Fuzzy Goal Programming Procedures for Multi-Level Multi-Objective Linear Fractional Programming Problems

This paper presents a fuzzy goal programming (FGP) procedure for solving bilevel multiobjective linear fractional programming (BL-MOLFP) problems. It makes an extension work of Moitra and Pal (2002) and Pal et al. (2003). In the proposed procedure, the membership functions for the defined fuzzy goals of the decision makers (DMs) objective functions at both levels as well as the membership functions for vector of fuzzy goals of the decision variables controlled by first-level decision maker are developed first in the model formulation of the problem. Then a fuzzy goal programming model to minimize the group regret of degree of satisfactions of both the decision makers is developed to achieve the highest degree (unity) of each of the defined membership function goals to the extent possible by minimizing their deviational variables and thereby obtaining the most satisfactory solution for both decision makers. The method of variable change on the under- and over-deviational variables of the membership goals associated with the fuzzy goals of the model is introduced to solve the problem efficiently by using linear goal programming (LGP) methodology. Illustrative numerical example is given to demonstrate the procedure.

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Interactive Fuzzy Goal Programming Based on Jacobian Matrix to Solve Decentralized Bi-level Multi-objective Fractional Programming Problems

International Journal of Fuzzy Systems ◽

10.1007/s40815-015-0036-1 ◽

2015 ◽

Vol 17 (4) ◽

pp. 499-508 ◽

Cited By ~ 13

Author(s):

M. Duran Toksarı ◽

Yasemin Bilim

Keyword(s):

Goal Programming ◽

Fractional Programming ◽

Jacobian Matrix ◽

Fuzzy Goal Programming ◽

Multi Objective ◽

Fuzzy Goal ◽

Interactive Fuzzy Goal Programming

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Solving multi-level multiobjective fractional programming problem with rough interval parameter under neutrosophic environment

RAIRO - Operations Research ◽

10.1051/ro/2021108 ◽

2021 ◽

Author(s):

FIROZ AHMAD

Keyword(s):

Goal Programming ◽

Fractional Programming ◽

Optimal Solution ◽

Fuzzy Goal Programming ◽

Programming Algorithm ◽

Objective Functions ◽

Multiobjective Fractional Programming ◽

Upper Approximation ◽

Fuzzy Goal ◽

Multi Level

In this study, a novel algorithm is developed to solve the multi-level multiobjective fractional programming problems, using the idea of a neutrosophic fuzzy set. The co-efficients in each objective functions is assumed to be rough intervals. Furthermore, the objective functions are transformed into two sub-problems based on lower and upper approximation intervals. The marginal evaluation of pre-determined neutrosophic fuzzy goals for all objective functions at each level is achieved by different membership functions, such as truth, indeterminacy/neutral, and falsity degrees in neutrosophic uncertainty. In addition, the neutrosophic fuzzy goal programming algorithm is proposed to attain the highest degrees of each marginal evaluation goals by reducing their deviational variables and consequently obtain the optimal solution for all the decision-makers at all levels. To verify and validate the proposed neutrosophic fuzzy goal programming techniques, a numerical example is adressed in a hierarchical decision-making environment along with the conclusions.

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