Relations and relation matrices are important concepts in set theory and intelligent computation. Some general uncertainty measures for fuzzy relations are proposed by generalizing Shannon’s information entropy. Then, the proposed measures are used to calculate the diversity quantity of multiple classifier systems and the granularity of granulated problem spaces, respectively. As a diversity me...

Recently, resolving the problem of evaluation and ranking the potential suppliers has become as a key strategic factor for business firms. With the development of intelligent and automated information systems in the information era, the need for more efficient decision making methods is growing. The VIKOR method was developed to solve multiple criteria decision making (MCDM) problems with confl...

Heart rate variability (HRV) is the variation of the time interval between consecutive heartbeats and depends on the extrinsic regulation of the heart rate. It can be quantified using nonlinear methods such as entropy measures, which determine the irregularity of the time intervals. In this work, approximate entropy (ApEn), sample entropy (SampEn), fuzzy entropy (FuzzyEn) and fuzzy measure entr...

A new concept of the inclusion measure for intuitionistic fuzzy sets is proposed by the axiomatic definition. Also, the distance measures, similarity measures and information entropy are recalled and summarized. Most of important, some relationships among distance measure, information entropy, and inclusion measure of IFSs are then investigated. Finally, we obtain some important theorems by whi...

The entropy of intuitionistic fuzzy sets is used to indicate the degree of fuzziness of an interval-valued intuitionistic fuzzy set(IvIFS). In this paper, we deal with the entropies of IvIFSs. Firstly, we propose a set of entropies on IvIFSs with a parameter λ ∈ [0,+∞), which generalizes the entropy measure defined by Gao, for IvIFSs, and then we prove that the new entropy is an increasing func...

By utilizing the ideas of fuzzy-weighted entropy and directed divergence appropriately selecting weights, several new measures fuzzy cross-entropy have been generated. Concurrently, some weighted suggested based on

in today’s competitive market, for a business firm to win higher profit among its rivals, it is of necessity to evaluate, and rank its potential customer segments to improve its customer relationship management (crm). this brings the importance of having more efficient decision making methods considering the current fast growing information era. these decisions usually involve several criteria,...

In this paper, the Kapur cross-entropy minimization model for portfolio selection problem is discussed under fuzzy environment, which minimizes the divergence of the fuzzy investment return from a priori one. First, three mathematical models are proposed by defining divergence as cross-entropy, average return as expected value and risk as variance, semivariance and chance of bad outcome, respec...