The concept of an antipodal bipolar fuzzy graph of a given bipolar fuzzy graph is introduced. Characterizations of antipodal bipolar fuzzy graphs are presented when the bipolar fuzzy graph is complete or strong. Some isomorphic properties of antipodal bipolar fuzzy graph are discussed. The notion of self median bipolar fuzzy graphs of a given bipolar fuzzy graph is also introduced.

We introduce the notion of bipolar fuzzy Lie sub-superalgebras (resp. bipolar fuzzy ideals) and present some of their properties. First we investigate the properties of bipolar fuzzy Lie sub-superalgebras and bipolar fuzzy ideals under homomorphisms of Lie superalgebras. Next we study bipolar fuzzy bracket product, solvable bipolar fuzzy ideals and nilpotent bipolar fuzzy ideals of Lie superalg...

We propose a meta-heuristic algorithm for clustering objects that are described on multiple incommensurable attributes defined on different scale types. We make use of a bipolar-valued dual similaritydissimilarity relation and perform the clustering process by first finding a set of cluster cores and then building a final partition by adding the objects left out to a core in a way which best fi...

In the present paper, Radial Basis Function interpolations are applied to approximate a fuzzy function $tilde{f}:Rrightarrow mathcal{F}(R)$, on a discrete point set $X={x_1,x_2,ldots,x_n}$, by a fuzzy-valued function $tilde{S}$. RBFs are based on linear combinations of terms which include a single univariate function. Applying RBF to approximate a fuzzy function, a linear system wil...

In this paper, we extend the concept of set-valued fuzzy measures (introduced and studied by Guo and Zhang [2004. On set-valued fuzzy measures. Information Sciences 160 (2004) 13–25]) to the class of multivalued set functions taking values in the family of non-empty closed subsets of a real normed space. Also, we introduce the notions of atom and non-atomicity of a multivalued set function and ...

The purpose of this paper is to give convergence theorems both for closed convex set valued and relative fuzzy valued martingales, and suband supermartingales. These kinds of martingales, suband super-martingales are the extension of classical real valued martingales, suband super-martingales. Here we compare two kinds of convergences, in the Hausdor metric and in the Kuratowski-Mosco sense. We...

Neutrosophic sets was defined by Smarandache, which is a generalized of fuzzy sets and intuitionistic fuzzy sets. A single valued neutrosophic set is an instance of neutrosophic sets defined by Wang et al. (2005). In this study, we introduce similarity measure on two single valued neutrosophic sets. We develop an entropy of single valued neutrosophic sets. Finally, we give an example which demo...