Systems of First-Order Linear Fuzzy Initial Value Problems and Their Applications

• Published in: INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGENT SYSTEMS Vol. 24; no. 2; pp. 171 - 180
• Main Authors: Nagalakshmi, Soma, Suresh, Kumar Grande, Agarwal, Ravi P.
• Format: Journal Article
• Language: English
• Published: 한국지능시스템학회 01.06.2024
• Subjects: 전기공학; System of first-order linear fuzzy initial value problems; Horizontal membership function; n-dimensional granular metric; n-dimensional granular derivative
• ISSN: 1598-2645; 2093-744X
• DOI: 10.5391/IJFIS.2024.24.2.171

This study primarily addresses solutions to a system of first-order linear fuzzy initial valueproblems in the context of granular differentiability, and explores the real-life applicationsof such systems. We recall the concepts of the horizontal membership function, granularmetrics, limits, continuity, differentiability, and integrability for fuzzy functions with n-dimensional fuzzy numbers. We then present a fundamental theorem that establishes theexistence and uniqueness of solutions for both homogeneous and nonhomogeneous systemsof first-order linear fuzzy initial value problems. In addition, we describe an algorithm forsolving nonhomogeneous systems under granular differentiability. Finally, we provide real-lifeapplications - including models for lidocaine and irregular heartbeats, Richardson’s arms race,and radioactive decay phenomena in a fuzzy environment - to demonstrate the practical utilityof the proposed algorithm. KCI Citation Count: 0