Superiority of Proportional Fuzzy Sets to Decimal-Valued Fuzzy Set Extensions

Abstract

Determination of membership, non-membership, and hesitancy degrees in the ordinary fuzzy sets and their extensions have not been sufficiently discussed in the literature. This study focusses on the ways of determining these degrees and tries to conclude which way is better than the others. We apply the same questionnaire to the participants of our experiment in four different days and want them to determine the membership degrees of the elements in the sets based on two different techniques. The aim of the experiment is to determine which way yields more stable degrees from the participants in different days.