Fuzzy semi-orders: The case of t-norms without zero divisors
For crisp relations the concept of a semi-order can be stated in a number of equivalent ways. When trying to extend this concept to the fuzzy setting, we observe that the (generalized) definitions fail to be equivalent. In this contribution, we discuss which is the most natural definition of a fuzzy semi-order, and study the hierarchy among the alternative definitions, in particular when using a t-norm without zero divisors. (C) 2011 Elsevier B.V. All rights reserved.
semi-order t-norm without zero divisors ferrers property semitransitivity fuzzy relation additive fuzzy preference structure