Adaptive strategies for system of fuzzy differential equation: application of arms race model

Authors

Sankar Prasad Mondal - Department of Mathematics, Midnapore College (Autonomous), Midnapore, West Midnapore-721101, West Bengal, India
Najeeb Alam Khan - Department of Mathematics, University of Karachi, Karachi 75270, Pakistan
Oyoon Abdul Razzaq - Department of Humanities and Natural Sciences, Bahria University, Karachi 75260, Pakistan
Tapan Kumar Roy - Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah-03, West Bengal, India

Abstract

The paper presents adaptive stratagems to scrutinize the system of first order fuzzy differential equations (SFDE) in two modes, fuzzy and in crisp sense. Its fuzzy solutions are carried out using two approaches, namely, Zadeh's extension principle and generalized Hukuhara derivative (gH-derivative). While, different defuzzification techniques; central of area method (COA), bisector of area method (BOA), largest of maxima (LOM), smallest of maxima (SOM), mean of maxima (MOM), regular weighted point method (RWPM), graded mean integration value (GMIV), and center of approximated interval (COAI), are employed to discuss the crisp solutions. Moreover, the arms race model (ARM), which have a significant implication in international military planning, are pragmatic examples of system of first order differential equations, but not studied in fuzzy sense, hitherto. Therefore, ARM is re-established and studied here with fuzzy numbers to estimate its uncertain parameters, as a practical utilization of SFDE. Additionally, an illustrative example of ARM is undertaken to clarify the appropriateness of the proposed approaches.

Keywords

Fuzzy differential equation, defuzzification, Hukuhara derivative, extension principle

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