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...

Abstract: In this paper, the concept of semiring of generalized interval-valued intuitionistic fuzzy matrices are introduced and have shown that the set of GIVIFMs forms a distributive lattice. Also, prove that the GIVIFMs form an generalized interval valued intuitionistic fuzzy algebra and vector space over [0,1]. Some properties of GIVIFMs are studied using the definition of comparability of ...

Interval-valued intuitionistic fuzzy number uses membership degree and non-member ship degree to express a decision-maker’s hesitation, which make decision-maker express his/her opinion in uncertainty decision-making environment easily. The comparison between some intervalvalued intuitionistic fuzzy numbers can not be undertaken because of its limitation. In application such as weak consistency...

In this paper, (α,β)-interval valued set is studied. The order relation on defined. It shown that complete lattice by giving the definitions of infumum and supremum these sets. Then, negation function sets introduced. 
 With help ,(α,β)-interval intuitionistic fuzzy are fundamental algebraic properties examined. level subsets given. Some propositions examples

Combining intuitionistic fuzzy sets and filter theory,we studied interval valued intuitionistic (T, S)-fuzzy filters on lattice implication algebras. some relation properties of it are obtained, the relation between intuitionistic (T, S)-fuzzy filters and intuitionistic fuzzy set are discussed.The investigation method and content of lattice implication algebras are extended. Mathematics Subject...

Soft set theory, fuzzy set theory and rough set theory are all mathematical tools for dealing with uncertainties and are closely related. Feng et al. introduced the notions of rough soft set, soft rough set and soft rough fuzzy set by combining fuzzy set, rough set and soft set all together. This paper is devoted to the discussions of the combinations of intervalvalued intuitionistic fuzzy set,...

We describe the formal equivalence between interval valued and intuitionistic fuzzy subsets. We then discuss the role of fuzzy set methods in multi-criteria decision-making. We note that when an application involves non-standard, interval valued or intuitionistic fuzzy subsets, a problem arises in choosing a best alternative. This problem is a result of the fact that the membership grades of th...

On the basis of the concept of the interval valued intuitionistic fuzzy sets introduced by K.Atanassov, the notion of interval valued intuitionistic fuzzyHv-submodules of anHv-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 in...

After the introduction of fuzzy set by Zadeh in 1965 [1], there have been a number of generalizations of this fundamental concept. In 1967, Goguen [2] proposed the concept of L-fuzzy set. The idea of interval valued fuzzy set is given by Zadeh in 1975 [3]. Type 2 fuzzy sets were poposed by Zadeh in [4]. Attanasove introduced intuitionistic fuzzy sets in 1986 [5]. Interval valued intuitionistic ...