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**A cooperative fuzzy game theoretic approach to multiple objective design optimization.**
*(English)*
Zbl 0901.90136

Summary: The utility and applicability of cooperative game theory in an engineering design process is examined. It is shown how game theory may be used as a tool for solving multiple objective optimization (MOO) problems. The concepts in cooperative game theory and fuzzy set theory are combined to yield a new optimization method referred to herein as cooperative fuzzy games. The concept of cooperative fuzzy games can be applied to solve not only well- and ill-structured single and MOO problems, but also preliminary decision making and design problems where only a feasible solution is sought and no objective functions are specified. A completely general formulation capable of solving decision making problems with partly crisp and partly fuzzy objective functions, as well as partly crisp and partly fuzzy constraints is presented. It is shown that existing techniques for solving crisp and fuzzy mathematical programming problems are special cases of this general formulation. The computational procedure is illustrated via an application to an MOO problem dealing with the design of high speed mechanisms.

### MSC:

90B50 | Management decision making, including multiple objectives |

91A80 | Applications of game theory |

91A12 | Cooperative games |

### Keywords:

cooperative game theory; engineering design process; multiple objective optimization; fuzzy set theory
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\textit{A. K. Dhingra} and \textit{S. S. Rao}, Eur. J. Oper. Res. 83, No. 3, 547--567 (1995; Zbl 0901.90136)

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### References:

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