[Paper Review] Hybrid Fuzzy-Linear Programming Approach for Multi Criteria Decision Making Problems

Sonja Yrjo Olavi Petrovic-Lazarevic, Ajith Abraham|ArXiv.org|May 5, 2004

Multi-Criteria Decision MakingDecision Sciences16 references20 citations

TL;DR

This paper proposes a hybrid fuzzy-linear programming approach to solve multi-criteria decision-making problems in manufacturing by modeling fuzzy parameters through preference-based membership functions. The method integrates fuzzy set theory with linear programming, demonstrating through a real case study that fuzzy optimization achieves superior or comparable satisfaction levels compared to non-fuzzy linear programming, particularly in balancing conflicting objectives under uncertainty.

ABSTRACT

The purpose of this paper is to point to the usefulness of applying a linear mathematical formulation of fuzzy multiple criteria objective decision methods in organising business activities. In this respect fuzzy parameters of linear programming are modelled by preference-based membership functions. This paper begins with an introduction and some related research followed by some fundamentals of fuzzy set theory and technical concepts of fuzzy multiple objective decision models. Further a real case study of a manufacturing plant and the implementation of the proposed technique is presented. Empirical results clearly show the superiority of the fuzzy technique in optimising individual objective functions when compared to non-fuzzy approach. Furthermore, for the problem considered, the optimal solution helps to infer that by incorporating fuzziness in a linear programming model either in constraints, or both in objective functions and constraints, provides a similar (or even better) level of satisfaction for obtained results compared to non-fuzzy linear programming.

Motivation & Objective

• To develop a practical decision-making framework for business and manufacturing systems under uncertainty.
• To address the limitations of traditional linear programming in handling imprecise or subjective objectives and constraints.
• To integrate fuzzy set theory with linear programming for improved flexibility in multi-objective optimization.
• To validate the proposed method using a real-world manufacturing case study.
• To demonstrate the superiority of fuzzy linear programming in achieving balanced, satisfactory solutions across multiple conflicting criteria.

Proposed method

• Fuzzy parameters in linear programming are modeled using preference-based membership functions to represent decision-makers' subjective judgments.
• The fuzzy multi-objective model transforms crisp objectives and constraints into fuzzy sets with membership degrees.
• A hybrid approach combines fuzzy set theory with linear programming techniques to optimize the degree of satisfaction across multiple objectives.
• The model is solved by converting the fuzzy problem into a crisp linear program using a weighted aggregation or max-min approach.
• The solution process incorporates decision-maker preferences through membership function design, reflecting trade-offs between objectives.
• The method is implemented and tested on a real manufacturing plant case study involving production planning and resource allocation.

Experimental results

Research questions

• RQ1 How can fuzzy set theory be effectively integrated into linear programming to handle uncertainty in multi-criteria decision-making?
• RQ2 What is the impact of incorporating fuzziness in objective functions and constraints on solution quality and decision satisfaction?
• RQ3 How does the proposed hybrid approach compare to classical non-fuzzy linear programming in real-world applications?
• RQ4 Can fuzzy linear programming achieve better or comparable satisfaction levels across multiple conflicting objectives?
• RQ5 To what extent does the use of preference-based membership functions improve the practicality of optimization models in manufacturing?

Key findings

• The fuzzy linear programming approach achieved higher or equivalent satisfaction levels compared to non-fuzzy linear programming in the case study.
• Incorporating fuzziness in both objective functions and constraints led to more balanced and practical solutions.
• The method effectively handled conflicting objectives such as cost minimization and production efficiency in a real manufacturing environment.
• Empirical results confirmed that the fuzzy model provides a more flexible and realistic framework for decision-making under uncertainty.
• The proposed technique demonstrated robustness and adaptability in real-world implementation, supporting better managerial decisions.
• The study confirmed that fuzzy modeling enhances the interpretability and applicability of linear programming in complex, multi-criteria settings.