Interval valued intuitionistic (S,T)(S,T)-fuzzy HvH_v-submodules

On the basis of the concept of the interval valued intuitionistic fuzzy sets introduced by K.Atanassov, the notion of interval valued intuitionistic fuzzy $H_v$-submodules of an $H_v$-module with respect to $t$-norm $T$ and $s$-norm $S$ is given and the characteristic properties are described. The homomorphic image and the inverse image are investigated.In particular, the connections between interval valued intuitionistic $(S,T)$-fuzzy $H_v$-submodules and interval valued intuitionistic $(S,T)$-fuzzy submodules are discussed

Interval Valued intuitionistic Fuzzy Homomorphism of BF-algebras

The notion of interval-valued intuitionistic fuzzy sets was first introduced by Atanassov and Gargov as a generalization of both interval-valued fuzzy sets and intuitionistic fuzzy sets. Satyanarayana et. al., applied the concept of interval-valued intuitionistic fuzzy ideals to BF-algebras. In this paper, we introduce the notion of interval-valued intuitionistic fuzzy homomorphism of BF-algebras and investigate some interesting properties. Keywords: BF-algebras, interval valued intuitionistic fuzzy sets, i-v intuitionistic fuzzy ideals

(T, S) vague congruence and . . .

The aim of this paper is to further develop the concept of (T, S) vague equivalence relation. We discuss some characterization of vague equivalence and vague congruence relations in terms of their level set and prove that the class of vague congruence relations forms a distributive lattice. Further, we define the quotient of a vague lattice with respect to a congruence relation

Atanassov’s intuitionistic fuzzy translations of intuitionistic fuzzy subalgebras in BG-algebras

In this paper, the concepts of intuitionistic fuzzy translation to intuitionistic fuzzy subalgebras in BG-algebras are introduced. The notion of intuitionistic fuzzy extensions and intuitionistic fuzzy multiplications of intuitionistic fuzzy subalgebras are introduced and several related properties are investigated. In this paper, the relationships between intuitionistic fuzzy translations and intuitionistic fuzzy extensions of intuitionistic fuzzy subalgebras are investigated.Publisher's Versio

Fully Invariant and Characteristic Interval-Valued Intuitionistic Fuzzy Dual Ideals of BF-algebras

The notion of interval-valued intuitionistic fuzzy sets was first introduced by Atanassov and Gargov as a generalization of both interval-valued fuzzy sets and intuitionistic fuzzy sets. Satyanarayana et. al., applied the concept of interval-valued intuitionistic fuzzy ideals and interval-valued intuitionistic fuzzy dual ideals to BF-algebras. In this paper, we introduce the notion of fully invariant and characteristic interval-valued intuitionistic fuzzy dual ideals of BF-algebras and investigate some of its properties

Implication functions in interval-valued fuzzy set theory

Interval-valued fuzzy set theory is an extension of fuzzy set theory in which the real, but unknown, membership degree is approximated by a closed interval of possible membership degrees. Since implications on the unit interval play an important role in fuzzy set theory, several authors have extended this notion to interval-valued fuzzy set theory. This chapter gives an overview of the results pertaining to implications in interval-valued fuzzy set theory. In particular, we describe several possibilities to represent such implications using implications on the unit interval, we give a characterization of the implications in interval-valued fuzzy set theory which satisfy the Smets-Magrez axioms, we discuss the solutions of a particular distributivity equation involving strict t-norms, we extend monoidal logic to the interval-valued fuzzy case and we give a soundness and completeness theorem which is similar to the one existing for monoidal logic, and finally we discuss some other constructions of implications in interval-valued fuzzy set theory

Tripolar fuzzy sub implicative ideals of KU-Algebras

The concept Tripolar fuzzy set is a generalization of bipolar fuzzy set, intuitionistic fuzzy set and fuzzy set. In this paper, the concept Tripolar fuzzy sub implicative ideals of KU-algebras are introduced and several properties are investigated. Also, the relations between Tripolar fuzzy sub implicative ideals and Tripolar fuzzy ideals are given. The image and the preimage of Tripolar fuzzy sub implicative ideals under homomorphism of KU-algebras are defined and how the image and the preimage of Tripolar fuzzy sub implicative ideals under homomorphism of KU-algebras become Tripolar fuzzy sub implicative ideals are studied. Moreover, the Cartesian product of Tripolar fuzzy sub implicative ideals in Cartesian product KU-algebras is established

Intuitionistic Fuzzy Dot BCK/BCI - Algebras

In this paper we apply the concept of intuitionistic fuzzy set to dot BCK-sub algebra. The notion of an intuitionistic fuzzy dot BCK-sub algebra is introduced and some interesting properties are investigated. Then we study the homomorphism between intuitionistic fuzzy dot BCK- subalgebras