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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Vydáno v:Mathematical and computer modelling Ročník 54; číslo 11; s. 3153 - 3163
Hlavní autoři: Sakawa, Masatoshi, Katagiri, Hideki, Matsui, Takeshi
Médium: Journal Article
Jazyk:angličtina
Vydáno: Kidlington Elsevier Ltd 01.12.2011
Elsevier
Témata:
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
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
ISSN:0895-7177, 1872-9479
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Shrnutí: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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ISSN:0895-7177
1872-9479
DOI:10.1016/j.mcm.2011.08.006