Fuzzy sets approaches to statistical parametric and nonparametric tests: Research Articles

  • Authors:

  • Cengiz Kahraman;Cafer Erhan Bozdag;Da Ruan;Ahmet Fahri Özok

  • Affiliations:

  • Department of Industrial Engineering, Istanbul Technical University, Maçka 34357, Istanbul, Turkey;Department of Industrial Engineering, Istanbul Technical University, Maçka 34357, Istanbul, Turkey;Belgian Nuclear Research Centre (SCK•CEN), Boeretang 200, B-2400 Mol, Belgium;Department of Industrial Engineering, Istanbul Technical University, Maçka 34357, Istanbul, Turkey

  • Venue:
  • International Journal of Intelligent Systems - Intelligent and Soft Computing Techniques for Information Processing
  • Year:
  • 2004

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Abstract

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.