Additive Generators of Discrete Conjunctive Aggregation Operations

This paper deals with a class of conjunction-like binary operations defined on a finite totally ordered set. The concept of additive generator of a discrete conjunctive aggregation operation is introduced and we obtain a description of those operations having an additive generator by means of nonstr...

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Bibliographic Details
Published inIEEE transactions on fuzzy systems Vol. 15; no. 6; pp. 1046 - 1052
Main Authors Mayor, G., Monreal, J.
Format Journal Article
LanguageEnglish
Published New York IEEE 01.12.2007
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Additive generator
Additives
Agglomeration
Character generation
Computer science
conjunction
discrete binary operation
discrete t-norm
dual cone
Equations
Fuzzy logic
Fuzzy systems
Gamma -algorithm
Generators
Government
Mathematical analysis
Mathematics
polyhedral convex cone
system of linear inequalities
Tin
Uncertainty
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ISSN1063-6706
1941-0034
DOI10.1109/TFUZZ.2007.903321

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Summary:This paper deals with a class of conjunction-like binary operations defined on a finite totally ordered set. The concept of additive generator of a discrete conjunctive aggregation operation is introduced and we obtain a description of those operations having an additive generator by means of nonstrict Archimedean t-norms. The main goal is to give a procedure for deciding whether a conjunctive aggregation operation is additively generated or not. The problem of the existence of additive generators for discrete t-norms is also discussed.
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ISSN:1063-6706
1941-0034
DOI:10.1109/TFUZZ.2007.903321