Title: Fuzzy information inequalities and application in pattern recognition

Authors: Sapna Gahlot; Ram Naresh Saraswat

Addresses: Department of Mathematics and Statistics, Manipal University Jaipur, Jaipur, Rajasthan – 303007, India ' Department of Mathematics and Statistics, Manipal University Jaipur, Jaipur, Rajasthan – 303007, India

Abstract: In mathematics, an inequality is a relation that compares two numbers or other mathematical expressions in a non-equal way. Inequalities play an important role in finding relationships and solving real-life problems. Although there are many fuzzy inequalities exist in the literature, which are unable to provide solutions for specific cases. The prime objective of this paper is to establish new fuzzy information inequalities under Jensen's inequality and Csiszar's f-fuzzy divergence measure. A new fuzzy relative information of type k and its cases is proposed. Using the proposed fuzzy inequalities, some new bounds of well-known fuzzy information divergence measures in terms of fuzzy chi-square measure, fuzzy Kullback-Leibler measure and fuzzy Hellinger measure are obtained. The direct applications of the proposed fuzzy inequalities in pattern recognition is discussed in this paper. Fuzzy information inequalities also play an important role in medical diagnosis, decision making, etc. and can be extended to Chebyshev's inequality, holder's inequality, and so on, and by this we can solve any other real-life related issues. It is a more convenient and reliable method than others.

Keywords: fuzzy set; fuzzy f-measures; inequalities; pattern recognition.

DOI: 10.1504/IJMOR.2022.127731

International Journal of Mathematics in Operational Research, 2022 Vol.23 No.4, pp.456 - 480

Received: 25 May 2021
Accepted: 29 Aug 2021
Published online: 15 Dec 2022 *

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