Quotient space theory (QST), a new granule computing tool dealing with imprecise, incomplete and uncertain knowledge, uses a triplet, including the universe, its structure and attributes, to describe a problem space or simply a space. As one of important theories of granular computing (GrC), QST is very helpful to the study of cognitive informatics (CI). This article summarizes the quotient spa...

The present paper studies fuzzy matroids in view of degree. First wegeneralize the notion of $(L,M)$-fuzzy independent structure byintroducing the degree of $M$-fuzzy family of independent $L$-fuzzysets with respect to a mapping from $L^X$ to $M$. Such kind ofdegrees is proved to satisfy some axioms similar to those satisfiedby $(L,M)$-fuzzy independent structure. ...

Abstract An E -fuzzy group is a lattice-valued algebraic structure, defined on a crisp algebra which is not necessarily a group. The crisp equality is replaced by a particular fuzzy one denoted by E . Classical group-like properties are formulated as appropriate fuzzy identities special lattice theoretic formulas. We prove basic features of E -fuzzy groups: properties of the unit and inverses, ...

In this paper we look at two categories, the category F of fuzzy subsets and a quotient category F=M of fuzzy sets. The category F=M is an extension of the category of sets, and the standard constructions in fuzzy set theory arise naturally within this category.

This paper aims to introduce fuzzy congruence relations over Heyting algebras (HA) and give constructions of quotient Heyting algebras induced by fuzzy congruence relations on HA. The Fuzzy First, Second and Third Isomorphism Theorems of HA are established. MSC: 06D20, 06D72, 06D75.

Recommended by Akbar Rhemtulla We introduce the notion of fuzzy ideals in nearrings with respect to a t-norm T and investigate some of their properties. Using T-fuzzy ideals, characterizations of Artinian and Noetherian nearrings are established. Some properties of T-fuzzy ideals of the quotient nearrings are also considered.

In 1965, Zadeh [14] introduced the concept of fuzzy subsets and studied their properties on the parallel lines to set theory. In 1971, Rosenfeld [10] defined the fuzzy subgroup and gave some of its properties. Rosenfeld’s definition of a fuzzy group is a turning point for pure mathematicians. Since then, the study of fuzzy algebraic structure has been pursued in many directions such as groups, ...

In this paper we introduce and analyze the notion of fuzzy hyperideal of a fuzzy hyperring. Then we investigate some properties based on homomorphisms between fuzzy hyperrings. Also, we try to extend the notion of cuts in fuzzy structures for fuzzy hyperrings. We study the quotient structure of a fuzzy hyperring and also we define fuzzy hypercongruences. Then we investigate some connections bet...

Using the notion of fuzzy small submodules of a module, we introduce the concept of fuzzy coessential extension of a fuzzy submodule of a module. We attempt to investigate various properties of fuzzy small submodules of a module. A necessary and sufficient condition for fuzzy small submodules is established. We investigate the nature of fuzzy small submodules of a module under fuzzy direct sum....