Abstract: We consider the condition of the same ordering of objects due to using the convolution of utility functions and membership functions. It turns out that the same order takes place when the each utility function of an attribute is constructed as a convolution of fuzzy membership functions of this attribute. To transform membership functions to utility function of an attribute the formula was deduced. The example illustrates that transforming. The paper provides examples of application of the transformation of membership functions in the utility function, and vice versa.

Keywords: utility function, membership function, additive and multiplicative convolution.

ACM Classification Keywords: G. Mathematics of Computing, I.2.1 Applications and Expert Systems.

Link:

STUDY RELATIONSHIP BETWEEN UTILITY FUNCTION AND MEMBERSHIP FUNCTION IN THE PROBLEM OF OBJECT RANKING1

Stanislav V. Mikoni, Marina I. Garina

http://foibg.com/ibs_isc/ibs-27/ibs-27-p08.pdf