scholarly journals Enhanced Two-Step Method via Relaxed Order ofα-Satisfactory Degrees for Fuzzy Multiobjective Optimization

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Na Wang ◽  
Chaofang Hu ◽  
Wuxi Shi ◽  
Chunbo Xiu ◽  
Yimei Chen
Keyword(s):  
Multiobjective Optimization ◽  
Set Theory ◽  
Optimization Problem ◽  
Fuzzy Numbers ◽  
Fuzzy Relations ◽  
Preemptive Priority ◽  
Step Method ◽  
Satisfactory Solution ◽  
Order Constraint ◽  
Fuzzy Parameters

An enhanced two-step method via relaxed order of satisfactory degrees for fuzzy multiobjective optimization is proposed in this paper. By introducing the concept of fuzzy numbers andα-level set theory, fuzzy parameters are taken as variables, and all the objectives are transformed into fuzzy goals involving three fuzzy relations. The order ofα-satisfactory degrees which means the objectives with higher priority achieving higher satisfactory degree is applied to model preemptive priority requirement. This strict order constraint is relaxed by priority variable to find the preferred solution satisfying optimization and priority. The original optimization problem is divided into two steps to be solved iteratively. The M-α-Pareto optimality of the solution is ensured, and the satisfactory solution can be acquired by regulating the slack parameterΔδor changingα. The numerical examples demonstrate the power of the proposed method.

ENHANCED INTERACTIVE SATISFYING OPTIMIZATION APPROACH TO MULTIPLE OBJECTIVE OPTIMIZATION WITH PREEMPTIVE PRIORITIES

2006 ◽  
Vol 05 (01) ◽  
pp. 47-63 ◽  
Author(s):  
CHAOFANG HU ◽  
SHAOYUAN LI
Keyword(s):  
Optimization Problem ◽  
Optimization Method ◽  
Previous Method ◽  
Optimization Models ◽  
Multiple Objective ◽  
Multiple Objective Optimization ◽  
Optimization Approach ◽  
Fuzzy Relations ◽  
Objective Functions ◽  
Preemptive Priority

This paper proposes an enhanced interactive satisfying optimization method based on goal programming for the multiple objective optimization problem with preemptive priorities. Based on the previous method, the approach presented makes the higher priority achieve the higher satisfying degree. For three fuzzy relations of the objective functions, the corresponding optimization models are proposed. Not only can satisfying results for all the objectives be acquired, but the preemptive priority requirement can also be simultaneously actualized. The balance between optimization and priorities is realized. We demonstrate the power of this proposed method by illustrative examples.

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.

A Study on Cooperative Continuous Static Games without Differentiability under Fuzzy Environment

2022 ◽  
Vol 11 (1) ◽  
pp. 0-0
Keyword(s):  
Fuzzy Numbers ◽  
Optimal Solution ◽  
Solution Concept ◽  
Proper Understanding ◽  
Fuzzy Environment ◽  
The Stability ◽  
The Right ◽  
The Cost ◽  
Stability Sets ◽  
Fuzzy Parameters

In this study, a fuzzy cooperative continuous static game (PQFCCSG) with n players having fuzzy parameters in all of the cost functions and the right- hand-side of constraints is characterized. Their fuzzy parameters are represented by piecewise quadratic fuzzy numbers. The α-pareto optimal solution concept is specified. In addition, the stability sets of the first and second kind without differentiability are conceptualized and established. An illustrated numerical example is discussed for proper understanding and interpretation of the proposed concept.

Multi-objective Portfolio Optimization Problem with Trapezoidal Fuzzy Parameters

2021 ◽  
pp. 281-293
Author(s):  
Claudia Guadalupe Gómez-Santillán ◽  
Alejandro Estrada Padilla ◽  
Héctor Fraire-Huacuja ◽  
Laura Cruz-Reyes ◽  
Nelson Rangel-Valdez ◽  
...  
Keyword(s):  
Portfolio Optimization ◽  
Optimization Problem ◽  
Multi Objective ◽  
Portfolio Optimization Problem ◽  
Fuzzy Parameters
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