Fuzzy data analysis and classification

Abstract

In analyzing and classifying data from a statistical perspective, fuzzy sets and logic have become a valuable tool either to model and handle imprecise data or to establish flexible techniques to deal with precise data.From the very beginning of his 52 years-old theory, Professor Zadeh highlighted that "Probability theory/statistics and fuzzy logic should be viewed as complementary rather than competitive," and he anticipated and encouraged the materialization of such a complementarity. Nowadays, this assertion is a reality, as shown by the many related papers, specialized conferences, special sessions and tracks in general conferences, and so on.This special issue started in 2015, with the 50th anniversary of the seminal paper on fuzzy sets by Zadeh (1965), aiming to collect a sample of research papers about the current trends on the combination of fuzzy sets/logic and data analysis/classification. When this special issue was almost ready for publication, Zadeh unfortunately passed away at age 96 (February 4, 1921-September 6, 2017. We wish this special issue to be dedicated to Professor Zadeh, as a modest part of the many tributes that he will receive, and intending to show that fuzzy sets/logic and data analysis/classification can certainly work in synergy.

Fuzzy Cluster Analysis: Pseudometrics and Fuzzy Clusters

“…Для нечітких інтуїціонівістських множин питання введення метрик розглядаються в [8]. Огляд підходів до формалізації задач нечіткого кластерного аналізу та найбільш повний перелік методів та алгоритмів їхнього розв'язування наведено у [9]; розглядаються як випадки нечітких даних, так і розробка нечітких методів та алгоритмів для розв'язування задач з чіткими даними. Використанню кластерного аналізу в інтелектуальних системах присвячена монографія [10], у якій ґрунтовно викладені питання застосування чітких та нечітких алгоритмів для задач нечіткого кластерного аналізу.…”

Bayesian Topological Learning for Classifying the Structure of Biological Networks

“…Some researchers map the PDs into Hilbert spaces to adopt traditional machine learning tools (see e.g., Di Fabio and Ferri (2015); Turner et al (2014); Adams et al (2017); Bubenik (2015); Reininghaus et al (2015)). Direct use of PDs for statistical inference and classification has been developed by several authors such as Maroulas et al (2019Maroulas et al ( , 2020; Marchese and Maroulas (2018); Bobrowski et al (2017); Fasy et al (2014); Mileyko et al (2011); Robinson and Turner (2017).…”

Statistical Parameters Based on Fuzzy Measures

“…The field of fuzzy probability and statistics [9][10][11][12][13][14] has received significant attention during the last two decades. The contributions in this field can be classified into two basic groups according to the underlying approach they follow [15].…”