Augmented Fuzzy Lagrange penalty method for fuzzy nonlinear programming problems
TL;DR
The proposed Augmented Fuzzy Lagrange Multiplier Method employs novel fuzzy arithmetic operations and ranking techniques tailored to the parametric representation of Triangular Fuzzy Numbers, enabling precise handling of both equality and inequality constraints.
Abstract
This article introduces the Augmented Fuzzy Lagrange Multiplier Method (AFLM) as an advanced technique for solving fuzzy nonlinear programming problems (FNLPP) without requiring conversion into crisp equivalents. Unlike traditional methods, which may lead to information loss, AFLM directly transforms constrained fuzzy optimization problems into unconstrained ones while preserving the fuzzy characteristics of the data. The proposed method employs novel fuzzy arithmetic operations and ranking techniques tailored to the parametric representation of Triangular Fuzzy Numbers (TFN), enabling precise handling of both equality and inequality constraints. A key contribution of this work is the development of a convergence theorem and a supporting lemma, ensuring the theoretical soundness of AFLM. The effectiveness of the approach is demonstrated through numerical comparisons, highlighting its ability to achieve more accurate and interpretable solutions than existing methods. The results underscore AFLMs significance as a powerful tool for addressing optimization problems in uncertain environments, making it a valuable asset for decision-makers in fuzzy nonlinear programming problems.