Abstract:
The aim of this work is to introduce a new measure of inclusion which allows a given
fuzzy set to contain another to some degree between 0 and 1. Firstly, this idea fuzzifies
Zadeh’s fuzzy set containment which is a crisp property. Later on, various researchers
have set out to define alternative inclusion measure. The fuzzy inclusion is not only tnorms
dependent but its properties also depend on the properties of the fuzzy implicator
being used to define it. Our main work in this regard is to introduce a fuzzy inclusion
measure with Reichenbach implicator and product t-norms and t-conorms. So, product tnorm
is a representative of strict t-norm class. We try to cover a class when we work with
product t-norm, t-conorms and Reichenbach implicator. Only a few authors (Sinha and
Dougherty, 1993) have considered axiomatic properties of fuzzy inclusion measure. In
this thesis, we offer inclusion measure properties with the modification of Sinha and
Dougherty’s axioms. We apply some of these properties in medical diagnosis to check
the impact of our results. We also compare our results with Lukasiewicz’ results in
medical diagnosis problems. Lukasiewicz t-norm is a representative of nilpotent t-norm
class.