A survey on the enumeration of classes of logical connectives and aggregation functions defined on a finite chain, with new results

The enumeration of logical connectives and aggregation functions defined on a finite chain has been a hot topic in the literature for the last decades. Multiple advantages can be derived from knowing a general formula about their cardinality, for instance, the ability to anticipate the computational...

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Bibliographic Details
Published in:Fuzzy sets and systems Vol. 490; p. 109023
Main Authors: Munar, Marc, Couceiro, Miguel, Massanet, Sebastia, Ruiz-Aguilera, Daniel
Format: Journal Article
Language:English
Published: Elsevier B.V 15.08.2024
Elsevier
Subjects:
Aggregation functions
Computer Science
Discrete implications
Discrete t-norms
Enumeration
Finite chains
Logical connectives
Aggregation functions
Logical connectives
Enumeration
Discrete t-norms
Discrete implications
Finite chains
discrete implications
aggregation functions
enumeration
logical connectives
finite chains
discrete t-norms
ISSN:0165-0114, 1872-6801
Online Access:Get full text
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Summary:The enumeration of logical connectives and aggregation functions defined on a finite chain has been a hot topic in the literature for the last decades. Multiple advantages can be derived from knowing a general formula about their cardinality, for instance, the ability to anticipate the computational cost required for generating operators with different properties. This is of paramount importance in image processing and decision making scenarios, where the identification of the most optimal operator is essential. Furthermore, it facilitates the examination of how constraining a certain property is in relation to its parent class. As a consequence, this paper aims to compile the main existing formulas and the methodologies with which they have been derived. Additionally, we introduce some novel formulas for the number of smooth discrete aggregation functions with neutral element or absorbing element, idempotent conjunctions, and commutative and idempotent conjunctions.
ISSN:0165-0114
1872-6801
DOI:10.1016/j.fss.2024.109023