Journal
FUZZY SETS AND SYSTEMS
Volume 203, Issue -, Pages 17-32Publisher
ELSEVIER
DOI: 10.1016/j.fss.2012.03.009
Keywords
Fuzzy connectives (operators); Granular membership; phi-Consistent granular descriptors of fuzzy sets; Operator-consistent granular descriptor of fuzzy sets; Granular mapping; Interval optimization; Particle swarm optimization
Funding
- Government of Japan
- Japan Society for Promotion of Science (JSPS)
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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 phi, which gives rise to the concept of phi-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 phi-consistent optimization process is provided through particle swarm optimization. Further conceptual and representation issues impacted processing fuzzy sets are discussed as well. (C) 2012 Elsevier B.V. All rights reserved.
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