Geometric programming problem with single-term exponents subject to max-product fuzzy relational equations
In this paper, an optimization model for minimizing an objective function with single-term exponents subject to fuzzy relational equations specified in max-product composition is presented. The solution set of such a fuzzy relational equation is a non-convex set. First, we present some properties fo...
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| Vydáno v: | Mathematical and computer modelling Ročník 53; číslo 1; s. 55 - 62 |
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| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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Kidlington
Elsevier Ltd
2011
Elsevier |
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| ISSN: | 0895-7177, 1872-9479 |
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| Abstract | In this paper, an optimization model for minimizing an objective function with single-term exponents subject to fuzzy relational equations specified in max-product composition is presented. The solution set of such a fuzzy relational equation is a non-convex set. First, we present some properties for the optimization problem under the assumptions of both negative and nonnegative exponents in the objective function. Second, an efficient procedure is developed to find an optimal solution without looking for all the potential minimal solutions and without using the value matrix. An example is provided to illustrate the procedure. |
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| AbstractList | In this paper, an optimization model for minimizing an objective function with single-term exponents subject to fuzzy relational equations specified in max-product composition is presented. The solution set of such a fuzzy relational equation is a non-convex set. First, we present some properties for the optimization problem under the assumptions of both negative and nonnegative exponents in the objective function. Second, an efficient procedure is developed to find an optimal solution without looking for all the potential minimal solutions and without using the value matrix. An example is provided to illustrate the procedure. |
| Author | Ahat, Rashida Zhou, XueGang |
| Author_xml | – sequence: 1 givenname: XueGang surname: Zhou fullname: Zhou, XueGang email: xgzhou@yahoo.cn organization: Department of Applied Mathematics, GuangDong University of Finance, Guangzhou, Guangdong, 510521, China – sequence: 2 givenname: Rashida surname: Ahat fullname: Ahat, Rashida organization: School of Mathematics and System Science of Xinjiang University, Wulumuqi, Xinjiang, 830046, China |
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| Keywords | Fuzzy relational equations Fuzzy optimization Max-product composition Geometric programming Convex set Optimization method Numerical analysis Applied mathematics Optimal solution Variational calculus Mathematical model Computer aided analysis Mathematical programming |
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| SubjectTerms | Calculus of variations and optimal control Convex and discrete geometry equations Exact sciences and technology Fuzzy optimization Fuzzy relational equations Geometric programming Geometry Mathematical analysis Mathematics Max-product composition Methods of scientific computing (including symbolic computation, algebraic computation) Numerical analysis Numerical analysis. Scientific computation Numerical methods in mathematical programming, optimization and calculus of variations Numerical methods in optimization and calculus of variations Sciences and techniques of general use system optimization |
| Title | Geometric programming problem with single-term exponents subject to max-product fuzzy relational equations |
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