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Entropy 2018, 20(6), 424; https://doi.org/10.3390/e20060424

Energy and Entropy Measures of Fuzzy Relations for Data Analysis

1
Dipartimento di Architettura, Università degli Studi di Napoli Federico II, Via Toledo 402, 80134 Napoli, Italy
2
Centro Interdipartimentale di Ricerca A. Calza Bini, Università degli Studi di Napoli Federico II, Via Toledo 402, 80134 Napoli, Italy
*
Author to whom correspondence should be addressed.
Received: 18 April 2018 / Revised: 25 May 2018 / Accepted: 30 May 2018 / Published: 31 May 2018
(This article belongs to the Special Issue Entropy and Complexity of Data)
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Abstract

We present a new method for assessing the strength of fuzzy rules with respect to a dataset, based on the measures of the greatest energy and smallest entropy of a fuzzy relation. Considering a fuzzy automaton (relation), in which A is the input fuzzy set and B the output fuzzy set, the fuzzy relation R1 with greatest energy provides information about the greatest strength of the input-output, and the fuzzy relation R2 with the smallest entropy provides information about uncertainty of the input-output relationship. We consider a new index of the fuzziness of the input-output based on R1 and R2. In our method, this index is calculated for each pair of input and output fuzzy sets in a fuzzy rule. A threshold value is set in order to choose the most relevant fuzzy rules with respect to the data. View Full-Text
Keywords: fuzzy energy; fuzzy entropy; fuzzy rules; fuzzy relations fuzzy energy; fuzzy entropy; fuzzy rules; fuzzy relations
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Di Martino, F.; Sessa, S. Energy and Entropy Measures of Fuzzy Relations for Data Analysis. Entropy 2018, 20, 424.

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