Abstract
In this paper, a new method is proposed for testing fuzzy hypotheses based on the following two generalized p-values: (1) the generalized p-value of null fuzzy hypothesis against alternative fuzzy hypothesis and (2) the generalized p-value of alternative fuzzy hypothesis against null fuzzy hypothesis. In the proposed method, each generalized p-value is formulated on the basis of Zadeh’s probability measure of fuzzy events. The introduced p-value method has several advantages over the common p-value methods for testing fuzzy hypotheses. A few illustrative examples and also an agricultural example, based on a real-world data set, are given to clarify the proposed method.
Highlights
After the inception of the concept of fuzzy set by Zadeh [23], many statistitions have extended different methods of testing statistical hypotheses using the fuzzy set theory, e.g. see [3, 4, 18, 19]
Fuzzy Hypothesis and Its Boundary Here, we review some basic concepts about fuzzy hypotheses from Taheri and Behboodian [18] and Parchami et al [15], which are used in Section “Testing Fuzzy Hypotheses Based on a New p-Value-Based Approach”
H0 b(θ ) θ H0 b(θ )dθ is the normalized membership function of the boundary in the fuzzy null hypothesis, t is the observed value of test statistic (T) and mH0 b is the median of the weighted distribution of T(X) under the boundary of the fuzzy null hypothesis H 0 b
Summary
After the inception of the concept of fuzzy set by Zadeh [23], many statistitions have extended different methods of testing statistical hypotheses using the fuzzy set theory, e.g. see [3, 4, 18, 19]. Considering the above discussion, the main problem studied in this work is to test fuzzy hypotheses H 0 : θ is H0(θ ), H 1 : θ is H1(θ ), based on a random sample from a p.d.f. or p.m.f. f (x; θ), θ ∈ (for more details, see Definition 1).
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
