scholarly journals A Multi-Level Multi-Objective Quadratic Programming Problem with Fuzzy Parameters on Objective Functions

2016 ◽  
Vol 15 (5) ◽  
pp. 6738-6748 ◽  
Author(s):  
Usama Emam
Keyword(s):  
Quadratic Programming ◽  
Programming Problem ◽  
Decision Model ◽  
Fuzzy Numbers ◽  
Quadratic Programming Problem ◽  
Objective Functions ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Multi Level ◽  
Fuzzy Parameters

This paper proposes an algorithm to solve multi-level multi-objective quadratic programming problem with fuzzy parameters in the objective functions, This algorithm uses the tolerance membership function concepts and multi-objective optimization at each level to develop a fuzzy Max-Min decision model for generating satisfactory solution after applying linear ranking method on trapezoidal fuzzy numbers in the objective functions, An illustrative example is included to explain the results.

scholarly journals TOPSIS Based Algorithm for Solving Multi-objective Multi-level Programming Problem with Fuzzy Parameters

2018 ◽  
Author(s):  
Surapati Pramanik ◽  
Partha P. Dey ◽  
Florentin Smarandache
Keyword(s):  
Programming Problem ◽  
Optimal Solution ◽  
Distance Functions ◽  
Ideal Solution ◽  
Multi Objective ◽  
Cut Method ◽  
Multi Level ◽  
Compromise Optimal Solution ◽  
Negative Ideal Solution ◽  
Fuzzy Parameters

The paper proposes TOPSIS method for solving multi-objective multi-level programming problem (MO-MLPP) with fuzzy parameters via fuzzy goal programming (FGP). At first, - cut method is used to transform the fuzzily described MO-MLPP into deterministic MO-MLPP. Then, for specific , we construct the membership functions of distance functions from positive ideal solution (PIS) and negative ideal solution (NIS) of all level decision makers (DMs). Thereafter, FGP based multi-objective decision model is established for each level DM for obtaining individual optimal solution. A possible relaxation on decisions for all DMs is taken into account for satisfactory solution. Subsequently, two FGP models are developed and compromise optimal solutions are found by minimizing the sum of negative deviational variables. To recognize the better compromise optimal solution, the concept of distance functions is utilized. Finally, a novel algorithm for MO-MLPP involving fuzzy parameters is provided and an illustrative example is solved to verify the proposed procedure.

Interactive α-satisfactory method for multi-objective optimization with fuzzy parameters and linguistic preference

2020 ◽  
pp. 1-16
Author(s):  
Chaofang Hu ◽  
Yuting Zhang
Keyword(s):  
Optimization Problem ◽  
Original Problem ◽  
Fuzzy Numbers ◽  
Test Model ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Satisfactory Method ◽  
Domain Of Parameters ◽  
Α Level ◽  
Fuzzy Parameters

 An interactive α-satisfactory method via relaxed order of desirable α-satisfactory degrees is proposed for multi-objective optimization with fuzzy parameters and linguistic preference in this paper. Fuzzy parameters existing in objectives and constraints of multi-objective optimization are defined as fuzzy numbers and α-level set is used to build the feasible domain of parameters. On the basis, the original problem with fuzzy parameters is transformed into multi-objective optimization with fuzzy goals. Linguistic preference of decision-maker is modelled by the relaxed order of desirable α-satisfactory degrees of all the objectives. In order to achieve a compromise between optimization and preference, the multi-objective optimization problem is divided into two single-objective sub-problems: the preliminary optimization and the linguistic preference optimization. A preferred solution can be found by parameter adjustment of inner-outer loop. The minimum stable relaxation algorithm of parameter is developed for calculating the relaxation bound of maximum desirable satisfaction difference. The M-α-Pareto optimality of solution is guaranteed by the test model. The effectiveness, flexibility and sensitivity of the proposed method are well demonstrated by numerical example and application example to heat conduction system.

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