Chapter

Fuzzy Multi-Criteria Decision Making

Volume 16 of the series Springer Optimization and Its Applications pp 375-408

Interactive Fuzzy Multi-Objective Stochastic Linear Programming

  • Masatoshi SakawaAffiliated withDepartment of Artificial Complex Systems Engineering, Graduate School of Engineering, Hiroshima University
  • , Kosuke KatoAffiliated withDepartment of Artificial Complex Systems Engineering, Graduate School of Engineering, Hiroshima University

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Abstract

Two major approaches to deal with randomness or ambiguity involved in mathematical programming problems have been developed. They are stochastic programming approaches and fuzzy programming approaches. In this chapter, we focus on multiobjective linear programming problems with random variable coefficients in objective functions and/or constraints. Using several stochastic models such as an expectation optimization model, a variance minimization model, a probability maximization model, and a fractile criterion optimization model in chance constrained programming, the stochastic programming problems are transformed into deterministic ones. As a fusion of stochastic approaches and fuzzy ones, after determining the fuzzy goals of the decision maker, several interactive fuzzy satisfying methods to derive a satisfying solution for the decision maker by updating the reference membership levels are presented.

Key words

Fuzzy mathematical programming multi-criteria analysis linear programming stochastic programming interactive programming