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Granular representation and granular computing with fuzzy sets
- Source :
-
Fuzzy Sets & Systems . 9/16/2012, Vol. 203, p17-32. 16p. - Publication Year :
- 2012
-
Abstract
- Abstract: In this study, we introduce a concept of a granular representation of numeric membership functions of fuzzy sets, which offers a synthetic and qualitative view at fuzzy sets and their ensuing processing. The notion of consistency of the granular representation is formed, which helps regard the problem as a certain optimization task. More specifically, the consistency is referred to a certain operation , which gives rise to the concept of -consistency. Likewise introduced is a concept of granular consistency with regard to a collection of several operations, Given the essential role played by logic operators in computing with fuzzy sets, detailed investigations include and- and or-consistency as well as (and, or)-consistency of granular representations of membership functions with the logic operators implemented in the form of various t-norms and t-conorms. The optimization framework supporting the realization of the -consistent optimization process is provided through particle swarm optimization. Further conceptual and representation issues impacted processing fuzzy sets are discussed as well. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 01650114
- Volume :
- 203
- Database :
- Academic Search Index
- Journal :
- Fuzzy Sets & Systems
- Publication Type :
- Academic Journal
- Accession number :
- 77337889
- Full Text :
- https://doi.org/10.1016/j.fss.2012.03.009