In recent times, intuitionistic fuzzy sets introduced by Atanassov has been one of the most powerful and flexible approaches for dealing with complex and uncertain situations of real world. In particular, the concept of divergence between intuitionistic fuzzy sets is important since it has applications in various areas such as image segmentation, decision making, medical diagnosis, pattern reco...

The theory of neighborhood systems is abstracted from the geometric notion of "near" or "negligible distances." It is a "new" theory of the classical concept of neighborhood systems within the context of advanced computing. By definition neighborhood systems include both rough sets and topological spaces as special cases. The deeper and more interesting part is in its interactions with fuzzy se...

in this paper, we introduce and study the concept of $r$-fuzzy regular semi open (closed) sets in smooth topological spaces. by using $r$-fuzzy regular semi open (closed) sets, we define a new fuzzy closure operator namely $r$-fuzzy regular semi interior (closure) operator. also, we introduce fuzzy regular semi continuous and fuzzy regular semi irresolute mappings. moreover, we investigate the ...

In this study, we first introduce the fuzzy sets, soft sets, fuzzy soft sets and their related properties. We then present the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) that is one of classical Multiple Attribute Decision Making (MADM) methods. We also present the Grey Relation Method. In the main part of this study, we extend the TOPSIS method on the fuzzy soft se...

This paper presents a novel adaptive neuro-fuzzy inference system based on interval Gaussian type-2 fuzzy sets in the antecedent part and Gaussian type-1 fuzzy sets as coefficients of linear combination of input variables in the consequent part. The capability of the proposed ANFIS2 for function approximation and dynamical system identification is remarkable. The structure of ANFIS2 is very sim...

An adaptive neuro fuzzy inference system based on interval Gaussian type-2 fuzzy sets in the antecedent part and Gaussian type-1 fuzzy sets as coefficients of linear combination of input variables in the consequent part is presented in this paper. The capability of the proposed method (we named ANFIS2) for function approximation and dynamical system identification is remarkable. The structure o...

In this paper, countable compactness and the Lindel¨of propertyare defined for L-fuzzy sets, where L is a complete de Morgan algebra. Theydon’t rely on the structure of the basis lattice L and no distributivity is requiredin L. A fuzzy compact L-set is countably compact and has the Lindel¨ofproperty. An L-set having the Lindel¨of property is countably compact if andonly if it is fuzzy compact. ...

This work is towards the study of the relationship between fuzzy preordered sets and Alexandrov (left/right) fuzzy topologies based on generalized residuated lattices here the fuzzy sets are equipped with generalized residuated lattice in which the commutative property doesn't hold. Further, the obtained results are used in the study of fuzzy automata theory.

In this paper, the notion of generalized regular fuzzy irresolute, generalized regular fuzzy irresolute open  and generalized regular fuzzy irresolute closed maps in fuzzy  topological spaces are introduced and studied. Moreover, some separation axioms and $r$-GRF-separated sets are established. Also, the relations between generalized regular fuzzy continuous maps and generalized regular fuzzy ...