J-partitions

In this paper, the concept of a J-partition is introduced as a generalization of that of a classical partition. The approach is based on the observation that for any two members of a classical semi-partition, the nonemptiness of their intersection implies their equality. This observation is generalized to J-semi-partitions using degrees of compatibility and equality based on a t-norm J and its biresidual operator E-J. By imposing an additional covering condition, the concept of a J-partition is obtained. An interesting numerical characterization of J-partitions is proved, leading to a desired one-to-one correspondence between J-partitions and J-equivalences. Moreover, the refinement of J-partitions is discussed. In particular, it is shown that the J*-refinement of any two J-partitions of a given universe is again a J-partition of that universe if and only if the t-norm J* dominates the t-norm J. (C) 1998 Elsevier Science B.V. All rights reserved.