Dominance in the family of Sugeno-Weber t-norms
Manuel Kauers, Veronika Pillwein, and Susanne Saminger-Platz
TL;DR
This paper proves the dominance relationship within the Sugeno Weber t-norm family using quantifier elimination, establishing that dominance forms a transitive order among these t-norms.
Contribution
It introduces a formal proof of dominance and transitivity in the Sugeno Weber t-norm family using a quantifier elimination algorithm.
Findings
Dominance is proven within the Sugeno Weber t-norm family.
Dominance relation is transitive, forming an order.
Quantifier elimination is used as the proof method.
Abstract
The dominance relationship between two members of the family of Sugeno Weber t-norms is proven by using a quantifer elimination algorithm. Further it is shown that dominance is a transitive, and therefore also an order relation, on this family of t-norms.
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Taxonomy
TopicsFuzzy Logic and Control Systems · Advanced Algebra and Logic · Rough Sets and Fuzzy Logic