On Extended L r -Norm-Based Derivatives to Intuitionistic Fuzzy Sets

A. S. Wungreiphi (), Fokrul Alom Mazarbhuiya () and Mohamed Shenify
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A. S. Wungreiphi: School of Fundamental and Applied Sciences, Assam Don Bosco University, Sonapur 782402, Assam, India
Fokrul Alom Mazarbhuiya: School of Fundamental and Applied Sciences, Assam Don Bosco University, Sonapur 782402, Assam, India
Mohamed Shenify: College of Computer Science and IT, Albaha University, KSA, Albaha 65527, Saudi Arabia

Mathematics, 2023, vol. 12, issue 1, 1-19

Abstract: The study of differential equation theory has come a long way, with applications in various fields. In 1961, Zygmund and Calderón introduced the notion of derivatives to metric L r , which proved to be better in applications than approximate derivatives. However, most of the studies available are on Fuzzy Set Theory. In view of this, intuitionistic fuzzy L r -norm-based derivatives deserve study. In this study, the L r -norm-based derivative for intuitionistic fuzzy number valued functions is introduced. Some of its basic properties are also discussed, along with numerical examples. The results obtained show that the proposed derivative is not dependent on the existence of the Hukuhara difference. Lastly, the Cauchy problem for the intuitionistic fuzzy differential equation is discussed.

Keywords: fuzzy set; intuitionistic fuzzy number; Hukuhara differentiable; generalized Hukuhara differentiable (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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