{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,25]],"date-time":"2026-01-25T00:35:55Z","timestamp":1769301355148,"version":"3.49.0"},"reference-count":30,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2021,4,26]],"date-time":"2021-04-26T00:00:00Z","timestamp":1619395200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Cluster techniques are used in hotspot spatial analysis to detect hotspots as areas on the map; an extension of the Fuzzy C-means that the clustering algorithm has been applied to locate hotspots on the map as circular areas; it represents a good trade-off between the accuracy in the detection of the hotspot shape and the computational complexity. However, this method does not measure the reliability of the detected hotspots and therefore does not allow us to evaluate how reliable the identification of a hotspot of a circular area corresponding to the detected cluster is; a measure of the reliability of hotspots is crucial for the decision maker to assess the need for action on the area circumscribed by the hotspots. We propose a method based on the use of De Luca and Termini\u2019s Fuzzy Entropy that uses this extension of the Fuzzy C-means algorithm and measures the reliability of detected hotspots. We test our method in a disease analysis problem in which hotspots corresponding to areas where most oto-laryngo-pharyngeal patients reside, within a geographical area constituted by the province of Naples, Italy, are detected as circular areas. The results show a dependency between the reliability and fluctuation of the values of the degrees of belonging to the hotspots.<\/jats:p>","DOI":"10.3390\/e23050531","type":"journal-article","created":{"date-parts":[[2021,4,27]],"date-time":"2021-04-27T02:31:43Z","timestamp":1619490703000},"page":"531","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Fuzzy Entropy-Based Spatial Hotspot Reliability"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5690-5384","authenticated-orcid":false,"given":"Ferdinando","family":"Di Martino","sequence":"first","affiliation":[{"name":"Dipartimento di Architettura, Universit\u00e0 degli Studi di Napoli Federico II, Via Toledo 402, 80134 Napoli, Italy"},{"name":"Centro Interdipartimentale di Ricerca in Urbanistica Alberto Calza Bini, Universit\u00e0 degli Studi di Napoli Federico II, Via Toledo 402, 80134 Napoli, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4303-2884","authenticated-orcid":false,"given":"Salvatore","family":"Sessa","sequence":"additional","affiliation":[{"name":"Dipartimento di Architettura, Universit\u00e0 degli Studi di Napoli Federico II, Via Toledo 402, 80134 Napoli, Italy"},{"name":"Centro Interdipartimentale di Ricerca in Urbanistica Alberto Calza Bini, Universit\u00e0 degli Studi di Napoli Federico II, Via Toledo 402, 80134 Napoli, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,4,26]]},"reference":[{"key":"ref_1","first-page":"281","article-title":"Some Methods for Classification and Analysis of Multivariate Observations","volume":"Volume 1","author":"Neyman","year":"1967","journal-title":"Proceedings of the fifth Berkeley Symposium on Mathematical Statistics and Probability"},{"key":"ref_2","unstructured":"Shekhar, S., Xiong, H., and Zhou, X. 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