Interactive fuzzy random two-level linear programming through fractile criterion optimization
In this paper, assuming cooperative behavior of the decision makers, solution methods for decision making problems in hierarchical organizations under fuzzy random environments are considered. To deal with the formulated two-level linear programming problems involving fuzzy random variables, α -leve...
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| Published in: | Mathematical and computer modelling Vol. 54; no. 11; pp. 3153 - 3163 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
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Elsevier Ltd
01.12.2011
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| ISSN: | 0895-7177, 1872-9479 |
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| Abstract | In this paper, assuming cooperative behavior of the decision makers, solution methods for decision making problems in hierarchical organizations under fuzzy random environments are considered. To deal with the formulated two-level linear programming problems involving fuzzy random variables,
α
-level sets of fuzzy random variables are introduced and an
α
-stochastic two-level linear programming problem is defined for guaranteeing the degree of realization of the problem. Taking into account the vagueness of judgments of decision makers, fuzzy goals are introduced and the
α
-stochastic two-level linear programming problem is transformed into the problem to maximize the satisfaction degree for each fuzzy goal. Through the use of the fractile criterion optimization model, the transformed stochastic two-level programming problem can be reduced to a deterministic one. Interactive fuzzy programming to obtain a satisfactory solution for the decision maker at the upper level in consideration of the cooperative relation between decision makers is presented. It is shown that all of the problems to be solved in the proposed interactive fuzzy programming can be easily solved by the simplex method, the sequential quadratic programming or the combined use of the bisection method and the sequential quadratic programming. An illustrative numerical example is provided to demonstrate the feasibility and efficiency of the proposed method. |
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| AbstractList | In this paper, assuming cooperative behavior of the decision makers, solution methods for decision making problems in hierarchical organizations under fuzzy random environments are considered. To deal with the formulated two-level linear programming problems involving fuzzy random variables, α-level sets of fuzzy random variables are introduced and an α-stochastic two-level linear programming problem is defined for guaranteeing the degree of realization of the problem. Taking into account the vagueness of judgments of decision makers, fuzzy goals are introduced and the α-stochastic two-level linear programming problem is transformed into the problem to maximize the satisfaction degree for each fuzzy goal. Through the use of the fractile criterion optimization model, the transformed stochastic two-level programming problem can be reduced to a deterministic one. Interactive fuzzy programming to obtain a satisfactory solution for the decision maker at the upper level in consideration of the cooperative relation between decision makers is presented. It is shown that all of the problems to be solved in the proposed interactive fuzzy programming can be easily solved by the simplex method, the sequential quadratic programming or the combined use of the bisection method and the sequential quadratic programming. An illustrative numerical example is provided to demonstrate the feasibility and efficiency of the proposed method. In this paper, assuming cooperative behavior of the decision makers, solution methods for decision making problems in hierarchical organizations under fuzzy random environments are considered. To deal with the formulated two-level linear programming problems involving fuzzy random variables, α -level sets of fuzzy random variables are introduced and an α -stochastic two-level linear programming problem is defined for guaranteeing the degree of realization of the problem. Taking into account the vagueness of judgments of decision makers, fuzzy goals are introduced and the α -stochastic two-level linear programming problem is transformed into the problem to maximize the satisfaction degree for each fuzzy goal. Through the use of the fractile criterion optimization model, the transformed stochastic two-level programming problem can be reduced to a deterministic one. Interactive fuzzy programming to obtain a satisfactory solution for the decision maker at the upper level in consideration of the cooperative relation between decision makers is presented. It is shown that all of the problems to be solved in the proposed interactive fuzzy programming can be easily solved by the simplex method, the sequential quadratic programming or the combined use of the bisection method and the sequential quadratic programming. An illustrative numerical example is provided to demonstrate the feasibility and efficiency of the proposed method. |
| Author | Matsui, Takeshi Sakawa, Masatoshi Katagiri, Hideki |
| Author_xml | – sequence: 1 givenname: Masatoshi surname: Sakawa fullname: Sakawa, Masatoshi email: sakawa@hiroshima-u.ac.jp – sequence: 2 givenname: Hideki surname: Katagiri fullname: Katagiri, Hideki email: katagiri-h@hiroshima-u.ac.jp – sequence: 3 givenname: Takeshi surname: Matsui fullname: Matsui, Takeshi email: tak-matsui@hiroshima-u.ac.jp |
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| Keywords | Fractile criterion optimization Level set Two-level linear programming problem Interactive decision making Gaussian distribution Fuzzy random variable Fuzzy mathematical programming Stochastic model Decision making Optimization method Linear programming Quadratic programming Stochastic programming Numerical analysis Applied mathematics Sequential method Simplex method Optimality criterion Mathematical model Random variable Computer aided analysis Mathematical programming |
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| SubjectTerms | decision making Exact sciences and technology Fractile criterion optimization Fuzzy mathematical programming Fuzzy random variable Gaussian distribution Interactive decision making Level set linear programming Mathematical analysis Mathematics Methods of scientific computing (including symbolic computation, algebraic computation) Numerical analysis Numerical analysis. Scientific computation Numerical methods in mathematical programming Numerical methods in mathematical programming, optimization and calculus of variations Sciences and techniques of general use Two-level linear programming problem |
| Title | Interactive fuzzy random two-level linear programming through fractile criterion optimization |
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