Fuzzy unconstrained parametric geometric programming problem and its application. (English) Zbl 1356.90174

Mandal, Wasim Akram; Islam, Sahidul

J. Fuzzy Set Valued Anal. 2016, No. 2, 125-139 (2016).

Summary: In this paper, we have proposed fuzzy unconstrained geometric programming (GP) problem and modified geometric programming (MGP) problem with negative or positive integral degree of difficulty. Geometric programming technique provides a powerful tool for solving optimization problems. Here we use nearest interval approximation method to convert a triangular fuzzy number to an interval number. In this paper, we transform this interval number to a parametric interval-valued functional form and then solve the parametric problem by geometric programming technique. Here some necessary theorems have been derived. Finally, these are illustrated by numerical examples and applications.

MSC:

90C70	Fuzzy and other nonstochastic uncertainty mathematical programming
90C90	Applications of mathematical programming

Keywords:

unconstrained problem; modified fuzzy geometric programming problem; fuzzy numbers; interval-valued function