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 ...

We give a geometrical interpretation of the interval-valued fuzzy set (IVFS). Based on the geometrical background, we propose new distance measures between IVFSs and compare these measures with distance measures proposed by Burillo and Bustince (1996) and Grzegorzewski (2004), respectively. Furthermore, we extend three methods for measuring distances between IVFSs to interval-valued intuitionis...

Recently, the rough set and fuzzy set theory have generated a great deal of interest among more and more researchers. Granular computing (GrC) is an emerging computing paradigm of information processing and an approach for knowledge representation and data mining. The purpose of granular computing is to seek for an approximation scheme which can effectively solve a complex problem at a certain ...

In this paper, we shall present the strong laws of large numbers for fuzzy set-valued random variables in the sense of ∞ H d . The results are based on the result of single-valued random variables obtained by Taylor [1] and set-valued random variables obtained by Li Guan [2].

The purpose of this paper is to study common fixed point theorems for six (four single-valued and two set-valued) mappings in fuzzy metric space using general contractive condition of integral type, without assuming compatibility and continuity of any mapping on non complete metric spaces. To prove the theorems, we use a non compatible condition, that is, weak commutativity of type (Kh)in fuzzy...

Lattice-valued up-sets and down-sets of a poset are investigated under the cutworthy approach. It is proved that the collections of all lattice valued up-sets and down-sets of a given poset are complete lattices under fuzzy inclusion. Properties of these are investigated. For a given collection of crisp up-sets of a poset, necessary and sufficient conditions are given under which the family rep...

On the basis of the concept of interval valued intuitionistic fuzzy set introduced by K. Atanassov [3], the notion of interval valued intuitionistic fuzzy subsemigroup (ideal, bi-ideal, (1, 2)-ideal) of a semigroup with respect to t-norm T and s-norm S is given and the characteristic properties are described. The homomorphic image and inverse image are investigated. In particular, by the help o...

9:00 am – 10:30 am János C. Fodor, Bernard De Baets, Tomasa Calvo, Structure of uninorms with given continuous underlying t-norms and t-conorms Glad Deschrijver, Etienne E. Kerre, The residuation principle for intuitionistic fuzzy t-norms 11.00 am – 12:30 am Michal Baczynski, On the characterizations of intuitionistic fuzzy implications Carol L. Walker, Elbert A. Walker, T-norms on fuzzy sets o...

The concept of duality, stating that something can or must coexist with its opposite, makes fuzzy logic seem natural, even inevitable. In fact, there are infinite degrees of uncertainty between the certainty of being and not being. This imperfection inherent to information represented in natural language has been treated mathematically using the theory of fuzzy sets. Thus, fuzzy logic introduce...

Neutrosophic set is a powerful general formal framework, which generalizes the concept of the classic set, fuzzy set, interval valued fuzzy set, intuitionistic fuzzy set, and interval-valued intuitionistic fuzzy set from philosophical point of view. However, it will be difficult to apply in real science and engineering areas, while a simplified neutrosophic set (SNS) is a subclass of a neutroso...