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

  • Authors:
  • S. Yamak;O. Kazancı;D. Bayrak

  • Affiliations:
  • Department of Mathematics, Karadeniz Technical University, 61080 Trabzon, Turkey;Department of Mathematics, Karadeniz Technical University, 61080 Trabzon, Turkey;Department of Mathematics, Karadeniz Technical University, 61080 Trabzon, Turkey

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2011

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Abstract

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.