Divergence Measure For Fuzzy Sets Research Articles

An Extended Shapley TODIM Approach Using Novel Exponential Fuzzy Divergence Measures for Multi-Criteria Service Quality in Vehicle Insurance Firms

Classification of the divergence measure for fuzzy sets (FSs) has been a successful approach since it has been utilized in several disciplines, e.g., image segmentation, pattern recognition, decision making, etc. The objective of the manuscript is to show the advantage of the combined methodology. A comparison clearly shows the usefulness of the proposed technique over the existing ones under the fuzzy environment. This study presents novel exponential-type divergence measures with some elegant features, which can be applied to FSs. Next, a TODIM (an acronym in Portuguese for Interactive Multicriteria Decision Making) approach derived from prospect theory, Shapley function, and divergence measure for multi-criteria decision-making (MCDM) is proposed. Besides, for the reason of evaluating the dominance degree of the option, and the weights of the criteria, proposed divergence measures are implemented. Evaluating and selecting the service quality is the most important issue in management; it has a direct influence on the way the manufacturer performs its tasks. Selecting the service quality can be thought of as a problem of MCDM involving numerous contradictory criteria (whether of a quantitative or qualitative nature) for the evaluation processes. In recent years, the service quality assessment is becoming increasingly complex and uncertain; as a result, some criteria assessment processes cannot be efficiently done by numerical assessments. In addition, decision experts (DEs) may not always show full rationality in different real-life situations that need decision making. Here, a real service quality evaluation problem is considered to discuss the efficacy of the developed methods. The algorithm (TODIM based on the Shapley function and divergence measures) has a unique procedure among MCDM approaches, which is demonstrated for the first time in this paper.

Unified Fuzzy Divergence Measures with Multi-Criteria Decision Making Problems for Sustainable Planning of an E-Waste Recycling Job Selection

In the literature of information theory and fuzzy set doctrine, there exist various prominent measures of divergence; each possesses its own merits, demerits, and disciplines of applications. Divergence measure is a tool to compute the discrimination between two objects. Particularly, the idea of divergence measure for fuzzy sets is significant since it has applications in several areas viz., process control, decision making, image segmentation, and pattern recognition. In this paper, some new fuzzy divergence measures, which are generalizations of probabilistic divergence measures are introduced. Next, we review two different generalizations of the following measures. Firstly, directed divergence (Kullback–Leibler or Jeffrey invariant) and secondly, Jensen difference divergence, based on these measures, we develop a class of unified divergence measures for fuzzy sets (FSs). Then, a method based on divergence measure for fuzzy sets (FSs) is proposed to evaluate the multi-criteria decision-making (MCDM) problems under the fuzzy atmosphere. Lastly, an illustrative example of the recycling job selection problem of sustainable planning of the e-waste is presented to demonstrate the reasonableness and usefulness of the developed method.

A novel feature selection method using fuzzy rough sets

The fuzzy set theory and the rough set theory are two distinct but complementary theories that deal with uncertainty in data. The salient features of both the theories are encompassed in the domain of the fuzzy rough set theory so as to cope with the problems of vagueness and indiscernibility in real world data. This hybrid theory has been found to be a potential tool for data mining, particularly useful for feature selection. Most of the existing approaches to fuzzy rough sets are based on fuzzy relations. In this paper, a new definition for fuzzy rough sets in an information system based on the divergence measure of fuzzy sets is introduced. The properties of the fuzzy rough approximations are explored. Moreover, an algorithm for feature selection using the proposed approximations is presented and experimented using real data sets.