A novel concept of quaternionic fuzzy sets (QFSs) is presented in this paper. QFSs are a generalization traditional and complex based on quaternions. The novelty that the range membership function set quaternions with modulus less than or equal to one, which real imaginary parts can be used for four different features. discussion made intuitive interpretation quaternion-valued grades possible a...

Molodtsov introduced the theory of soft sets, which can be used as a general mathematical tool for dealing with uncertainty. This paper aims to introduce the concept of the type-2 fuzzy soft set by integrating the type-2 fuzzy set theory and the soft set theory. Some operations on the type-2 fuzzy soft sets are given. Furthermore, we investigate the decision making based on type-2 fuzzy soft se...

Hierarchical structures and uncertainty measures are two main aspects in granular computing, approximate reasoning and cognitive process. Typical hesitant fuzzy sets, as a prime extension of fuzzy sets, are more flexible to reflect the hesitance and ambiguity in knowledge representation and decision making. In this paper, we mainly investigate the hierarchical structures and uncertainty measure...

Fuzzy decision making is the collection of single or multicriteria techniques aiming at selecting the best alternative in case of imprecise, incomplete, and vague data. This chapter reviews the fuzzy decision making literature and summarizes the review results by tabular and graphical illustrations. The classification is based on the new extensions of fuzzy sets: Intuitionistic, hesitant, and t...

an orthogonal approach to the fuzzification of both multisets and hybridsets is presented. in particular, we introduce $l$-multi-fuzzy and$l$-fuzzy hybrid sets, which are general enough and in spirit with thebasic concepts of fuzzy set theory. in addition, we study the properties ofthese structures. also, the usefulness of these structures is examined inthe framework of mechanical multiset proc...

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, 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 ...