Preprint Article Version 1 This version is not peer-reviewed

Energy and Entropy Measures of Fuzzy Relations for Data Analysis

Version 1 : Received: 18 April 2018 / Approved: 18 April 2018 / Online: 18 April 2018 (16:45:58 CEST)

A peer-reviewed article of this Preprint also exists.

Di Martino, F.; Sessa, S. Energy and Entropy Measures of Fuzzy Relations for Data Analysis. Entropy 2018, 20, 424. Di Martino, F.; Sessa, S. Energy and Entropy Measures of Fuzzy Relations for Data Analysis. Entropy 2018, 20, 424.

Journal reference: Entropy 2018, 20, 424
DOI: 10.3390/e20060424

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 relationship input-output. We consider a new index of the fuzziness of the input-output based over 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 for choosing the most relevant fuzzy rules with respect to the data.

Subject Areas

fuzzy entropy; fuzzy energy; fuzzy rules; fuzzy sets; fuzzy relations

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