Generalized Hellinger’s Fuzzy Divergence Measure and Its Applications

2016 ◽  
pp. 107-121 ◽  
Author(s):  
Anshu Ohlan ◽  
Ramphul Ohlan
Keyword(s):  
Divergence Measure ◽  
Fuzzy Divergence

scholarly journals Logarithmic Divergence Measure for Fuzzy Matrix and Application

2021 ◽  
Vol 8 ◽  
pp. 1-20
Author(s):  
Alka Rani ◽  
Omdutt Sharma ◽  
Priti Gupta
Keyword(s):  
Decision Making ◽  
Real Life ◽  
Divergence Measure ◽  
Logarithmic Divergence ◽  
Fuzzy Matrix ◽  
Decision Making Problem ◽  
Fuzzy Divergence

This paper introduces a new divergence measure for a fuzzy matrix with proof of its validity. In addition, the properties are proved for the new fuzzy divergence measure. A method to solve decision making problem is developed by using the proposed fuzzy divergence measure. Finally, the application of this fuzzy divergence measure to decision making is shown using real-life example

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

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1452
Author(s):  
Arunodaya Raj Mishra ◽  
Pratibha Rani ◽  
Abbas Mardani ◽  
Reetu Kumari ◽  
Edmundas Kazimieras Zavadskas ◽  
...  
Keyword(s):  
Decision Making ◽  
Service Quality ◽  
Real Life ◽  
Multicriteria Decision Making ◽  
Divergence Measure ◽  
Divergence Measures ◽  
Shapley Function ◽  
Service Quality Evaluation ◽  
Segmentation Pattern ◽  
Fuzzy Divergence

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.

On Generalized Fuzzy Entropy and Fuzzy Divergence Measure with Applications

2019 ◽  
Vol 8 (3) ◽  
pp. 47-69 ◽  
Author(s):  
Surender Singh ◽  
Sonam Sharma
Keyword(s):  
Fuzzy Set ◽  
Multiple Attribute Decision Making ◽  
Point Of View ◽  
Fuzzy Entropy ◽  
Entropy Measure ◽  
Divergence Measure ◽  
Linguistic Variables ◽  
Directed Divergence ◽  
Multiple Attribute ◽  
Fuzzy Divergence

Entropy in a fuzzy set measures the amount of ambiguity/imprecision presented in the fuzzy set. In this article, the authors introduce a generalized fuzzy entropy measure and demonstrate its effectiveness in Multiple Attribute Decision Making (MADM) and superiority from the point of view of structured linguistic variables. This article also introduces a generalized fuzzy directed divergence and investigates its properties. Further, this article demonstrates the effectiveness of the proposed generalized directed divergence in pattern recognition.

GENERALIZED FUZZY DIVERGENCE MEASURE, PATTERN RECOGNITION AND INEQUALITIES

2022 ◽  
Vol 11 (1) ◽  
pp. 0-0
Keyword(s):  
Pattern Recognition ◽  
Convex Function ◽  
Convex Functions ◽  
Divergence Measure ◽  
Fuzzy Information ◽  
Information Inequalities ◽  
Fuzzy Concept ◽  
Divergence Measures ◽  
Fuzzy Divergence

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.

New generalized intuitionistic fuzzy divergence measure with applications to multi-attribute decision making and pattern recognition

2020 ◽  
Vol 13 ◽  
Author(s):  
Adeeba Umar ◽  
Ram Naresh Saraswat
Keyword(s):  
Decision Making ◽  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
The Other ◽  
Divergence Measure ◽  
Intuitionistic Fuzzy ◽  
Multi Attribute Decision Making ◽  
Prime Objective ◽  
Fuzzy Divergence

Background: The notion of fuzzy set was introduced by Zadeh. After that, many researchers extended the concept of fuzzy sets in different ways. Atanassov introduced the concept of intuitionistic fuzzy sets as an extension of fuzzy sets. This concept is applied in many fields such as bio-informatics, image processing, decision making, feature selection, pattern recognition etc. Objectives: The prime objective of this paper is to introduce a new generalized intuitionistic fuzzy divergence measure with proof of its validity and discussions on its elegant properties. Applications of the proposed divergence measure in multi-attribute decision making and pattern recognition are also discussed with some numerical illustrations. Further, the proposed divergence measure is compared with other methods for solving MADM and pattern recognition problems which exist in the literature. Methods: Divergence measure method is used to measure the divergence between two given sets. Also, the results of the other existing measures are also given to compare with the proposed measure. Results: We see that our proposed divergence measure found much better results in comparison with the other existing methods. Conclusion: A new divergence measure for intuitionistic fuzzy sets is introduced with some of its properties. Applications of the proposed divergence measure to pattern recognition and MADM are illustrated through examples. The comparison of the proposed method with the existing methods shows the legacy of the results of the proposed method. It is concluded that the proposed divergence measure is effective for solving real world problems related to MADM and pattern recognition.

AN AXIOMATIC DEFINITION OF FUZZY DIVERGENCE MEASURES

2008 ◽  
Vol 16 (01) ◽  
pp. 1-17 ◽  
Author(s):  
INÉS COUSO ◽  
SUSANA MONTES
Keyword(s):  
Real Number ◽  
Divergence Measure ◽  
Essential Information ◽  
Divergence Measures ◽  
Axiomatic Definition ◽  
One To One ◽  
Definition Of ◽  
Fuzzy Divergence ◽  
Fuzzy Subsets

The representation of the degree of difference between two fuzzy subsets by means of a real number has been proposed in previous papers, and it seems to be useful in some situations. However, the requirement of assigning a precise number may lead us to the loss of essential information about this difference. Thus, (crisp) divergence measures studied in previous papers may not distinguish whether the differences between two fuzzy subsets are in low or high membership degrees. In this paper we propose a way of measuring these differences by means of a fuzzy valued function which we will call fuzzy divergence measure. We formulate a list of natural axioms that these measures should satisfy. We derive additional properties from these axioms, some of them are related to the properties required to crisp divergence measures. We finish the paper by establishing a one-to-one correspondence between families of crisp and fuzzy divergence measures. This result provides us with a method to build a fuzzy divergence measure from a crisp valued one.

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