On Fuzzy Differential Inequalities with Upper and Lower Solutions

Year 2021, Issue: 37, 68 - 75, 31.12.2021

Ali Yakar Seda Çağlak

https://doi.org/10.53570/jnt.1034452

Abstract

In this article, by using the technique of upper and lower solutions, some comparison results for first-order fuzzy differential equations are established. Hukuhara derivative, Hukuhara difference, and partial orderings are used for proving theorems. We extend our results to initial time difference case as well. Also, the practicality of these comparison results is demonstrated by giving an example.

Keywords

Fuzzy number, upper and lower solutions, Hukuhara derivative

References

• L. A. Zadeh, Fuzzy sets, World Scientific, 1996.
• C.-W. Chen, Stability Conditions of Fuzzy Systems and Its Application to Structural and Mechanical Systems, Advances in Engineering Software 37 (9) (2006) 624–629.
• Q. Shen, B. Jiang, V. Cocquempot, Fault-Tolerant Control for T–S Fuzzy Systems with Application to Near-Space Hypersonic Vehicle with Actuator Faults, IEEE Transactions on Fuzzy Systems 20 (4) (2011) 652–665.
• T. Terano, K. Asai, M. Sugeno, Fuzzy Systems Theory and Its Applications, Academic Press Professional, Inc., 1992.
• B. Bede, Fuzzy Sets, Springer, 2013. .
• M. Hukuhara, Integration des Applications Mesurables dont la Valeur est un Compact Convexe, Funkcialaj Ekvacioj 10 (3) (1967) 205–223.
• P. Diamond, P. Kloeden, Metrics of Fuzzy Sets: Theory and Applications, World Scientific, 1994.
• R. Rodríguez-López, Comparison Results for Fuzzy Differential Equations, Information Sciences 178 (6) (2008) 1756–1779.
• R. Rodríguez-López, Monotone Method for Fuzzy Differential Equations, Fuzzy Sets and Systems 159 (16) (2008) 2047–2076.
• T. Allahviranloo, Fuzzy Fractional Differential Operators and Equations, Vol. 397, Springer, 2020.
• M. L. Puri, D. A. Ralescu, Differentials of Fuzzy Functions, De Gruyter Mouton, 2011.