Heyting Wajsberg Algebras as an Abstract Environment Linking Fuzzy and Rough Sets
Generate an AI Snapshot to get a quick, structured summary of this paper.
A concise AI-generated summary of the paper will appear here once you click Generate AI Snapshot.
TL;DR
It is shown that standard Pawlak approach to rough sets is a model of this structure and it is possible to obtain a de Morgan Brouwer-Zadeh (BZ) distributive lattice with respect to the partial order induced from the ?
Abstract
Heyting Wajsberg (HW) algebras are introduced as algebraic models of a logic equipped with two implication connectives, the Heyting one linked to the intuitionistic logic and the Wajsberg one linked to the Lukasiewicz approach to many-valued logic. On the basis of an HW algebra it is possible to obtain a de Morgan Brouwer-Zadeh (BZ) distributive lattice with respect to the partial order induced from the Lukasiewicz implication. Modal-like operators are also defined generating a rough approximation space. It is shown that standard Pawlak approach to rough sets is a model of this structure