On fuzzy methodology to solve multi-objective linear optimization problem in fully intuitionistic fuzzy environment

Fuzzy harmonic mean-based method for solving intuitionistic fuzzy multi-objective linear fractional optimization problems and its application in organizational planning

Penalized Intuitionistic Fuzzy Goal Programming Method for Solving Multi-Objective Decision-Making Problems

Many applicable problems have multi-goals that optimize simultaneously, and decision-makers set imprecise aspiration levels for each goal. Although such types of problems solved by fuzzy optimization are common in the literature, intuitionistic fuzzy optimization techniques are more efficient to handle than fuzzy and classical optimization. This research study focused on establishing a novel method by combining the penalty function method with an interactive goal programming methodology for addressing multi-objective decision-making problems in an intuitionistic fuzzy environment. One of the challenge that exists in the literature of the optimization method under an imprecise decision environment is that it is not guaranteed to generate a Pareto-optimal solution for the introduced problem. Therefore, in order to ensure the Pareto-optimality of the obtained solution, the suggested method has developed a new aggregation operator, an appropriate relaxation of the constraint set, and a well-structured extended Yager membership function.In addition, unlike other methods in the literature, the suggested method gives decision-makers the option to penalize the most unsatisfied objective function at a specific attained solution instead of starting from scratch and working their way through the problem. To illustrate the proposed method, we used a numerical example.

Augmented Fuzzy Lagrange penalty method for fuzzy nonlinear programming problems

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.

On Solving the Fuzzy Assignment Problem with Restrictions using the Fuzzy DEMATEL approach

The fuzzy assignment problem represents a significant optimization methodology employed for the distribution of finite resources to various tasks within uncertain contexts. In real-world decision-making scenarios, the assignment process frequently encounters a multitude of constraints and ambiguous data, thereby rendering traditional optimization techniques less effective. The proposed framework utilizes triangular fuzzy numbers to encapsulate uncertainty in decision-making parameters and assesses the inter-dependencies among restriction criteria via fuzzy DEMATEL analysis. By elucidating the causal relationships and the extent of influence among constraints, the model facilitates more informed assignment decisions in the face of imprecise conditions. The methodology empowers decision-makers to prioritize pivotal constraints and enhance allocation efficiency while taking into account the inter-dependencies among criteria. A numerical example is provided to illustrate the applicability and efficacy of the proposed approach. The results indicate that the integration of fuzzy DEMATEL with fuzzy assignment with restrictions modeling yields a systematic and dependable decision-support framework for addressing intricate assignment challenges in uncertain environments.

​Optimality conditions of fuzzy fractional optimization and its application in the problems of energy efficiency optimization

Fuzzy-valued fractional optimization is an important topic in uncertain mathematical programming. It is related to efficiency-oriented decision-making problems in management, economics, and engineering. For example, in communication systems, energy-efficiency optimization in non-orthogonal multiple access systems naturally involves fractional objectives and uncertain parameters. However, optimality conditions for fuzzy-valued fractional optimization problems under granular differentiability have not been sufficiently studied. Therefore, this paper investigates Karush--Kuhn--Tucker (KKT) optimality conditions for fuzzy-valued fractional optimization problems under granular differentiability. First, horizontal membership functions are used to characterize fuzzy numbers and incorporate fuzzy parameters into the fractional optimization framework, providing a parameterized basis for granular analysis. Second, under granular differentiability and convexity assumptions, the relationship between the fuzzy-valued fractional optimization problem (FVFOP) and its associated fuzzy-valued optimization problem (FVOP) is established through a Dinkelbach-type transformation. Based on this relationship, KKT optimality conditions are derived for the original FVFOP. Finally, numerical examples are provided to illustrate the feasibility of the proposed theoretical results. The framework is further applied to energy-efficiency optimization in non-orthogonal multiple access systems and fuel-efficiency optimization in multi-generator systems, showing its potential relevance to efficiency-oriented decision-making under fuzzy uncertainty.

Unsupervised Fuzzy Multi-Objective Optimization for Complex Decision-Making Problems

Many real-world optimization problems involve multiple competing objectives, where the exact weighting is often difficult to define. Traditional fuzzy logic approaches for decision-making, while useful for handling uncertainty, require evaluating all combinations to find the optimal solution. For instance, in logistical scenarios where the optimal location must be determined, fuzzy logic would require evaluating every point on the map, which is time-consuming and computationally expensive. This paper presents an unsupervised neuro-fuzzy optimization model that addresses these problems. Our approach combines a multimodal neural network with differentiable fuzzy objectives for efficient optimization. The model provides robust solutions across various applications, including location selection, network infrastructure, and energy distribution. By leveraging differentiable fuzzy objectives, it can handle complex multi-objective tasks while ensuring high performance and scalability. This method significantly improves traditional optimization techniques and is highly applicable in dynamic, real-time environments.