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# Mathematical Modeling and Evaluation of Reliability Parameters Based on Survival Possibilities under Uncertain Environment

Alhanouf Alburaikan1, Hamiden Abd El-Wahed Khalifa1,2, Pavan Kumar3,*, Seyedali Mirjalili4,6, Ibrahim Mekawy5

1 Department of Mathematics, College of Science and Arts, Qassim University, Al-Badaya, 51951, Saudi Arabia
2 Department of Operations Research, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza, 12613, Egypt
3 Division of Mathematics, School of Advanced Science and Languages, VIT Bhopal University, Sehore, 466114, India
4 Centre for Artificial Intelligence Research and Optimization, Torrens University Australia, Brisbane, 4006, Australia
5 Department of Mathematics, College of Science and Arts, Qassim University, Ar Rass, 6688, Saudi Arabia
6 YFL (Yonsei Frontier Lab), Yonsei University, Seoul, 03722, Korea

* Corresponding Author: Pavan Kumar. Email:

(This article belongs to this Special Issue: Extension, Modeling and Applications of Fuzzy Set Theory in Engineering and Science)

Computer Modeling in Engineering & Sciences 2023, 134(3), 1943-1956. https://doi.org/10.32604/cmes.2022.021815

## Abstract

In this article, mathematical modeling for the evaluation of reliability is studied using two methods. One of the methods, is developed based on possibility theory. The performance of the reliability of the system is of prime concern. In view of this, the outcomes for the failure are required to evaluate with utmost care. In possibility theory, the reliability information data determined from decision-making experts are subjective. The same method is also related to the survival possibilities as against the survival probabilities. The other method is the one that is developed using the concept of approximation of closed interval including the piecewise quadratic fuzzy numbers. In this method, a decision-making expert is not sure of his/her estimates of the reliability parameters. Numerical experiments are performed to illustrate the efficiency of the suggested methods in this research. In the end, the paper is concluded with some future research directions to be explored for the proposed approach.

## Keywords

Alburaikan, A., Abd, H., Kumar, P., Mirjalili, S., Mekawy, I. (2023). Mathematical Modeling and Evaluation of Reliability Parameters Based on Survival Possibilities under Uncertain Environment. CMES-Computer Modeling in Engineering & Sciences, 134(3), 1943–1956.

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