in this paper we define intuitionistic fuzzy metric and normedspaces. we first consider finite dimensional intuitionistic fuzzy normed spacesand prove several theorems about completeness, compactness and weak convergencein these spaces. in section 3 we define the intuitionistic fuzzy quotientnorm and study completeness and review some fundamental theorems. finally,we consider some properties of...

The aim of this paper is to introduce the notion of anti fuzzy (prime) deductive system in BL-algebra and to investigate their properties. It is shown that the set of all deductive systems (with the empty set) of a BL-algebra X is equipotent to a quotient of the set of all anti fuzzy deductive systems of X. The anti fuzzy prime deductive system theorem of BL-algebras is also proved. Anti Fuzzy ...

Park et al. (2011) introduced the concept of generalized intuitionistic fuzzy soft sets, which can be seen as an effective mathematical tool to deal with uncertainties. In this paper, the concept of generalized intuitionistic fuzzy soft equality is introduced and some related properties are derived. It is proved that generalized intuitionistic fuzzy soft equality is congruence relation with res...

Let R be a commutative ring with non-zero identity and let M be a non-zero unitary R-module. The concept of fuzzy coprimary submodule as a dual notion of fuzzy primary one will be introduced and some of its properties will be studied. Among other things, the behavior of this concept with respect to fuzzy localization formation and fuzzy quotient will be examined.

The quotient space theory based on fuzzy tolerance relation is put forward to solve the problem of clustering in this paper. The similarity matrix does not always satisfy ultrametric inequality, theoretically and practically. We give the method to construct the hierarchical quotient space chain if the similarity matrix is only reflexive and symmetric. We consider not only the subset of data (cl...

By means of a kind of new idea, we consider  the $(in,ivq)$-fuzzy$h$-ideals of a hemiring.  First, the concepts of $(in,ivq)$-fuzzyleft(right) $h$-ideals of a hemiring are provided and some relatedproperties are investigated. Then, a kind  of quotient hemiring  ofa hemiring by an $(in,ivq)$-fuzzy $h$-ideal is presented andstudied. Moreover, the notions of generalized $varphi$-compatible$(in,ivq...

This  paper extends the notion of fuzzy $BCK$-subalgebras to fuzzy hyper $BCK$-subalgebras and defines an extended fuzzy $BCK$-subalgebras. This study  considers  a type of fuzzy hyper  $BCK$-ideals  in this  hyperstructure  and  describes   the  relationship  between hyper  $BCK$-ideals and  fuzzy hyper  $BCK$-ideals.  In fact, it tries to introduce   a  strongly  regular  relation  on hyper $...