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Parametric Conditions for a Monotone TSK Fuzzy Inference System to be an n-Ary Aggregation Function
- Source :
- IEEE Transactions on Fuzzy Systems. 29:1864-1873
- Publication Year :
- 2021
- Publisher :
- Institute of Electrical and Electronics Engineers (IEEE), 2021.
-
Abstract
- Despite the popularity and practical importance of the fuzzy inference system (FIS), the use of an FIS model as an n -ary aggregation function, which is characterized by both the monotonicity and boundary properties, is yet to be established. This is because research on ensuring that FIS models satisfy the monotonicity property, i.e., monotone FIS, is relatively new, not to mention the additional requirement of satisfying the boundary property. The aim of this article, therefore, is to establish the parametric conditions for the Takagi–Sugeno–Kang (TSK) FIS model to operate as an n -ary aggregation function (hereafter denoted as n -TSK-FIS) via the specifications of fuzzy membership functions and fuzzy rules. An absorption property with fuzzy rules interpretation is outlined, and the use of n -TSK-FIS as a uninorm is explained. Exploiting the established parametric conditions, a framework for which an n -TSK-FIS model can be constructed from data samples is formulated and analyzed, along with a number of remarks. Synthetic data sets and a benchmark example on education assessment are presented and discussed. To be best of the authors’ knowledge, this article serves as the first use of the TSK-FIS model as an n -ary aggregation function.
- Subjects :
- Applied Mathematics
Boundary (topology)
Monotonic function
Function (mathematics)
Fuzzy logic
Data modeling
Interpretation (model theory)
Monotone polygon
Computational Theory and Mathematics
Artificial Intelligence
Control and Systems Engineering
Applied mathematics
Mathematics
Parametric statistics
Subjects
Details
- ISSN :
- 19410034 and 10636706
- Volume :
- 29
- Database :
- OpenAIRE
- Journal :
- IEEE Transactions on Fuzzy Systems
- Accession number :
- edsair.doi...........674fbc50e62c333443f0f4f02d8931fa