hv-ring, where , are any two of {$epsilon$, q,$epsilon$ $vee$ q, $epsilon$ $wedge$ q} with $ alpha$ $neq$ $epsilon$ $wedge$ q. since the concept of ($epsilon$, $epsilon$ $vee$ q)-fuzzy hv-ideals is an important and ...

module over a ring is a general mathematical concept for many examples of mathematicalobjects that can be added to each other and multiplied by scalar numbers.in this paper, we consider a module over a ring as a universe and by using the notion of reference points, we provide local approximations for  subsets of the universe.