Affiliation:
1. Dpt. de Ciències Matemàtiques i Informàtica, Universitat de les Illes Balears, 07071 Palma de Mallorca, Spain
Abstract
We study some properties of De Morgan triplets. Firstly, we introduce submodular De Morgan triplets and we study its relationships with subdistributive ones. Moreover, we characterize them both in the strict and non strict archimedean cases. Secondly, we introduce the concepts of modularity, distributivity and (S, T)-distributivity degrees and we give some general results. Afterwards we apply these concepts to two particular cases, Lukasiewicz triplets and a kind of strict De Morgan triplets (Product triplets). For the Lukasiewicz ones we prove that all three degrees range over (0, 1/2]. For Product triplets, a recipe to calculate these degrees is given. In particular we present examples with distributivity degree r for all r ∈ (0, 1) and examples with (S, T)-distributivity and modularity degrees taking all values in (0, 3/4].
Publisher
World Scientific Pub Co Pte Lt
Subject
Artificial Intelligence,Information Systems,Control and Systems Engineering,Software
Cited by
20 articles.
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