Control and Optimization
Fatemeh Babakordi; Nemat Allah Taghi-Nezhad
Abstract
This paper presents the introduction of two novel equation types: the partial hesitant fuzzy equation and the half hesitant fuzzy equation. Additionally, an efficient method is proposed to solve these equations by defining four solution categories: Controllable, Tolerable Solution ...
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This paper presents the introduction of two novel equation types: the partial hesitant fuzzy equation and the half hesitant fuzzy equation. Additionally, an efficient method is proposed to solve these equations by defining four solution categories: Controllable, Tolerable Solution Set (TSS), Controllable Solution Set (CSS), and Algebraic Solution Set (ASS). Furthermore, the paper establishes eight theorems that explore different types of solutions and lay out the conditions for the existence and non-existence of hesitant fuzzy solutions. The practicality of the proposed method is demonstrated through numerical examples.
Fatemeh Babakordi; Tofigh Allahviranloo
Abstract
Solving fuzzy linear systems has been widely studied during the last decades. However, there are still many challenges to solving fuzzy linear equations, as most of the studies have used the principle of extension, which suffers from shortcomings such as the lack ...
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Solving fuzzy linear systems has been widely studied during the last decades. However, there are still many challenges to solving fuzzy linear equations, as most of the studies have used the principle of extension, which suffers from shortcomings such as the lack of solution, achieving solutions under very strong conditions, large support of the obtained solutions, inaccurate or even incorrect solutions due to not utilizing all the available information, complicated process and high computational load. These problems motivated us to present a fuzzy Cramer method for solving fuzzy linear equations, which uses arithmetic operations based on the Transmission Average (TA). In this study, fully fuzzy linear systems in the form of $ \tilde{A}\tilde{X}=\tilde{B} $, and dual fuzzy linear systems in the form of $ \tilde{A}\tilde{X}+\tilde{B}=\tilde{C}\tilde{X}+\tilde{D} $ are solved using the proposed fuzzy Cramer method, and numerical examples are provided to confirm the effectiveness and applicability of the proposed method.
