Inclusion measures, similarity measures, and the fuzziness of fuzzy sets and their relations

Abstract

The inclusion measure, the similarity measure, and the fuzziness of fuzzy sets are three important measures in fuzzy set theory. In this article, we investigate the relations among inclusion measures, similarity measures, and the fuzziness of fuzzy sets, prove eight theorems that inclusion measures, similarity measures, and the fuzziness of fuzzy sets can be transformed by each other based on their axiomatic definitions, and propose some new formulas to calculate inclusion measures, similarity measures, and the fuzziness of fuzzy sets. These results can be applied in many fields, such as pattern recognition, image processing, fuzzy neural networks, fuzzy reasoning, and fuzzy control. © 2006 Wiley Periodicals, Inc. Int J Int Syst 21: 639–653, 2006.

Cite this work

No public copy is stored for this record, so only the metadata is cited.

Stored only when both papers are in the corpus — 80 citations exist upstream.

Papers that cite the same references — the relational fallback while embeddings are still backfilling.