On Normal-Valued Basic Pseudo Hoops
Michal Botur, Anatolij Dvure\v{c}enskij, and Tomasz Kowalski
TL;DR
This paper investigates the properties of basic pseudo hoops, demonstrating their satisfaction of the Riesz Decomposition Property, visualizing them via functions on ordered sets, and characterizing normal-valued cases with a countable set of equations.
Contribution
It establishes that all pseudo hoops satisfy the Riesz Decomposition Property and provides a new visualization method, along with a characterization of normal-valued basic pseudo hoops.
Findings
Pseudo hoops satisfy the Riesz Decomposition Property
Visualization of basic pseudo hoops via functions on ordered sets
Normal-valued basic pseudo hoops characterized by a countable set of equations
Abstract
We show that every pseudo hoop satisfies the Riesz Decomposition Property. We visualize basic pseudo hoops by functions on a linearly ordered set. Finally, we study normal-valued basic pseudo hoops giving a countable base of equations for them.
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Taxonomy
TopicsAdvanced Algebra and Logic · Rough Sets and Fuzzy Logic · Fuzzy and Soft Set Theory