Control and Optimization
Farid Pourofoghi; Davood Darvishi Salokolaei
Abstract
Fractional programming is a significant nonlinear planning tool within operation research. It finds applications in diverse domains such as resource allocation, transportation, production programming, performance evaluation, and finance. In ...
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Fractional programming is a significant nonlinear planning tool within operation research. It finds applications in diverse domains such as resource allocation, transportation, production programming, performance evaluation, and finance. In practical scenarios, uncertainties often make it challenging to determine precise coefficients for mathematical models. Consequently, utilizing indefinite coefficients instead of definite ones is recommended in such cases. Grey systems theory, along with probability theory, randomness, fuzzy logic, and rough sets, is an approach that addresses uncertainty. In this study, we address the problem of linear fractional programming with grey coefficients in the objective function. To tackle this problem, a novel approach based on the variable change technique proposed by Charnes and Cooper, along with the convex combination of intervals, is employed. The article presents an algorithm that determines the solution to the grey fractional programming problem using grey numbers, thus capturing the uncertainty inherent in the objective function. To demonstrate the effectiveness of the proposed method, an example is solved using the suggested approach. The result is compared with solutions obtained using the whitening method, employing Hu and Wong's technique and the Center and Greyness Degree Ranking method. The comparison confirms the superiority of the proposed method over the whitening method, thus suggesting adopting the grey system approach in such situations.
Razieh Farokhzad Rostami
Abstract
Fixed point theorems can be used to prove the solvability of optimization problems, differential equations and equilibrium problems, and the intrinsic flexibility of probabilistic metric spaces makes it possible to extend the idea of contraction mapping in several inequivalent ways. ...
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Fixed point theorems can be used to prove the solvability of optimization problems, differential equations and equilibrium problems, and the intrinsic flexibility of probabilistic metric spaces makes it possible to extend the idea of contraction mapping in several inequivalent ways. In this paper, we extend very recent fixed point theorems in the setting of Menger probabilistic metric spaces. We present some fixed point theorems for self-mappings satisfying a generalized (ϕ , ψ ) - contractive condition in Menger probabilistic metric spaces which are contractions used extensively in global optimization problems. On the other hand, we consider a more general class of auxiliary functions in the contractivity condition and prove the existence of fixed points of non-expansive mappings on Menger probabilistic metric spaces.
