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.

scholarly journals Bounds on Nonsymmetric Divergence Measure in terms of Other Symmetric and Nonsymmetric Divergence Measures

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
K. C. Jain ◽  
Praphull Chhabra
Keyword(s):  
Divergence Measure ◽  
Chi Square ◽  
Information Inequalities ◽  
Divergence Measures ◽  
Special Cases ◽  
Variational Distance

Vajda (1972) studied a generalized divergence measure of Csiszar’s class, so called “Chi-m divergence measure.” Variational distance and Chi-square divergence are the special cases of this generalized divergence measure at m=1 and m=2, respectively. In this work, nonparametric nonsymmetric measure of divergence, a particular part of Vajda generalized divergence at m=4, is taken and characterized. Its bounds are studied in terms of some well-known symmetric and nonsymmetric divergence measures of Csiszar’s class by using well-known information inequalities. Comparison of this divergence with others is done. Numerical illustrations (verification) regarding bounds of this divergence are presented as well.

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.

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.

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

Symmetry ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 90 ◽  
Author(s):  
Pratibha Rani ◽  
Kannan Govindan ◽  
Arunodaya Raj Mishra ◽  
Abbas Mardani ◽  
Melfi Alrasheedi ◽  
...  
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Waste Recycling ◽  
Multi Criteria Decision Making ◽  
Divergence Measure ◽  
Divergence Measures ◽  
Job Selection ◽  
Sustainable Planning ◽  
Control Decision ◽  
Fuzzy Divergence

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.

Jensen-Tsalli’s Intuitionistic Fuzzy Divergence Measure and Its Applications in Medical Analysis and Pattern Recognition

2019 ◽  
Vol 27 (01) ◽  
pp. 145-169 ◽  
Author(s):  
Rajesh Joshi ◽  
Satish Kumar
Keyword(s):  
Pattern Recognition ◽  
Medical Diagnosis ◽  
Intuitionistic Fuzzy Set ◽  
Divergence Measure ◽  
Flexible Tool ◽  
Numerical Examples ◽  
Pattern Recognition Problem ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Divergence ◽  
Medical Analysis

Vagueness in scientific studies poses a challenge. Intuitionistic Fuzzy Set (IFS) theory has emerged as a powerful and flexible tool to counter such challenge. So, there is a need to develop such measures which can not only measure the vagueness but also quantify the differences in underlying IFSs. The aim of this communication is to introduce one such divergence measure called Intuitionistic Fuzzy Jensen-Tsalli Divergence measure in the settings of IFS theory. The presence of parameters makes the proposed divergence measure flexible and competent for applications. Besides discussing some of its major properties, the findings are applied in pattern recognition problem and in medical diagnosis of some diseases with same set of symptoms. The performance of the proposed measure is genuinely compared with some other existing measures in literature through numerical examples based on medical diagnosis and pattern recognition.

Extreme-point solutions in Markov decision processes

1983 ◽  
Vol 20 (04) ◽  
pp. 835-842
Author(s):  
David Assaf
Keyword(s):  
Convex Function ◽  
Extreme Point ◽  
Markov Decision Processes ◽  
Convex Functions ◽  
Sufficient Conditions ◽  
Decision Processes ◽  
Markov Decision ◽  
Full Solution

The paper presents sufficient conditions for certain functions to be convex. Functions of this type often appear in Markov decision processes, where their maximum is the solution of the problem. Since a convex function takes its maximum at an extreme point, the conditions may greatly simplify a problem. In some cases a full solution may be obtained after the reduction is made. Some illustrative examples are discussed.

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