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dc.contributor.authorZhang, G.
dc.contributor.authorDillon, Tharam S
dc.contributor.authorCai, K.
dc.contributor.authorMa, J.
dc.contributor.authorLu, J.
dc.identifier.citationZhang, Guangquan and Dillon, Tharam S and Cai, Kai and Ma, Jun and Lu, Jie. 2009. Operation properties and δ-equalities of complex fuzzy sets. International Journal of Approximate Reasoning. 50 (8): pp. 1227-1249.

A complex fuzzy set is a fuzzy set whose membership function takes values in the unit circle in the complex plane. This paper investigates various operation properties and proposes a distance measure for complex fuzzy sets. The distance of two complex fuzzy sets measures the difference between the grades of two complex fuzzy sets as well as that between the phases of the two complex fuzzy sets. This distance measure is then used to define equalities of complex fuzzy sets which coincide with those of fuzzy sets already defined in the literature if complex fuzzy sets reduce to real-valued fuzzy sets. Two complex fuzzy sets are said to be d-equal if the distance between them is less than 1 d. This paper shows how various operations between complex fuzzy sets affect given δ-equalities of complex fuzzy sets. An example application of signal detection demonstrates the utility of the concept of δ-equalities of complex fuzzy sets in practice.

dc.subjectfuzzy set
dc.subjectComplex fuzzy set
dc.subjectdistance measure
dc.titleOperation properties and δ-equalities of complex fuzzy sets
dc.typeJournal Article
dcterms.source.titleInternational Journal of Approximate Reasoning

The link to the journal’s home page is: Copyright © 2009 Elsevier B.V. All rights reserved

curtin.departmentDigital Ecosystems and Business Intelligence Institute (DEBII)
curtin.accessStatusOpen access
curtin.facultyCurtin Business School
curtin.facultyThe Digital Ecosystems and Business Intelligence Institute (DEBII)

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