Defuzzification of a Fuzzy p-value by the Signed Distance: Application on Real Data

Abstract

We develop a fuzzy hypothesis testing approach where we consider the fuzziness of data and the fuzziness of the hypotheses as well. We give the corresponding fuzzy p-value with its $\alpha$-cuts. In addition, we use the so-called “signed distance” operator to defuzzify this p-value and we provide the convenient decision rule. Getting a defuzzified p-value and being able to interpret it can be of good use in many situations. We illustrate our testing procedure by a detailed numerical example where we study a right one-sided fuzzy test and compare it with a classical one. We close the paper by an application of the method on a survey from the financial place of Zurich, Switzerland. We display the decisions related to tests on the mean made on a set of variables of the sample. Both fuzzy and classical tests are conducted. One of our main findings is that despite the fact that each of both approaches have a different decision rule in terms of interpretation, the decisions made are by far the same. In this perspective, we can state that the fuzzy testing procedure can be seen as a generalization of the classical one.