2010 24th IEEE International Conference on Advanced Information Networking and Applications (2010)

Perth, Australia

Apr. 20, 2010 to Apr. 23, 2010

ISSN: 1550-445X

ISBN: 978-0-7695-4018-4

pp: 1218-1224

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/AINA.2010.78

ABSTRACT

A complex fuzzy relation is defined as a fuzzy relation whose membership function takes values in the unit circle on a complex plane. This paper first investigates various operation properties of a complex fuzzy relation. It then defines the distance measure of two complex fuzzy relations that can measure the differences between the grades as well as the phases of two complex fuzzy relations. This distance measure is used to define delta-equalities of complex fuzzy relations that coincide with those of fuzzy relations already defined in the literature if complex fuzzy relations reduce to real-valued fuzzy relations. Two complex fuzzy relations are said to be delta-equal if the distance between them is less than 1-δ. This paper shows how various operations between complex fuzzy relations, including T-norms and S-norms, affect given delta-equalities of complex fuzzy relations. Finally, fuzzy inference is examined in the framework of delta- equalities of complex fuzzy relations.

INDEX TERMS

Complex fuzzy set, Fuzzy set, Distance measure, d- equality, Fuzzy relations, Fuzzy inference

CITATION

K. Cai, J. Ma, T. S. Dillon, G. Zhang and J. Lu, "Delta-equalities of Complex Fuzzy Relations,"

*2010 24th IEEE International Conference on Advanced Information Networking and Applications(AINA)*, Perth, Australia, 2010, pp. 1218-1224.

doi:10.1109/AINA.2010.78

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