Testing fuzzy hypotheses with crisp data

Arnold, Bernhard F.

doi:10.1016/s0165-0114(96)00258-8

Cited by 73 publications

(28 citation statements)

References 4 publications

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“…And they were developed several years after fuzzy sets were introduced. Among them, one can highlight -the fuzzy linear regression ideas between non-fuzzy input and output data, by considering the problem as a linear programming one [see, for instance, the first formulation by Tanaka et al (1982) and Tanaka and Watada (1988)], -hypothesis fuzzy testing, testing of fuzzy hypotheses, and fuzzy estimation regarding non-fuzzy parameters on the basis of non-fuzzy data [see, for instance, Watanabe and Imaizumi (1993), Arnold (1998), Buckley (2004), Hryniewicz (2006), Parchami et al (2009)], -fuzzy statistical quality control [see, for instance, Grzegorzewski and Hryniewicz (2000)], -statistical decision problems with fuzzy utilites/losses [see, for instance, Gil and Jain (1992), Gil and López-Díaz (1996)]. …”

Section: On the Fuzzy Analysis And The Fuzzy Classification Of Non-fumentioning

confidence: 99%

Fuzzy data analysis and classification

D’Urso

Alvarez

2017

Adv Data Anal Classif

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In analyzing and classifying data from a statistical perspective, fuzzy sets and logic have become a valuable tool either to model and handle imprecise data or to establish flexible techniques to deal with precise data.From the very beginning of his 52 years-old theory, Professor Zadeh highlighted that "Probability theory/statistics and fuzzy logic should be viewed as complementary rather than competitive," and he anticipated and encouraged the materialization of such a complementarity. Nowadays, this assertion is a reality, as shown by the many related papers, specialized conferences, special sessions and tracks in general conferences, and so on.This special issue started in 2015, with the 50th anniversary of the seminal paper on fuzzy sets by Zadeh (1965), aiming to collect a sample of research papers about the current trends on the combination of fuzzy sets/logic and data analysis/classification. When this special issue was almost ready for publication, Zadeh unfortunately passed away at age 96 (February 4, 1921-September 6, 2017. We wish this special issue to be dedicated to Professor Zadeh, as a modest part of the many tributes that he will receive, and intending to show that fuzzy sets/logic and data analysis/classification can certainly work in synergy.

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Section: On the Fuzzy Analysis And The Fuzzy Classification Of Non-fumentioning

confidence: 99%

Fuzzy data analysis and classification

D’Urso

Alvarez

2017

Adv Data Anal Classif

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“…Viertl (2011) andFilzmoser andViertl (2004) also extend a concept of fuzzy p value when the observations are fuzzy and hypotheses are crisp. Arnold (1996Arnold ( , 1998 proposed a method for testing fuzzy hypotheses about the population parameter with crisp data. He provided some definitions for the probability of type-I and type-II errors and presented the best test for the oneparameter exponential family.…”

Section: A Comparison Studymentioning

confidence: 99%

“…Below is a brief review of some studies relevant to the present work. Arnold (1996Arnold ( , 1998 presented an approach for testing fuzzily formulated hypotheses based on crisp data, in which he proposed and considered generalized definitions of the probabilities of the errors of type-I and type-II. Viertl (2006Viertl ( , 2011 used the extension principle to obtain the generalized estimators for a crisp parameter based on fuzzy data.…”

Section: Introductionmentioning

confidence: 99%

Parametric testing statistical hypotheses for fuzzy random variables

Hesamian

Shams

2015

Soft Comput

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In this paper, a method is proposed for testing statistical hypotheses about the fuzzy parameter of the underlying parametric population. In this approach, using definition of fuzzy random variables, the concept of the power of test and p value is extended to the fuzzy power and fuzzy p value. To do this, the concepts of fuzzy p value have been defined using the α-optimistic values of the fuzzy observations and fuzzy parameters. This paper also develop the concepts of fuzzy type-I, fuzzy type-II errors and fuzzy power for the proposed hypothesis tests. To make decision as a fuzzy test, a well-known index is employed to compare the observed fuzzy p value and a given significance value. The result provides a fuzzy test function which leads to some degrees to accept or to reject the null hypothesis. As an application of the proposed method, we focus on the normal fuzzy random variable to investigate hypotheses about the related fuzzy parameters. An applied example is provided throughout the paper clarifying the discussions made in this paper.

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“…For example, Delgado et al [12] considered the problem of fuzzy hypotheses testing with crisp data. Arnold [8] and Arnold [9] presented an approach to test fuzzily formulated hypotheses, in which he considered the fuzzy constraints on Types I and II errors. Holena [19] considered a fuzzy generalization of a sophisticated approach to exploratory data analysis.…”

Section: Introductionmentioning

confidence: 99%