Unified Fuzzy Divergence Measures with Multi-Criteria Decision Making Problems for Sustainable Planning of an E-Waste Recycling Job Selection (original) (raw)
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Divergence measure is an important tool for determining the amount of discrimination between two probability distributions. Since the introduction of fuzzy sets, divergence measures between two fuzzy sets have gained attention for their applications in various fields. Exponential entropy measure has some advantages over Shannon's entropy. In this paper, we used the idea of Jensen Shannon divergence to define a new divergence measure called 'fuzzy Jensen-exponential divergence (FJSD)' for measuring the discrimination/difference between two fuzzy sets. The measure is demonstrated to satisfy some very elegant properties, which shows its strength for applications in multi-criteria decision making problems. Further, we develop a method to solve multi-criteria decision making problems under fuzzy phenomenon by utilizing the proposed measure and demonstrate by a numerical example.
On New Generalized Fuzzy Directed Divergence Measure and Its Application in Decision Making Problem
Mathematics and Statistics, 2021
The concept of fuzzy sets presented by Zadeh has conquered an enormous achievement in numerous fields. Uncertainty in real world is ubiquitous. Entropy is an important tool with uncertainty and fuzziness. In this article, we propose new measure of directed divergence on fuzzy set. The extension of the fuzzy sets and one that integrated with other theories have been applied by some researchers. To prove the validity of measure, some axioms are proved. Using the proposed measure, we generate a method about decision making criteria and give a suitable method. In this article, we describe directed divergence measure for fuzzy set. Properties of proposed measure are discussed. In the real world, the multicriteria decision making is a very practical method and has a wide range of uses. By using multicriteria decision making, we can find best choice among the given criteria. In recent years, many researchers extensively apply fuzzy directed divergence for multicriteria decision making. Also some researchers defined the application of parameterized Hesitant Fuzzy Soft Set theory in decision making. In this article, we shall investigate the multiple criteria decision making problem under fuzzy environment. Application of introduced measure is given for decision making problem. A numerical example is given for decision making problem. In a fuzzy multicriteria problem, the analysis is given by an illustration example of the new define approach regarding admission preference of a student for post graduate course of science stream.
New Fuzzy Divergence Measure and Its Applications in Multi-criteria Decision-Making Using New Tool
Springer Proceedings in Mathematics & Statistics, 2020
Various authors and researchers have established fuzzy divergence measures and their applications in multi-criteria decision making (MCDM), pattern recognition (PR), medical diagnosis (MD), fuzzy clustering, speech recognition etc. Here, we have derived a new fuzzy divergence measure and investigated their properties to existence and validity. Also investigated fuzzy divergence measure in PR, MCDM and MD. Compared the established results by various authors and researcher. Novelty of this research may be useful to industries for decision making, identifying the medical diseases and pattern recognition.
Granular Computing
Picture Fuzzy Sets (PFSs) originated by Cuong and Kreinovich are more capable to capture uncertain, inconsistent and vague information in multi-criteria decision making. In this paper, we propose a new picture fuzzy divergence measure based on Jensen-Tsallis function between PFSs. Further, the concept has been extended from fuzzy sets to novel picture fuzzy divergence measure. Besides the validation of the proposed measure, some of its key properties with specific cases are additionally talked about. The performance of the proposed measure is compared with other existing measures in the literature. Some illustrative examples are provided in the context of novel rapacious COVID-19 and pattern recognition which demonstrate the adequacy and practicality of the proposed approach in solving real-life problems.
Application of decision making using generalized measure of fuzzy directed divergence
Applied Mathematical Sciences
A measure of directed divergence is defined as the discrepancy of the probability distribution P from another probability Q. Kullback and Leibler [5] obtained a quantitative measure of directed divergence of one probability distribution from another probability distribution. Bhandari, Pal and Majumder [2] introduced new measures of fuzzy divergence, indicated its application to clustering problems and also applied to an object extraction problem. Since there are non-exponential growth models, innovation diffusion models, epidemic models, a variety of models in Economics, Social Sciences, Biology and even in Physical Sciences, we need a variety of information measures for each field to extend the scope of their applications. Hence the development of new generalized parametric measures is necessary. One such measure of fuzzy divergence has been developed in this paper. The validity of the divergence measures is examined. Further, the applications of fuzzy directed divergence in decision making has been discussed.
