FPV-package {FPV}

Testing Hypotheses via Fuzzy P-Value in Fuzzy Environment

Description

Statistical testing hypotheses has an important rule for making decision in practical and applied problems. In traditional testing methods, data, parameters, hypotheses and other elements of problem are considered crisp. But in applied sciences such as economics, agriculture and social sciences, it may be confront with vague definitions and fuzzy concepts. In such situations, the classical methods can not solve the vague test and they need to generalize for using in fuzzy environments. The vagueness entrance in testing hypotheses problem can be done via data or/and hypotheses. Therefore, the following three major problems can be usually considered for a fuzzy environment: (1) testing crisp hypotheses based on fuzzy data, (2) testing fuzzy hypotheses based on crisp data, and (3) testing fuzzy hypotheses based on fuzzy data. Similar to the classical testing hypotheses, one can consider different procedure methods for solving the above mentioned problems such as Neyman-Pearson, Bayes, likelihood ratio, minimax and p-value. Computing Fuzzy p-Value package, i.e. Fuzzy.p.value package, is an open source (LGPL 3) package for R which investigate on the above three problems on the basis of fuzzy p-value approach. All formulas and given examples are match with (Parchami and Mashinchi, 2016) to easily show the performance of the proposed methods.

Author(s)

Abbas Parchami (Department of Statistics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran)

Maintainer: Abbas Parchami <[e-mail]>

References

Filzmoser, P., and Viertl, R. (2004). Testing hypotheses with fuzzy data: the fuzzy p-value. Metrika 59: 21-29.

Gagolewski, M., Caha, J. (2015) FuzzyNumbers Package: Tools to deal with fuzzy numbers in R. R package version 0.4-1, https://cran.r-project.org/web/packages=FuzzyNumbers

Gagolewski, M., Caha, J. (2015) A guide to the FuzzyNumbers package for R (FuzzyNumbers version 0.4-1) http://FuzzyNumbers.rexamine.com

Holena, M. (2004). Fuzzy hypotheses testing in a framework of fuzzy logic. Fuzzy Sets and Systems 145: 229-252.

Parchami, A., Taheri, S. M., and Mashinchi, M. (2010). Fuzzy p-value in testing fuzzy hypotheses with crisp data. Statistical Papers 51: 209-226.

Parchami, A., Taheri, S. M., and Mashinchi, M. (2012). Testing fuzzy hypotheses based on vague observations: a p-value approach. Statistical Papers 53: 469-484.

Wang, X., Kerre, E. E. (2001). Reasonable properties for the ordering of fuzzy quantities (II). Fuzzy Sets and Systems 118: 387-405.

Viertl, R. (2011) Statistical methods for fuzzy data. Wiley, Chichester.

Yuan, Y. (1991). Criteria for evaluating fuzzy ranking methods. Fuzzy Sets Syst 43: 139-157.

See Also

FuzzyNumbers FuzzyNumbers.Ext.2 Fuzzy.p.value