GENERALIZED FUZZY DIVERGENCE MEASURE, PATTERN RECOGNITION AND INEQUALITIES

Many fuzzy information and divergence measures developed by various researchers and authors. Here, authors proposed new fuzzy divergence measure using the properties of convex function and fuzzy concept. The applications of novel fuzzy divergence measures in pattern recognition with case study, are discussed. Obtained various novel fuzzy information inequalities on fuzzy divergence measures. The new relations among new and existing fuzzy divergence measure by new f-divergence, Jensen inequalities, properties of convex functions and inequalities have studied. Finally, verified these results and proposed fuzzy divergence measures by numerical example.

A new divergence measure of interval-valued pythagorean fuzzy sets and its application

As the extension of the Fuzzy sets (FSs) theory, the Interval-valued Pythagorean Fuzzy Sets (IVPFS) was introduced which play an important role in handling the uncertainty. The Pythagorean fuzzy sets (PFSs) proposed by Yager in 2013 can deal with more uncertain situations than intuitionistic fuzzy sets because of its larger range of describing the membership grades. How to measure the distance of Interval-valued Pythagorean fuzzy sets is still an open issue. Jensen–Shannon divergence is a useful distance measure in the probability distribution space. In order to efficiently deal with uncertainty in practical applications, this paper proposes a new divergence measure of Interval-valued Pythagorean fuzzy sets,which is based on the belief function in Dempster–Shafer evidence theory, and is called IVPFSDM distance. It describes the Interval-Valued Pythagorean fuzzy sets in the form of basic probability assignments (BPAs) and calculates the divergence of BPAs to get the divergence of IVPFSs, which is the step in establishing a link between the IVPFSs and BPAs. Since the proposed method combines the characters of belief function and divergence, it has a more powerful resolution than other existing methods.

Information Generating Function of Ranked Set Samples

In the present paper, we study the information generating (IG) function and relative information generating (RIG) function measures associated with maximum and minimum ranked set sampling (RSS) schemes with unequal sizes. We also examine the IG measures for simple random sampling (SRS) and provide some comparison results between SRS and RSS procedures in terms of dispersive stochastic ordering. Finally, we discuss the RIG divergence measure between SRS and RSS frameworks.

A Novel Method for Conflict Data Fusion Using an Improved Belief Divergence Measure in Dempster–Shafer Evidence Theory

Dempster–Shafer (D-S) evidence theory plays an important role in multisource data fusion. Due to the nature of the Dempster combination rule, there can be counterintuitive results when fusing highly conflicting evidence data. To date, conflict management in D-S evidence theory is still an open issue. Inspired by evidence modification considering internal indeterminacy and external support, a novel method for conflict data fusion is proposed based on an improved belief divergence, evidence distance, and belief entropy. First, an improved belief divergence measure is defined to characterize the discrepancy and conflict between bodies of evidence (BOEs). Second, evidence credibility is generated to describe the external support based on the complementary advantages of the improved belief divergence and evidence distance. Third, belief entropy is utilized to quantify the internal indeterminacy and further determine evidence weight. Lastly, the classical Dempster combination rule is applied to fuse the BOEs modified by their credibility degrees and weights. As the results of numerical examples and an application show, the proposed divergence measure can overcome the invalidity of the existing measures in some special cases. Additionally, the proposed fusion method recognizes the correct target with the highest belief value of 98.96%, which outperforms other related methods in conflict management. The proposed fusion method also displays better convergence, validity, and robustness.