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Energy and Entropy Measures of Fuzzy Relations for Data Analysis
Ferdinando Di Martino1,2, Salvatore Sessa1,2
1Dipartimento di Architettura, Università degli Studi di Napoli Federico II, Via Toledo 402, 80134 Napoli, Italy.
Entropy (Basel, Switzerland)
|December 3, 2020
Summary
We developed a new fuzzy rule assessment method using fuzzy relation energy and entropy. This approach identifies the strongest and most certain fuzzy rules within a dataset for improved rule selection.
Area of Science:
- Fuzzy Logic and Machine Learning
- Data Mining and Rule Extraction
Background:
- Fuzzy rules are essential for expert systems and fuzzy control.
- Assessing the strength and relevance of fuzzy rules within datasets is crucial for effective model building.
Purpose of the Study:
- To introduce a novel method for evaluating the strength of fuzzy rules.
- To quantify the input-output relationship's certainty and uncertainty using fuzzy relations.
Main Methods:
- Utilizing measures of greatest energy and smallest entropy of fuzzy relations.
- Calculating a new index of input-output fuzziness based on these measures.
- Applying a threshold to select the most relevant fuzzy rules.
Main Results:
- The greatest energy fuzzy relation (R1) quantifies input-output strength.
- The smallest entropy fuzzy relation (R2) quantifies input-output uncertainty.
- A new fuzziness index effectively characterizes input-output relationships.
Conclusions:
- The proposed method provides a robust way to assess fuzzy rule relevance.
- This technique aids in selecting the most informative fuzzy rules from data.
- It enhances the interpretability and performance of fuzzy systems.
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