New Fuzzy Divergence Measure and its Applications: A New Approach
2020
Various authors and researchers have established fuzzy divergence measures and their applications in multi-criteria decision making (MCDM), pattern recognition (PR), medical diagnosis (MD), fuzzy clustering, speech recognition etc. Here, we have derived a new fuzzy divergence measure and investigated their properties to existence and validity. Also investi-gated fuzzy divergence measure in PR, MCDM and MD. Compared the established results by various authors and researcher. Novelty of this research may be useful to industries for decision making, identifying the medical diseases and pattern recognition.
Fuzzy directed divergence measureand its application to decision making
2018
Divergence or relative information is a measure of information associated with two probability distributions of a discrete random variable which is based in Shannon entropy. In this paper a new divergence measure and corresponding fuzzy directed divergence measure have been proposed. Comparative study of the proposed divergence measure with some existing divergence measure has been done with the help of numerical example. Further, the application of proposed fuzzy directed divergence is illustrated in decision making problems.
Decision-making in machine learning using novel picture fuzzy divergence measure
Neural Computing and Applications, 2021
Some tools such as entropy, divergence measures and similarity measures are applied to real-world phenomena like decision-making, robotics, pattern recognition, clustering, expert and knowledge-based system and medical diagnosis. An intuitionistic fuzzy set (IFS) comprises of membership function and non-membership function, but neutrality function is missing in IFS. Therefore, picture fuzzy set (PFS) is an excellent tool to handle such situations when there are answers like yes, no, abstain and refusal. PFS is the generalization of fuzzy set (FS) and intuitionistic fuzzy set (IFS) and shows better adaptation to various real-world problems. To draw conclusions for these problems, based on discrimination between two probability distributions, tools such as divergence measure play a crucial role. The aim of this study is to propose a divergence measure for picture fuzzy sets with its validity proof and to deliberate its key properties. Besides, the newly developed divergence measure is applied to decision-making in machine learning such as pattern recognition, medical diagnosis and clustering using numerical illustrations. To validate the proposed method and to check its effectiveness, expediency and legitimacy, a comparative analysis is given and also the superiority of the divergence measure is tested over the existing methods by comparing their results.
Divergence measure and its relation to nonspecificity of fuzzy sets
2013
Divergence measure is a tool used to quantify the discrimination of two subsets of universal set. In this paper, we proposed some relations between the divergence measure based on cardinalities of a fuzzy set and uncertainty due to nonspecificity of fuzzy set. Due to that relation, a new class of divergence measures are also obtained. The application of above measure in the field of image segmentation is also mentioned. AMS subject classification:
A Novel Multiple-Criteria Decision-Making Approach Based on Picture Fuzzy Sets
Journal of Function Spaces, 2022
Experts are using picture fuzzy sets (PFSs) in their probes to resolve the uncertain and vague information during the process of decision making because PFSs describe human attitudes naturally. Divergence measure (DM) plays a dominant role in discriminating between two distributions of probability and extracting consequences from that discrimination. In the present work, a novel picture fuzzy divergence measure (PF-DM) is developed between two PFSs. Some of the suggested measure’s important qualities are also discussed with particular situations to validate it. Based on the suggested PF-DM, a multiple-criteria decision-making (MCDM) model is established to grab the fuzzy information. The suggested measure’s performance is compared to that of various existing measures in the literature. An MCDM model has been proven for the usefulness of the suggested technique in dealing with real-life scenarios in the context of dengue sickness and pattern identification. Validation of the suggeste...