By Fuzzy theory we mean Zadeh’s mathematical theory of generalized sets and their associated logics. At this state of the art, fuzzy theory has provided significant contributions to artificial intelligence via a broader umbrella of soft computing. Like other theories of mathematics, such as number theory and potential theory, fuzzy theory has its own agenda, concepts, and techniques. However, j...

To measure the fuzziness of fuzzy sets, this paper introduces a distance-based and a fuzzy entropybased measurements. Then these measurements are generalized to measure the fuzziness of fuzzy partition, namely partition fuzziness. According to the relationship between the validity of fuzzy partition and its partition fuzziness, a family of cluster validity functions is proposed based on the mod...

Triangular intuitionistic fuzzy number (TIFN) is a more generalized platform for expressing imprecise, incomplete, and inconsistent information when solving multi-criteria decision-making problems, as well as for expressing and reflecting the evaluation information in several dimensions. In this paper, the TIFN has been applied for solving multi-criteria decision-making (MCDM) problems, first, ...

In 1970, Levine 1 introduced the notion of generalized closed sets in topological spaces as a generalization of closed sets. Since then, many concepts related to generalized closed sets were defined and investigated. In 1997, Balasubramanian and Sundaram 2 introduced the concepts of generalized closed sets in fuzzy setting. Also, they studied various generalizations fuzzy continues mappings. Re...

in this paper, a concept of generalized weakly contraction mappings in partially ordered fuzzy metric spaces is introduced and  coincidence point  theorems on partially ordered fuzzy metric spaces are proved. also, as the corollary of these theorems, some common fixed point theorems on partially ordered fuzzy metric spaces are presented.

in this paper we have generalized the concepts of ,q-fuzzy ideals, ,q-fuzzy quasi-ideals and,q-fuzzy bi-ideals by introducing the concepts of   k ,q -fuzzy ideals,   k ,q -fuzzy quasiideals and   k ,q -fuzzy bi-ideals in ternary semigroups and several related properties are investigated. different characterizations of regular and weakly regular ternary semigroups b...

-In the field of engineering and economic studies, mathematical manipulation of fuzzy numbers is cumbersome and does not provide a neatly ordered set of results in the same way that crisp numbers do. Moreover, the generalized fuzzy number (i.e. non-normalized and normalized fuzzy number) have been approved more flexible and more intelligent than the normalized fuzzy number since it takes the de...

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...

Abstract In this paper, we have introduced anti fuzzy quasi-ideals, anti fuzzy bi-(generalized bi-) ideals and anti fuzzy left (right, two-sided) ideals in LA-semigroup. Further we have characterized an intra-regular LA-semigroup by the properties of their anti fuzzy left (right, two-sided) ideals, anti fuzzy bi(generalized bi-)ideals, anti fuzzy interior ideals and anti fuzzy quasi-ideals. Fur...

The aim of this paper is to introduce the concept of Λ operator of a fuzzy set in a fuzzy bitopological space.Then we study (i, j)-fuzzy Λγ -set and its properties. Moreover, we define (i, j)-fuzzy Λ-closed set, (i, j)-fuzzy Λγ -closed set and (i, j)-fuzzy generalized closed set in fuzzy bitopological space. The concepts of (i, j)-fuzzy Λ-closed set and (i, j)-fuzzy generalized closed set are i...