Granular representation and granular computing with fuzzy sets

Adam Pedrycz, Kaoru Hirota, Witold Pedrycz*, Fangyan Dong

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

83 Citations (Scopus)

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 φ, which gives rise to the concept of φ-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 φ-consistent optimization process is provided through particle swarm optimization. Further conceptual and representation issues impacted processing fuzzy sets are discussed as well.

Original languageEnglish
Pages (from-to)17-32
Number of pages16
JournalFuzzy Sets and Systems
Volume203
DOIs
Publication statusPublished - 16 Sept 2012
Externally publishedYes

Keywords

  • Fuzzy connectives (operators)
  • Granular mapping
  • Granular membership
  • Interval optimization
  • Operator-consistent granular descriptor of fuzzy sets
  • Particle swarm optimization
  • φ-Consistent granular descriptors of fuzzy sets

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