Although the rough set and intuitionistic fuzzy set both capture the same notion, imprecision, studies on the combination of these two theories are rare. Rule extraction is an important task in a type of decision systems where condition attributes are taken as intuitionistic fuzzy values and those of decision attribute are crisp ones. To address this issue, this paper makes a contribution of th...

in this note we first redefine the notion of a fuzzy hypervectorspace (see [1]) and then introduce some further concepts of fuzzy hypervectorspaces, such as fuzzy convex and balance fuzzy subsets in fuzzy hypervectorspaces over valued fields. finally, we briefly discuss on the convex (balanced)hull of a given fuzzy set of a hypervector space.

our aim in this paper is to introduce the notion of fuzzy soft near-subtraction semigroupsand fuzzy soft ideals of near-subtraction semigroups. we discuss some important properties of these new fuzzy algebraic structure and investigate some examples and counter examples.

small polygroups are multi-valued systems that satisfy group-likeaxioms. using the notion of “belonging ($epsilon$)” and “quasi-coincidence (q)” offuzzy points with fuzzy sets, the concept of ($epsilon$, $epsilon$ $vee$ q)-fuzzy subpolygroups isintroduced. the study of ($epsilon$, $epsilon$ $vee$ q)-fuzzy normal subpolygroups of a polygroupare dealt with. characterization and some of the fundam...

generalized geraghty type fuzzy mappings oncomplete metric spaces are introduced and a fixed point theorem thatgeneralizes some recent comparable results for fuzzy mappings incontemporary literature is obtained. example is provided to show thevalidity of obtained results over comparable classical results for fuzzymappings in fixed point theory. as an application, existence of coincidencefuzzy p...

The complexities of modeling uncertain data in economics, engineering, environmental science, sociology, medical science and many other fields can not be successfully dealt with by classical methods. While probability theory, fuzzy set theory,rough set theory, vague set theory and the interval mathematics are useful approaches to describing uncertainty, each of these theories has its inherent d...

Fuzzy logics in Zadeh’s ‘narrow sense’ (Zadeh, 1988), i.e., truth functional logics referring to the real closed unit interval [0,1] as set of truth values, are often motivated as logics for ‘reasoning with imprecise notions and propositions’ (see, e.g., (Hájek, 1998)). However the relation between these logics and theories of vagueness, as discussed in a prolific discourse in analytic philosop...

Considering the increasing interest in fuzzy theory and possible applications, the concept of fuzzy metric space concept has been introduced by several authors from different perspectives. This paper interprets the theory in terms of metrics evaluated on fuzzy numbers and defines a strong Hausdorff topology. We study interrelationships between this theory and other fuzzy theories such as intuit...

in this article we consider the averaging method for differential inclusions with fuzzy right-hand side for the case when the limit of a method of an average does not exist.