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Fuzzy sets approaches to statistical parametric and nonparametric tests
Author(s) -
Kahraman Cengiz,
Bozdag Cafer Erhan,
Ruan Da,
Özok Ahmet Fahri
Publication year - 2004
Publication title -
international journal of intelligent systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.291
H-Index - 87
eISSN - 1098-111X
pISSN - 0884-8173
DOI - 10.1002/int.20037
Subject(s) - nonparametric statistics , wilcoxon signed rank test , parametric statistics , fuzzy logic , sign test , mathematics , statistical hypothesis testing , statistics , population , data mining , computer science , artificial intelligence , mann–whitney u test , demography , sociology
The parametric tests often require that the population distributions be normal or approximately so. Statistical methods that do not require the knowledge of the population distribution or its parameters are called nonparametric tests. In this article, first we review some industrial applications of fuzzy parametric tests. Then we present some new algorithms for fuzzy nonparametric tests, namely a fuzzy sign test and a fuzzy Wilcoxon signed‐ranks test. Later, we further give fuzzy parametric tests, fuzzy nonparametric tests, and their numerical applications, and also provide a comparison study on crisp and fuzzy nonparametric tests. When the data are vague, the result of the fuzzy nonparametric tests may be different from that of the crisp nonparametric tests. © 2004 Wiley Periodicals, Inc. Int J Int Syst 19: 1069–1087, 2004.