Fuzzy set and multi descriptions property

Multi descriptions property is a fundamental property on membership functions of fuzzy sets, which has not been attended so far. The property suggests that not all membership functions of fuzzy sets can be viewed as a simple number in the range of 0 and 1. In fact, membership function of an element in a fuzzy set should be viewed as the sum of strength of the element that show each attribute which describes the fuzzy set. Therefore, fuzzy sets operation such as union, intersection and subsethood measure need to be revised. By adopting multi descriptions property, this paper introduced a set of improvement based on Checklist Paradigm for these operations for type-1 fuzzy sets. Since the multi descriptions property may also appear in type-2 fuzzy sets, we proposed a method for the subsethood measurement, namely Representative Method. This Representative Method provides simple and fast approximate measurements for subsethood.