Continuous Fuzzy Sets as Probabilities of Continuous Fuzzy Events

Document type: Conference Papers
Peer reviewed: Yes
Author(s): Elisabeth Rakus-Andersson
Title: Continuous Fuzzy Sets as Probabilities of Continuous Fuzzy Events
Conference name: World Congress in Computational Intelligence 2010 - WCCI 2010
Year: 2010
Pagination: 1019-1025
ISBN: 978-1-4244-6920-8
Publisher: IEEE Society
City: Barcelona
ISI number: 000287453602028
Other identifiers: IEEE catalog number: CFP10FUZ-DVD
Organization: Blekinge Institute of Technology
Department: School of Engineering - Dept. Mathematics and Science (Sektionen för teknik – avd. för matematik och naturvetenskap)
School of Engineering S- 371 79 Karlskrona
+46 455 38 50 00
Authors e-mail:
Language: English
Abstract: In the first part of this study we explore continuous fuzzy numbers in the interval- and the alpha-cut forms to detect their similar nature. The conversion from one form to the other is a question of using the appropriate apparatus, which we also provide. Since the fuzzy numbers can reproduce fuzzy events we then will make a trial of extending the concept of fuzzy probability, defined by R. Yager for discrete fuzzy events, on continuous fuzzy events. In order to fulfill the task we utilize conclusions made about fuzzy numbers to propose an initial conception of approximating the Gauss curve by a particularly designed function originated from the pi-class functions. Due to the procedure of the approximation, characterized by an irrelevant cumulative error, we expand fuzzy probabilities of continuous fuzzy events in the form of continuous fuzzy sets. Furthermore, we assume that this sort of probability holds some conditions formulated for probabilities of discrete fuzzy events.
Subject: Mathematics\General
Mathematics\Probability and Statistics
Keywords: fuzzy number, alpha cut, probability of discrete fuzzy events, pi function, approximation of the Gaussian curve, continuous probabilitiy of a continuous fuzzy event