Intuitionistic Fuzzy Modal Operator was defined by Atanassov in cite{at3}in 1999. In 2001, cite{at4}, he introduced the generalization of thesemodal operators. After this study, in 2004, Dencheva cite{dencheva} definedsecond extension of these operators. In 2006, the third extension of thesewas defined in cite{at6} by Atanassov. In 2007,cite{gc1}, the authorintroduced a new operator over Intuit...

In this paper, we characterize the intuitionistic fuzzy δ-continuous, intuitionistic fuzzy weakly δ-continuous, intuitionistic fuzzy almost continuous, and intuitionistic fuzzy almost strongly θ-continuous functions in terms of intuitionistic fuzzy δ-closure and interior or θ-closure and interior.

The purpose of this paper is to introduce the concept of L-fuzzybilinear operators. We obtain a decomposition theorem for L-fuzzy bilinearoperators and then prove that a L-fuzzy bilinear operator is the same as apowerset operator for the variable-basis introduced by S.E.Rodabaugh (1991).Finally we discuss the continuity of L-fuzzy bilinear operators.

in some multi-attribute decision making (madm) problems, various relationships among the decision attributes should be considered. this paper investigates the prioritization relationship of attributes in madm with trapezoidal intuitionistic fuzzy numbers (trifns). trifns are a special intuitionistic fuzzy set on a real number set and have the better capability to model ill-known quantities. fir...

Molodstov introduced soft sets to deal with uncertainties and not clear objects. Researchers developed the relationship between soft sets and information systems. Fuzzification of the notions of soft sets and soft topology have been discussed in the literature. In this paper, we define and establish the topological structures of fuzzy soft semi-open sets and fuzzy soft semi-closed sets. We intr...

We study interior operators from the point of view of fuzzy set theory. The present approach generalizes the particular cases studied previously in the literature in two aspects. First, we use complete residuated lattices as structures of truth values generalizing thus several important cases like the classical Boolean case, (left-)continuous t-norms, MV-algebras, BL-algebras, etc. Second, and ...

This paper consider the   general  forms of $(alpha,beta)$-fuzzyleft ideals (right ideals, bi-ideals, interior ideals) of an orderedsemigroup, where$alpha,betain{in_{gamma},q_{delta},in_{gamma}wedgeq_{delta}, in_{gamma}vee q_{delta}}$ and $alphaneqin_{gamma}wedge q_{delta}$. Special attention is paid to$(in_{gamma},ivq)$-left ideals (right ideals, bi-ideals, interiorideals) and some related  pr...

olds ( α̃, β̃ ) and interval valued fuzzy generalized bi-ideals with thresholds ( α̃, β̃ ) , which are generalization of interval valued fuzzy ideals, interval valued fuzzy interior ideals, interval valued fuzzy quasi ideals and interval valued fuzzy generalized bi-ideals, in a semigroup are introduced, and related properties are investigated. Characterizations of regular semigroups by the properti...

In this paper, by presenting some notions and theorems, we obtaindifferent types of fuzzy topologies. In fact, we obtain someLowen-type  and Chang-type fuzzy topologies on general fuzzyautomata. To this end, first we define a Kuratowski fuzzy interioroperator which induces a  Lowen-type  fuzzy topology on the  set ofstates of a max- min general   fuzzy automaton. Also by  provingsome theorems, ...