Interactive fuzzy random cooperative two-level linear programming through level sets based probability maximization

► Cooperative random fuzzy two-level linear programming problems are considered. ► Fuzzy goals are introduced into the formulated two-level programming problems. ► New models are proposed through level sets and stochastic programming. ► Interactive fuzzy nonlinear programming to obtain a satisfactor...

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Bibliographic Details
Published in:Expert systems with applications Vol. 40; no. 4; pp. 1400 - 1406
Main Authors: Sakawa, Masatoshi, Matsui, Takeshi
Format: Journal Article
Language:English
Published: Amsterdam Elsevier Ltd 01.03.2013
Elsevier
Subjects:
Applied sciences
Computer science; control theory; systems
Computer systems and distributed systems. User interface
Decision making
Decision theory. Utility theory
Distribution theory
Exact sciences and technology
Fuzzy
Fuzzy logic
Fuzzy random variables
Fuzzy set theory
Interactive
Interactive decision making
Level sets
Linear programming
Mathematical programming
Mathematics
Maximization
Operational research and scientific management
Operational research. Management science
Probability and statistics
Probability maximization
Programming
Sciences and techniques of general use
Software
Statistics
Two-level linear programming problems
Fuzzy random variables
Two-level linear programming problems
Level sets
Probability maximization
Interactive decision making
Programming environment
Contour line
Set computation
Efficiency
Cooperation
Deterministic approach
Random variable
Judgment
Interactive programming
Probabilistic approach
Decision support system
Decision making
Linear programming
Fuzzy programming
Fuzzy set
Stochastic programming
Fuzzy logic
Linear transformation
Feasibility
Fuzzy decision
Random set
ISSN:0957-4174, 1873-6793
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Summary:► Cooperative random fuzzy two-level linear programming problems are considered. ► Fuzzy goals are introduced into the formulated two-level programming problems. ► New models are proposed through level sets and stochastic programming. ► Interactive fuzzy nonlinear programming to obtain a satisfactory solution is presented. ► An illustrative numerical example demonstrates the feasibility and efficiency of the proposed method. In this paper, assuming cooperative behavior of the decision makers, two-level linear programming problems under fuzzy random environments are considered. To deal with the formulated fuzzy random two-level linear programming problems, 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 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 probability maximization, the transformed stochastic two-level programming problem can be reduced to a deterministic one. Interactive fuzzy programming to derive a satisfactory solution for the decision maker at the upper level in consideration of the cooperative relation between decision makers is presented. An illustrative numerical example is provided to demonstrate the feasibility and efficiency of the proposed method.
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ISSN:0957-4174
1873-6793
DOI:10.1016/j.eswa.2012.08.048