General theory on fuzzy subgroupoids with respect to a t-norm T
In this paper we develop a general theory on fuzzy subgroupoids with respect to a t-norm T which includes many known concepts and results as its special cases. Particular attention is paid to the fuzzy subgroupoids induced by a probability space. The associative law and the existence of inverse elements are characteristic properties of a group. However, we found that they did not play an essential role in the approach of Anthony and Sherwood (Fuzzy Sets and Systems 7 (1982) 297-305). Therefore, by making some technical improvements, we show that the approach of Anthony and Sherwood can be successfully applied to deal with fuzzy subgroupoids and obtain similar results. (C) 2001 Elsevier Science B.V. All rights reserved.
fuzzy subgroupoid subgroupoid t-norm groupoid