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...

The evaluation is an important approach to promote the development of the E-Government. Since the rapid development of E-Government in the world, the E-Government performance evaluation has become a hot issue in the academia. In this paper, we develop a new evaluation method for the development of the E-Government based on the interval-valued intuitionistic fuzzy set which is a powerful techniq...

With the unit interval [0,1] as the truth value table, Chen and Wupresented the concept of  possibility computation over dcpos.Indeed, every possibility computation can be considered as a[0,1]-valued Scott open set on a dcpo. The aim of this paper is tostudy Chen-Wu's duality on quantale-valued setting. For clarity,with a commutative unital quantale $L$ as the truth value table, weintroduce a c...

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...

Deep scientific ideas have at least one distinctive property: they can be applied both by philosophers in abstract fundamental debates and by engineers in concrete practical applications. Mathematical approaches to modeling of vagueness also possess this property. Problems connected with vagueness have been discussed at the beginning of XXth century by philosophers, logicians and mathematicians...

Hesitancy is the most common problem in decision making, for which hesitant fuzzy set can be considered as a useful tool allowing several possible degrees of membership of an element to a set. Recently, another suitable means were defined by Zhiming Zhang [1], called interval valued intuitionistic hesitant fuzzy sets, dealing with uncertainty and vagueness, and which is more powerful than the h...