In this paper, the problem of measuring the degree of inclusion and similarity measure for two   interval-valued intuitionistic  fuzzy sets is considered. We propose inclusion and similarity measure by using  order on interval-valued intuitionistic fuzzy sets connected with lexicographical order. Moreover, some properties of inclusion and similarity measure and some correlation, between them an...

Interval-valued intuitionistic fuzzy sets (IVIFSs), a generalization of fuzzy sets, is characterized by an interval-valued membership function, an interval-valued non-membership function.The objective of this paper is to deal with criteria aggregation problems using IVIFSs where there exists a prioritization relationship over the criteria.Based on the ${L}$ukasiewicz triangular norm, we first p...

Interval-valued intuitionistic fuzzy sets (IVIFSs) are widely used to handle uncertainty and imprecision in decision making. However, in more complicated environment, it is difficult to express the uncertain information by an IVIFS with considering the decision-making preference. Hence, this paper proposes a group generalized interval-valued intuitionistic fuzzy soft set (G-GIVIFSS) which conta...

The relationship between the intuitionistic fuzzy sets and the algebraic hyperstructures is described in this paper. The concept of the quasi-coincidence of an intuitionistic fuzzy interval valued with an interval-valued intuitionistic fuzzy set is introduced and this is a natural generalization of the quasi-coincidence of an intuitionistic fuzzy point in intuitionistic fuzzy sets. By using thi...

it is firstly proved that the multi-input-single-output (miso) fuzzy systems based on interval-valued $r$- and $s$-implications can approximate any continuous function defined on a compact set to arbitrary accuracy.  a formula to compute the lower upper bounds on the number  of interval-valued fuzzy sets needed to achieve a pre-specified approximation  accuracy for an arbitrary multivariate con...

in this paper, the notions of $(t,s)$-composition matrix and$(t,s)$-interval-valued intuitionistic fuzzy equivalence matrix areintroduced where $(t,s)$ is a dual pair of triangular module. theyare the generalization of composition matrix and interval-valuedintuitionistic fuzzy equivalence matrix. furthermore, theirproperties and characterizations are presented. then a new methodbased on $tilde{...

interval-valued intuitionistic fuzzy sets (ivifss) are widely used to handle uncertainty and imprecision in decision making. however, in more complicated environment, it is difficult to express the uncertain information by an ivifs with considering the decision-making preference. hence, this paper proposes a group generalized interval-valued intuitionistic fuzzy soft set (g-givifss) which conta...

In this work, we shall present some novel process to measure the similarity between picture fuzzy sets. Firstly, we adopt the concept of intuitionistic fuzzy sets, interval-valued intuitionistic fuzzy sets and picture fuzzy sets. Secondly, we develop some similarity measures between picture fuzzy sets, such as, cosine similarity measure, weighted cosine similarity measure, set-theoretic similar...

This paper demonstrates twometa-mathematical propositions concerning the increasingly popular “intuitionistic” (= vague) approaches to fuzzy sets and fuzzy topology, as well as the closely related interval-valued (= grey) sets and interval-valued “intuitionistic” sets: (1) the term “intuitionistic” in these contexts is historically inappropriate given the standard mathematical usage of “intuiti...

In this paper, we research the relationship between entropy and similarity of interval valued intuitionistic fuzzy sets in detail and prove eight theorems that entropy and similarity of interval valued intuitionistic fuzzy sets can be transformed to each other based on their axiomatic definitions. Finally, we propose some formulaes to calculate entropy and similarity of interval valued intuitio...