Applications of Fuzzy Set Theory to Mathematical Programming

H.-J. ZIMMPRMANN

Chair of Operations Research, Aachen Institute of Technology

5100 Aachen, Templergraben 64, Federal Republic of Germany

FS 06

ABSTRACT

Mathematical programming is one of the areas to which fuzzy set theory has been applied extensively.

Primarily based on Bellman and Zadeh’s model of decision in fuzzy environments, models have been suggested which allow flexibility in constraints and fuzziness in the objective function in traditional linear and nonlinear programming, in integer and fractional programming, and in dynamic programming.

These models in turn have been used to offer computationally efficient approaches for solving vector maximum problems.

This paper surveys major models and theories in this area and offers some indication on future developments which can be expected.