First, we introduce the concept of intuitionistic fuzzy group congruenceand we obtain the characterizations of intuitionistic fuzzy group congruenceson an inverse semigroup and a T^{*}-pure semigroup, respectively. Also,we study some properties of intuitionistic fuzzy group congruence. Next, weintroduce the notion of intuitionistic fuzzy semilattice congruence and we givethe characterization of...

In this paper, the concept of intuitionistic fuzzy congruence relation on a residuated lattice is introduced and its properties is studied. The relationship between intuitionistic fuzzy filters and intuitionistic fuzzy congruence relations on a residuated lattice is obtain. Then the intuitionistic fuzzy congruence relation corresponding to a given intuitionistic fuzzy filter on residuated latti...

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...

On the basis of the concept of the interval valued intuitionistic fuzzy sets introduced by K. Atanassov, the notion of interval valued intuitionistic fuzzy subsemimodule of a semimodule with respect to t-norm T and s-norm S is given and the characteristic properties are described. The homomorphic image and inverse image are investigated. In particular, by the help of the congruence relations on...

In this paper, the notion of an interval valued intuitionistic fuzzy subsemiring (ideal) of a semiring with respect to t−norm T and s−norm S is given and the characteristic properties are described. The homomorphic image and inverse image are investigated. In particular, by the help of the congruence relations on semirings, new interval valued intuitionistic (S, T )−fuzzy subsemirings (ideals) ...

On the basis of the concept of interval valued intuitionistic fuzzy set introduced by K. Atanassov [3], the notion of interval valued intuitionistic fuzzy subsemigroup (ideal, bi-ideal, (1, 2)-ideal) of a semigroup with respect to t-norm T and s-norm S is given and the characteristic properties are described. The homomorphic image and inverse image are investigated. In particular, by the help o...

in this paper, we propose a new definition of intuitionistic fuzzyquasi-metric and pseudo-metric spaces based on intuitionistic fuzzy points. weprove some properties of intuitionistic fuzzy quasi- metric and pseudo-metricspaces, and show that every intuitionistic fuzzy pseudo-metric space is intuitionisticfuzzy regular and intuitionistic fuzzy completely normal and henceintuitionistic fuzzy nor...

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...

in this note we consider the notion of intuitionistic fuzzy (weak) dual hyper k-ideals and obtain related results. then we classify this notion according to level sets. after that we determine the relationships between intuitionistic fuzzy (weak) dual hyper k-ideals and intuitionistic fuzzy (weak) hyper k-ideals. finally, we define the notion of the product of two intuitionistic fuzzy (weak) du...

The concept of abstract algebra on intuitionistic fuzzy sets were introduced and some basic theorems proved by authors in 2017. In this study, homomorphism between algebras is defined, function examined then congruence relations are defined algebra. First third isomorphism introduced.