Dominates on Equivalence Classes of Semigroup Operations.
Abstract
Initially the problem was to study the dominates relation on a collection of semigroup operations called triangular norms. This led to an equivalent problem -- studying subadditivity of certain semigroup operations defined on the non-negative reals. The setting was later generalized to include both problems and to bring essentials of the problem into sharper focus. In the generalization, a partially ordered set S was endowed with the collection, Op(s), of all semigroup operations which had the same identity, e, and were non-decreasing in place. The dominates relation was defined on Op(S). The collection, Map(S), of order-preserving bijections from S to S map e to itself was used to partition Op(S) into equivalence classes -- two objects being placed in the same class if they were isomorphic via some member of Map(S). Dominates restricted to any equivalence class in via some member of Map(S). Dominates restricted to any equivalence class in Op(S) was shown to to exhibit a certain homogeniety relative to composition of elements in Map(S). Transitivity of dominates on an equivalence class was shown to be equivalent to an appropriate subset of Map(S) being alegbraically closed under composition. The equivalence classes determined by continuous triangular norms were characterized in terms of ordinal sums of semigroups. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1982
- Accession Number
- ADA128463
Entities
People
- Howard Sherwood
Organizations
- University of Central Florida