The main aim of this paper is to connect R-Fuzzy sets and type-2 fuzzy sets, so as to provide a practical means to express complex uncertainty without the associated difficulty of a type-2 fuzzy set. The paper puts forward a significance measure, to provide a means for understanding the importance of the membership values contained within an R-fuzzy set. The pairing of an R-fuzzy set and the si...

We will leave to later the explanation of exactly what the 95% confidence level means. For now, we’ll note that taken together the width of the interval and the confidence level provide a measure on the strength of the evidence supporting the hypothesis that the μ is close to our estimate x. You should think of the confidence level of an interval as analogous to the significance level of a NHST...

The present paper investigated academic self – efficacy beliefs of undergraduate mathematics education students with respect to gender, academic performance and grade level. The participants were a total of 244 undergraduate students (195 females and 49 males) enrolled to department of mathematics education (57 freshmen, 106 sophomores and 81 junior) of a government university located west side...

In testing hypotheses, we may confront with cases where data are recorded as non-precise (fuzzy) rather than crisp. In such situations, the classical methods of testing hypotheses are not capable and need to be generalized. In solving the problem of testing hypotheses based on fuzzy data, the fuzziness of the observed data leads to the fuzzy p-value. This paper has been focused to calculate fuz...

This paper reviews and compares two R packages ``FPV" and ``Fuzzy.p.value".These packages are designed for testing hypotheses in a fuzzy environment using a fuzzy $p$-value based approach.In fact, the packages ``FPV" and ``Fuzzy.p.value" propose some useful functions for testing hypotheses when the data / hypotheses are fuzzy rather than crisp.The proposed methods and function...

Dichotomization of the outcome by a single cut-off point is an important part of various medical studies. Usually the relationship between the resulted dichotomized dependent variable and explanatory variables is analyzed with linear regression, probit regression or logistic regression. However, in many real-life situations, a certain cut-off point dividing the outcome into two groups is unknow...

BACKGROUND A recent cross-national study demonstrated a curvilinear (inverted U-shaped curve) between elderly male suicide rates and the Human Development Index (HDI) fitting the quadratic equation y = a + bx - cx2 where y is the elderly male suicide rate, x is the HDI and a, b and c are constants). This study used only one-year cross-sectional data on suicide rates, and suicide rates can rando...

In this paper we introduce a neural network implementation of fuzzy mathematical morphology operators and apply it to image denoising. Using a supervised training method and differentiable equivalent representations for the fuzzy morphological operators, we derive efficient adaptation algorithms to optimize the structuring elements. We can then design fuzzy morphological filters for processing ...