Home Maria Oelinger Home Oelinger sitemap a – z

List of Contents     Rommelfanger     2.2     Lai, Hwang     Notations + Definitions

2.Fuzzy optimization by Kacprzyk and Orlovski

2.1 Introduction

2.1.1 Basics

General basis is the optimization model KO1 (No-Fuzzy):

z(x) =    c_j x_j     —>    Max

in compliance with the subconditions

 a_ij x_j  b_i i = 1,…,m

x_j    0, j = 1,…,n.

The fuzzification of this problem is realized by "blurring" the demand for maximization of the target function and the demand for the exact compliance with the inequations. Therefore the appreciation in accordance with Zimmermann (1975/76) is outlined:

This was the first attempt to fuzzifize optimization (resp. Linear Programming).
You can transform the optimization model KO1 as followed:

z(x) =    e_j x_j     —>   Min

in compliance with the subconditions

 a_ij x_j  b_i,   i = 1,…,m

obviously e_j = –c_j applies.

List of Contents     Rommelfanger     2.2     Lai, Hwang     Notations + Definitions

Feel free to send me email: maria@oelinger.de