Abstract
The paper deals with an application of probabilistic sets in system theory, especially in identification problems in systems described by means of max-min fuzzy relational equations. The identification procedures discussed are based on some ideas of iterative clustering techniques (ISODATA and FUZZY C-MEANS) which lead to a concrete method of determination of probabilistic sets. A vagueness function associated with the fuzzy relation of the system forms a validity indicator of the identification algorithm. Numerical examples containing fuzzy and nonfuzzy data form an illustration of the methods provided.
| Original language | English |
|---|---|
| Pages (from-to) | 1-13 |
| Number of pages | 13 |
| Journal | Fuzzy Sets and Systems |
| Volume | 10 |
| Issue number | 1-3 |
| DOIs | |
| Publication status | Published - 1983 |
| Externally published | Yes |
Keywords
- Clustering techniques
- Max-min fuzzy relational equation
- Probabilistic set
- Vagueness function
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Hirota, K., & Pedrycz, W. (1983). Analysis and synthesis of fuzzy systems by the use of probabilistic sets. Fuzzy Sets and Systems, 10(1-3), 1-13. https://doi.org/10.1016/S0165-0114(83)80098-0