Fuzzy Set Based Models in Design Optimization

1988 ◽  
Author(s):  
A. R. Diaz
Keyword(s):  
Multiobjective Optimization ◽  
Design Optimization ◽  
Fuzzy Sets ◽  
Engineering Design ◽  
Goal Programming ◽  
Fuzzy Set ◽  
Optimization Problem ◽  
Traditional Methods ◽  
Multiobjective Problems

Abstract A formulation for multiobjective optimization for engineering design based on fuzzy sets is presented. Models for the optimization problem and operations to introduce model variations are described formally. Under a reasonable set of rules it is shown that solutions to fuzzy multiobjective problems are weakly efficient and can reproduce solutions obtained by traditional methods such as compromise and goal programming. Results are easily implemented in computations.

Multiobjective Optimization Dealing With Uncertainty

1989 ◽  
Author(s):  
S. U. Mohandas ◽  
E. Sandgren
Keyword(s):  
Multiobjective Optimization ◽  
Natural Language ◽  
Design Optimization ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Optimization Problem ◽  
Objective Functions ◽  
Fuzzy Goals ◽  
Box Method ◽  
Multiobjective Design

Abstract An algorithm to handle uncertainty in a multiobjective design optimization problem is developed. The procedure is applied to three examples where objective functions in each of them compete against each other. The uncertainty in the description of objective functions is modeled by using fuzzy goals and the terms of natural language. Multiobjective function is formulated as a fuzzy set. The minimization is carried out using a combination of the Complex Box method and a technique of ranking of fuzzy sets.

Complex intuitionistic fuzzy Maclaurin symmetric mean operators and its application to emergency program selection

2021 ◽  
pp. 1-22
Author(s):  
Riaz Ali ◽  
Saleem Abdullah ◽  
Shakoor Muhammad ◽  
Muhammad Naeem ◽  
Ronnason Chinram
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Score Functions ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Program Selection ◽  
Maclaurin Symmetric Mean ◽  
Complex Intuitionistic Fuzzy Set

Due to the indeterminacy and uncertainty of the decision-makers (DM) in the complex decision making problems of daily life, evaluation and aggregation of the information usually becomes a complicated task. In literature many theories and fuzzy sets (FS) are presented for the evaluation of these decision tasks, but most of these theories and fuzzy sets have failed to explain the uncertainty and vagueness in the decision making issues. Therefore, we use complex intuitionistic fuzzy set (CIFS) instead of fuzzy set and intuitionistic fuzzy set (IFS). A new type of aggregation operation is also developed by the use of complex intuitionistic fuzzy numbers (CIFNs), their accuracy and the score functions are also discussed in detail. Moreover, we utilized the Maclaurin symmetric mean (MSM) operator, which have the ability to capture the relationship among multi-input arguments, as a result, CIF Maclarurin symmetric mean (CIFMSM) operator and CIF dual Maclaurin symmetric mean (CIFDMSM) operator are presented and their characteristics are discussed in detail. On the basis of these operators, a MAGDM method is presented for the solution of group decision making problems. Finally, the validation of the propounded approach is proved by evaluating a numerical example, and by the comparison with the previously researched results.

Adaptive Complex Method for Efficient Design Optimization

2007 ◽  
Author(s):  
Marcus Pettersson ◽  
Johan O¨lvander
Keyword(s):  
Design Optimization ◽  
Optimization Problem ◽  
Global Optimum ◽  
Direct Search ◽  
Complex Method ◽  
Efficient Design ◽  
Direct Search Methods ◽  
Simulation Based ◽  
Set Of Points ◽  
Quasi Newton

Box’s Complex method for direct search has shown promise when applied to simulation based optimization. In direct search methods, like Box’s Complex method, the search starts with a set of points, where each point is a solution to the optimization problem. In the Complex method the number of points must be at least one plus the number of variables. However, in order to avoid premature termination and increase the likelihood of finding the global optimum more points are often used at the expense of the required number of evaluations. The idea in this paper is to gradually remove points during the optimization in order to achieve an adaptive Complex method for more efficient design optimization. The proposed method shows encouraging results when compared to the Complex method with fix number of points and a quasi-Newton method.

Multi-criteria decision making and pattern recognition based on similarity measures for Fermatean fuzzy sets

2021 ◽  
pp. 1-17
Author(s):  
Changlin Xu ◽  
Juhong Shen
Keyword(s):  
Decision Making ◽  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Medical Diagnosis ◽  
Intuitionistic Fuzzy Set ◽  
Similarity Measures ◽  
New Method ◽  
Fuzzy Decision Making ◽  
Multi Criteria Decision Making

 Higher-order fuzzy decision-making methods have become powerful tools to support decision-makers in solving their problems effectively by reflecting uncertainty in calculations better than crisp sets in the last 3 decades. Fermatean fuzzy set proposed by Senapati and Yager, which can easily process uncertain information in decision making, pattern recognition, medical diagnosis et al., is extension of intuitionistic fuzzy set and Pythagorean fuzzy set by relaxing the restraint conditions of the support for degrees and support against degrees. In this paper, we focus on the similarity measures of Fermatean fuzzy sets. The definitions of the Fermatean fuzzy sets similarity measures and its weighted similarity measures on discrete and continuous universes are given in turn. Then, the basic properties of the presented similarity measures are discussed. Afterward, a decision-making process under the Fermatean fuzzy environment based on TOPSIS method is established, and a new method based on the proposed Fermatean fuzzy sets similarity measures is designed to solve the problems of medical diagnosis. Ultimately, an interpretative multi-criteria decision making example and two medical diagnosis examples are provided to demonstrate the viability and effectiveness of the proposed method. Through comparing the different methods in the multi-criteria decision making and the medical diagnosis application, it is found that the new method is as efficient as the other methods. These results illustrate that the proposed method is practical in dealing with the decision making problems and medical diagnosis problems.

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