The axiomatic characterizations onL-fuzzy covering-based approximation operators
| Autor: | Kai Hu, Qiu Jin, Fang Fang Zhao, Lingqiang Li |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Discrete mathematics
0209 industrial biotechnology Pure mathematics General set theory Mathematics::General Mathematics Zermelo–Fraenkel set theory Constructive set theory 02 engineering and technology Axiom schema Urelement Computer Science Applications Theoretical Computer Science Axiom of extensionality ComputingMethodologies_PATTERNRECOGNITION 020901 industrial engineering & automation Control and Systems Engineering Modeling and Simulation 0202 electrical engineering electronic engineering information engineering 020201 artificial intelligence & image processing Axiom of choice ComputingMethodologies_GENERAL Kripke–Platek set theory Information Systems Mathematics |
| Zdroj: | International Journal of General Systems. 46:332-353 |
| ISSN: | 1563-5104 0308-1079 |
| DOI: | 10.1080/03081079.2017.1308360 |
| Popis: | Axiomatic characterization is the foundation of L-fuzzy rough set theory: the axiom sets of approximation operators guarantee the existence of L-fuzzy relations or L-fuzzy coverings that reproduce the approximation operators. Axiomatic characterizations of approximation operators based on L-fuzzy coverings have not been fully explored, although those based on L-fuzzy relations have been studied thoroughly. Focusing on three pairs of widely used L-fuzzy covering-based approximation operators, we establish an axiom set for each of them, and their independence is examined. It should be noted that the axiom set of each L-fuzzy covering-based approximation operator is different from its crisp counterpart, with an either new or stronger axiom included in the L-fuzzy version. |
| Databáze: | OpenAIRE |
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