FGP Approach Based on Stanojevic’s Normalization Technique for Multi-level Multi-objective Linear Fractional Programming Problem with Fuzzy Parameters (original) (raw)
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Multilevel fractional programming problem based on fuzzy goal programming
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International Journal of Applied Mathematical Research, 2012
This paper presents a fuzzy goal programming (FGP) methodology for solving bi-level quadratic programming (BLQP) problems. In the FGP model formulation, firstly the objectives are transformed into fuzzy goals (membership functions) by means of assigning an aspiration level to each of them, and suitable membership function is defined for each objectives, and also the membership functions for vector of fuzzy goals of the decision variables controlled by decision maker at the first level are developed in the model formulation of the problem. To achieve the highest membership value of each of the fuzzy goals, we formulate the problem by minimizing the negative deviational variables and thereby obtaining the most satisfactory solution for all decision makers. A numerical example is given to demonstrate the proposed approach.
_______________________________________________________________________________ Abstract The motivation behind this paper is to present multi-level multi-objective quadratic fractional programming (ML-MOQFP) problem with fuzzy parameters in the constraints. ML-MOQFP problem is an important class of non-linear fractional programming problem. These type of problems arise in many fields such as production planning, financial and corporative planning, health care and hospital planning. Firstly, the concept of the-cut and fuzzy partial order relation are applied to transform the set of fuzzy constraints into a common crisp set. Then, the quadratic fractional objective functions in each level are transformed into non-linear objective functions based on a proposed transformation. Secondly, in the proposed model, separate non-linear membership functions for each objective function of the ML-MOQFP problem are defined. Then, the fuzzy goal programming (FGP) approach is utilized to obtain a compromise solution for the ML-MOQFP problem by minimizing the sum of the negative deviational variables. Finally, an illustrative numerical example is given to demonstrate the applicability and performance of the proposed approach.
• MULTI-OBJECTIVE LINEAR FRACTIONAL PROGRAMMING PROBLEM BASED ON FUZZY GOAL PROGRAMMING
International Journal of Mathematical Archive ( …, 2011
This paper presents fuzzy goal programming approach for solving multi-objective linear fractional programming problem with multiple linear fractional objective functions. To construct the fractional membership functions, optimal solution of the objective functions are determined subject to the system constraints. The fractional membership functions are transformed into linear membership functions by first order Taylor series approximation. Then fuzzy goal programming approach is used to obtain highest degree of each of membership goals by minimizing negative deviational variables. A numerical example is solved to demonstrate the efficiency of the proposed approach.
Priority Based Fuzzy Goal Programming Approach for Fractional Multilevel Programming Problems
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Goal programming problems are applied in an increasing variety of practical fields. As ambiguity and vagueness are natural and ever-present in real-life situations requiring solutions, it makes perfect sense to attempt to address them using fuzzy fractional programming problems. This paper presents a goal programming (GP) technique for fuzzy multi-objective linear fractional programming (FMOLFP) problems. In the proposed approach, we formulate a GP model for achievement of the highest membership value of each of fuzzy goals defined for the fractional objectives, using trapezoidal membership function. We introduce the method of variable change on the under- and over-deviational variables of the membership goals associated with the fuzzy goals to solve the problem efficiently by using linear goal programming (LGP) methodology. A few numerical examples are presented to illustrate the proposed method
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This paper presents a goal programming (GP) procedure for fuzzy multi objective linear fractional programming (MOLFP) problems under vague environment using tolerance limit. In the proposed approach, which is motivated by Mohamed (Fuzzy Sets and System 89 (1997) 215), GP model for achievement of the highest membership value of each of fuzzy, goals defined for the fractional objectives is formulated. In the solution process, the method of variable change under tolerance limit of the membership and non membership goal associated with the fuzzy goal of the model is introduced to solve the problem efficiently by using linear goal programming (LGP) methodology. The approach is illustrated by one numerical example.
Multi-level Multi-objective Linear plus Linear Fractional Programming Problem Based on FGP Approach
In the paper, multi- level multi-objective linear plus linear fractional programming problem is presented. The objective functions of level decision makers are characterized by linear plus linear fractional form of decision variables. Linear system constraints are considered. Each level decision maker possesses more than one objective functions. Membership function for each objective function is constructed by taking individual best solution of each objective function as aspiration level. The nonlinear membership functions are transformed into linear membership functions by using first order Taylor’s series. Three FGP models are developed to solve the converted multi-objective multi- level problems with linear constraints. Euclidean distance function is used to select the best compromise solution. A numerical example is solved to illustrate the proposed approach.