A solution to an open problem on the T-product of TL-fuzzy subgroups

• Published in: Fuzzy sets and systems Vol. 178; no. 1; pp. 102 - 106
• Main Authors: Yamak, S., Kazancı, O., Bayrak, D.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier B.V 01-09-2011; Elsevier
• Subjects: Applied sciences; Circuit properties; Computer science; control theory; systems; Digital circuits; Electric, optical and optoelectronic circuits; Electronic circuits; Electronics; Exact sciences and technology; Information, signal and communications theory; Mathematical methods; Miscellaneous; T-product; Telecommunications and information theory; Theoretical computing; TL-fuzzy subgroup; T-product; TL-fuzzy subgroup; Engineering; Fuzzy system; Necessary and sufficient condition; Information processing; Fuzzy set
• ISSN: 0165-0114; 1872-6801
• DOI: 10.1016/j.fss.2011.04.009

Many studies have investigated necessary and sufficient conditions whereby fuzzy subgroups of a Cartesian product of groups are a Cartesian product of fuzzy subgroups. Chon [Fuzzy subgroups as products, Fuzzy Sets and Systems 141 (2004) 505–508] found such conditions under minimum operation. He pointed out that the problem of finding necessary and sufficient conditions for
T-fuzzy subgroups under a t-norm operation is still open. In this study, we solve the problem and identify necessary and sufficient conditions under t-norm operation.