Abstract
In this article, a new fuzzy entropy measure of order α is proposed. The fuzzy entropy axiomatic requirements are discussed for the new measure, and an empirical comparison are made with several entropy measures including Shannon, Rényi and Kapur. It turns out, the proposed measure satisfies all axiomatic and outperform the other entropy measures in terms of the fuzziness degree.Â
Highlights
The novelty of fuzzy sets (FS) dated back to Zadeh (1965)
De-Luca and Termini (1972) proposed the first entropy extension of Shannon (1948) entropy; by suggesting a nonprobability Fuzzy entropy (FE), they defined the basic properties of the proposed FE as sharpness, maximality, resolutions and symmetry; which considered as a road map for developing any new FE measure
Some application of entropy in goodness of fit tests for non-fuzzy datasetsare possible to be generalized to the fuzzy entropy. (Zamanzadeand Mahdizadeh,(2016, 2017); Zamanzade andArghami, 2011;Zamanzade, 2014) as other applications were generalized to the fuzzy sets and fuzzy entropyin different fields, such as sampling, goodness of fit, testing, and many other fields
Summary
The novelty of fuzzy sets (FS) dated back to Zadeh (1965). The main idea of FS is to model non-statistical vague phenomena. Fuzziness as a feature of uncertainty can be explained as a result of a given decision on an event that to be considered as a member of a set or not In such cases, the event is considered as a fuzzy rather than sharply defined as collection of points (Zadeh, 1968). After, several authors introduced modified FE measures (Ohlan, 2015; Naidu et al, 2017; Zhang et al, 2012; Al-Sharhan et al.2001; Bhandari and Pal, 1993; Kapur, 1997;Parkash and Sharma, 2002) On another point, some application of entropy in goodness of fit tests for non-fuzzy datasetsare possible to be generalized to the fuzzy entropy.
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