Hybrid monotonic inclusion measure and its use in measuring similarity and distance between fuzzy sets

作者：Zhang Hong Ying; Zhang Wen Xiu

来源：Fuzzy Sets and Systems, 2009, 160(1): 107-118.

DOI：10.1016/j.fss.2008.06.002

• Fuzzy sets
• Inclusion measure
• Similarity measure
• Distance

In fuzzy set theory, all inclusion measure indicates the degree to which a given fuzzy set is contained in another fuzzy set. In this paper, we introduce a new definition of inclusion measure: hybrid monotonic inclusion measure (S inclusion measure for short). Some inclusion measures defined by other authors and us are proved to be S inclusion measures. Ill addition, as the rational generalization of crisp inclusion relation, we prove most of the S inclusion measures possess some kind of J-transitivity and some properties postulated by Sinha and Dougherty for a reasonable inclusion measure. Similarity measure and distance between two fuzzy sets derived from S inclusion measure possess properties of normal similarity measure and distance. Furthermore, some similarity measures possess J-transitivity and distributivity.

• 出版日期2009-1-1
• 单位西安交通大学