A Smoothing Approach for Minimizing A Linear Function Subject to Fuzzy Relation Inequalities with Addition–Min Composition

This paper mainly focuses on minimizing a linear function subject to fuzzy relation inequalities with addition–min composition. Although the problem has been proved to be equivalent to a linear programming, it is still difficult to efficiently solve when the numbers of constrains and variables come...

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Published inInternational journal of fuzzy systems Vol. 21; no. 1; pp. 281 - 290
Main Authors Guo, Fang-Fang, Shen, Jie
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2019
Springer Nature B.V
Subjects
Approximation
Artificial Intelligence
Cluster analysis
Composition
Computational Intelligence
Engineering
Fuzzy sets
Inequalities
Linear functions
Linear programming
Management Science
Maximum entropy method
Operations Research
Smoothing
Smoothing approximation
Addition–min composition
Optimization
Fuzzy relation inequality
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Abstract This paper mainly focuses on minimizing a linear function subject to fuzzy relation inequalities with addition–min composition. Although the problem has been proved to be equivalent to a linear programming, it is still difficult to efficiently solve when the numbers of constrains and variables come to about 200. In this paper, we devotes to constructing a smoothing approach for solving approximate solutions of the problem. Utilizing maximum entropy method, we approximate the constraints by continuously differentiable functions and prove that any cluster of an approximate solution sequence is an optimal point of the original problem. Numerical experiments show that the error of the approximate solutions is within a reasonable range. At the same time, compared to the linear programming approach, the smoothing approach costs much less computation time, especially for large-scale problems.
AbstractList This paper mainly focuses on minimizing a linear function subject to fuzzy relation inequalities with addition–min composition. Although the problem has been proved to be equivalent to a linear programming, it is still difficult to efficiently solve when the numbers of constrains and variables come to about 200. In this paper, we devotes to constructing a smoothing approach for solving approximate solutions of the problem. Utilizing maximum entropy method, we approximate the constraints by continuously differentiable functions and prove that any cluster of an approximate solution sequence is an optimal point of the original problem. Numerical experiments show that the error of the approximate solutions is within a reasonable range. At the same time, compared to the linear programming approach, the smoothing approach costs much less computation time, especially for large-scale problems.
Author Guo, Fang-Fang
Shen, Jie
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  givenname: Jie
  surname: Shen
  fullname: Shen, Jie
  organization: School of Mathematics, Liaoning Normal University
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Keywords Smoothing approximation
Addition–min composition
Optimization
Fuzzy relation inequality
Language English
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Snippet This paper mainly focuses on minimizing a linear function subject to fuzzy relation inequalities with addition–min composition. Although the problem has been...
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SubjectTerms Approximation
Artificial Intelligence
Cluster analysis
Composition
Computational Intelligence
Engineering
Fuzzy sets
Inequalities
Linear functions
Linear programming
Management Science
Maximum entropy method
Operations Research
Smoothing
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Title A Smoothing Approach for Minimizing A Linear Function Subject to Fuzzy Relation Inequalities with Addition–Min Composition
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