Work

Weaker forms of increasingness of binary operations and their role in the characterization of meet and join operations

Year: 2024

Type: article

Abstract: Due to the lack of transitivity of the pseudo-order relation of a proper trellis, its meet and join operations are not increasing. In this paper, we identify weaker forms of increasingness of binary operations that are satisfied by the meet and/or join operation of a trellis or lattice. Some of these forms coincide with the classical notion of increasingness when the trellis is a lattice. Furthermore, we demonstrate the role of these weaker forms in the characterization of the meet and join operations of a trellis, lattice or chain as specific idempotent operations.

Source: Fuzzy Sets and Systems

DOI: 10.1016/j.fss.2024.109116

Authors: Lemnaouar Zedam, Bernard De Baets

Language: English

Topic: Advanced Algebra and Logic

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,680

Funder: Arab Fund for Economic and Social Development

Award: G6182061428