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Numerous optimization problems comprise uncertain data in practical circumstances and such uncertainty can be suitably addressed using the concept of fuzzy logic. This pafa proposes a computationally efficient solution methodology to generate a set of fuzzy non-dominated solutions of a fully fuzzy multi-objective linear programming problem, which incorporates all its parameters and decision variables expressed in form of triangular fuzzy numbers. The fuzzy parameters associated with the objective functions are transformed into interval forms by utilizing the fuzzy-cuts, which subsequently generates the equivalent interval valued objective functions. The concept of centroid of triangular fuzzy numbers derives the deterministic form of the constraints. Furthermore, the scalarization process of weighting sum approach and certain concepts of interval analysis are used to generate the fuzzy non-dominated solutions from which the compromise solution can be determined based on the corresponding real valued expressions of fuzzy optimal objective values resulted due to the ranking function. Three numerical problems and one practical problem are solved for illustration and validation of the proposed approach. The computational results are also discussed as compared to some existing methods. [ABSTRACT FROM AUTHOR]

Numerous optimization problems comprise uncertain data in practical circumstances and such uncertainty can be suitably addressed using the concept of fuzzy logic. This paper proposes a computationally efficient solution methodology to generate a set of fuzzy non-dominated solutions of a fully fuzzy multi-objective linear programming problem, which incorporates all its parameters and decision variables expressed in form of triangular fuzzy numbers. The fuzzy parameters associated with the objective functions are transformed into interval forms by utilizing the fuzzy-cuts, which subsequently generates the equivalent interval valued objective functions. The concept of centroid of triangular fuzzy numbers derives the deterministic form of the constraints. Furthermore, the scalarization process of weighting sum approach and certain concepts of interval analysis are used to generate the fuzzy non-dominated solutions from which the compromise solution can be determined based on the corresponding real valued expressions of fuzzy optimal objective values resulted due to the ranking function. Three numerical problems and one practical problem are solved for illustration and validation of the proposed approach. The computational results are also discussed as compared to some existing methods.

Decision making problems with ambiguous data often arise in numerous practical fields which can be formulated as optimization models in fuzzy environment. This paper develops a new mathematical model using a proposed methodology to efficiently solve a multi-objective linear fuzzy fractional programming problem in trapezoidal fuzzy environment and generate a set of nondominated solutions. The concept of fuzzy cuts with different degrees of satisfaction is implemented which transforms the fuzzy optimization into an equivalent interval valued optimization. Subsequently, interval valued linear functions approximate the fuzzy valued fractional functions based on Taylor's series expansion. Finally, a proposed concept using weighting sum approach with varying weight vectors is utilized to design a mathematical model which generates the set of nondominated solutions. Two numerical examples including an existing problem and an additional practical problem in the field of production, are solved for the illustration of the proposed model. The results of the numerical problems are comparatively discussed with graphical analysis to justify the feasibility and applicability of the proposed model. [ABSTRACT FROM AUTHOR]