Kites and Pseudo BL-algebras
Anatolij Dvurecenskij, Tomasz Kowalski

TL;DR
This paper introduces a new construction called a kite for pseudo BL-algebras derived from $ ext{l}$-groups, unifies various fuzzy logic algebras, and explores their structural properties and variety classifications.
Contribution
It presents the kite construction for pseudo BL-algebras, connects it to known fuzzy logic algebras, and identifies new varieties including a countably infinite family.
Findings
Many fuzzy logic related algebras can be constructed as kites.
Subdirectly irreducible kites are characterized.
A new infinite family of pseudo BL-algebra varieties is described.
Abstract
We investigate a construction of a pseudo BL-algebra out of an -group called a kite. We show that many well-known examples of algebras related to fuzzy logics can be obtained in that way. We describe subdirectly irreducible kites. As another application, we exhibit a new countably infinite family of varieties of pseudo BL-algebras covering the variety of Boolean algebras.
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Taxonomy
TopicsAdvanced Algebra and Logic · Fuzzy and Soft Set Theory · Rough Sets and Fuzzy Logic
