Measuring the similarity between zSlices general type-2 fuzzy sets with non-normal Secondary membership functions

This paper presents a method of measuring the similarity between general type-2 fuzzy sets that may have non-normal secondary membership functions. Such fuzzy sets are increasingly common in applications such as the modelling of the subjective meaning of linguistic terms by groups of people. By building upon existing similarity measures in the literature, which thus far cannot compare such fuzzy sets, we derive an extended similarity measure which can be applied to both normal and non-normal (in terms of the secondary membership functions) general type-2 fuzzy sets. We provide proofs that the proposed method follows all of the common properties of a similarity measure and demonstrations are given to compare the proposed method with others in the literature

Measuring the similarity between zSlices general type-2 fuzzy sets with non-normal Secondary membership functions

This paper presents a method of measuring the similarity between general type-2 fuzzy sets that may have non-normal secondary membership functions. Such fuzzy sets are increasingly common in applications such as the modelling of the subjective meaning of linguistic terms by groups of people. By building upon existing similarity measures in the literature, which thus far cannot compare such fuzzy sets, we derive an extended similarity measure which can be applied to both normal and non-normal (in terms of the secondary membership functions) general type-2 fuzzy sets. We provide proofs that the proposed method follows all of the common properties of a similarity measure and demonstrations are given to compare the proposed method with others in the literature