We introduce the fuzzy measure as a unifying structure for modeling knowledge about an uncertain variable. We show that a large class of well established types of uncertainty representation can be modeled in this framework. A measure of entropy associated with a fuzzy measure is introduced and its manifestation for different fuzzy measures is described. The problem of uncertain decision making ...

The main purpose of this paper is to investigate the multi-criteria decision making (MCDM) under the completely unknown attributes weights. As the information collected from the various resources related to different criteria for assessing the best alternatives is always imprecise in nature. Thus, to handle the impreciseness in the data, fuzzy set theory has been used during the analysis and re...

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 aim of this paper is to extend the notion of topological entropy for fuzzy semidynamical systems created by a self-map on a fuzzy metric space. We show that if a metric space has two uniformly equivalent metrics, then fuzzy entropy is a constant up to these two metrics. We present a method to construct chaotic fuzzy semidynamical systems with arbitrary large fuzzy entropy. We also prove tha...

Fuzzy measures can flexibly describe the relative importance of decision criterion as well as their interactions in multicriteria decision making. Based on the diamond pairwise comparison, a new identification method of 2-order additive fuzzy measure is proposed. The relative weight and the interaction degree can be obtained simultaneously for every pair of criteria in the diamond pairwise comp...

In the literature of information theory, there is necessity for comparing the different measures of fuzzy entropy and this consequently, gives rise to the need for normalizing measures of fuzzy entropy. In this paper, we have discussed this need and hence developed some normalized measures of fuzzy entropy. It is also desirable to maximize entropy and to minimize directed divergence or distance...

Study of fuzzy entropy on intuitionistic fuzzy sets (IFSs) were proposed, and analyzed. Built in uncertainty in IFSs, it is named as hesitance. It is contained in fuzzy membership function in itself by definition. Hence, designing fuzzy entropy is not easy because there is no general entropy definition about IFSs. By considering existing fuzzy entropy definitions, fuzzy entropy on IFSs is desig...

Fuzzy systems are capable to model the inherent uncertainties in real world problems and implement human decision making. In this paper two issues related to fuzzy systems development are addressed and solutions are proposed and implemented. First issue is related to the high dimensional data sets. Such kinds of data sets lead to explode the search space of generated rules and results into dete...

In the present paper, a new entropy of order α and type β on Interval-Valued Intutionistic Fuzzy Sets (IVIFSs) along with their proofs of validity is proposed. It has been proved that the proposed entropy has monotonic decreasing behavior with respect to α and β. Further, a new algorithm for multiple attribute decision making method (MADM) has been provided using the benefit attributes and cost...