# Rédina BerkachyUniversité de Fribourg · Department of Informatics

Rédina Berkachy

PhD

## About

34

Publications

644

Reads

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82

Citations

Citations since 2016

Introduction

Rédina Berkachy currently works at the Applied Statistics and Modelling ASAM group of the Department of Informatics , Université de Fribourg. Rédina does research in Fuzzy Statistics, Data Mining, Computing in Economic and Social Sciences and Computing in Mathematics, Natural Science, Engineering and Medicine. Their most recent publication is 'Testing Fuzzy Hypotheses with Fuzzy Data and Defuzzification of the Fuzzy p-value by the Signed Distance Method.'

Additional affiliations

January 2016 - present

June 2014 - September 2014

**Murex SA**

Position

- Researcher

October 2013 - May 2014

## Publications

Publications (34)

We propose a practical procedure of construction of fuzzy confidence intervals by the likelihood method where the observations and the hypotheses are considered to be fuzzy. We use the bootstrap technique to estimate the distribution of the likelihood ratio. The chosen bootstrap algorithm consists on randomly drawing observations by preserving the...

The main focus of this book is on presenting advances in fuzzy statistics, and on proposing a methodology for testing hypotheses in the fuzzy environment based on the estimation of fuzzy confidence intervals, a context in which not only the data but also the hypotheses are considered to be fuzzy. The proposed method for estimating these intervals i...

Calculating the difference between fuzzy numbers is often seen as a complicated operation, mainly because of the semi-linear nature of the space of fuzzy numbers. In addition, in this space a universally acceptable method of total ordering does not yet exist. An efficient solution for these problems is to consider a suitable metric. The proposed me...

Data sets collected from real experiments are often affected by the randomness, while this information could have an imprecise nature. Therefore, in such random data sets, the probability theory could not always be sufficient for modelling this uncertainty. This latter requires complementary tools. Thus, a combination between probability and fuzzy...

Different methods of processing fuzzy information exist. We note, as instance, the Sugeno method (Takagi, and Sugeno (IEEE Trans Syst Man Cyb 15:116–132, 1985)) which allows to simplify the calculations based on an aggregation of the information, in the purpose of obtaining an interpretable solution. This method is often used in real time applicati...

As a first step, it is important to postulate the fundamental concepts of fuzzy sets as proposed in Zadeh (Inf Control 8:338–353, 1965). This chapter is then devoted to basic notions of fuzzy sets, the logical and arithmetic related-operations, and to the well-known extension principle. Detailed examples illustrate the different concepts.

We propose a R package called FuzzySTs, where numerous functions are implemented. This package aims to provide a complete framework of theoretical and applied fuzzy statistical tools as described in the previous chapters using a variety of calculation methods. It is completely self-sustaining and constitutes a coherent programming environment and u...

Linguistic questionnaires have gained lots of attention in the last decades. They are a prominent tool used in many fields to convey the opinion of people on different subjects. In this chapter, we propose a model for the assessment of linguistic questionnaires describing the global and individual evaluations, where we suppose that the sample weigh...

The aim of this chapter is to expose a multi-ways fuzzy analysis of variance (Mult-FANOVA) approach when the fuzziness is taken into consideration. This latter is based on a fuzzy regression model. As such, we expose two exploratory approaches: the first one by preserving the fuzzy nature of the calculated sums of squares using fuzzy approximations...

This chapter first shows the definition of a fuzzy hypothesis. We after display the construction of a given fuzzy confidence interval. One of the highlights of this chapter is a new procedure of construction of fuzzy confidence intervals by the likelihood ratio method using the bootstrap technique. Moreover, we show in detail the hypotheses testing...

The measure of poverty is an excellent field to apply fuzzy statistics. Indeed, nowadays, this measure is fast always considered as multidimensional. Furthermore, the evaluation of a poverty level, which is on a large scale subjective and varying between individuals and upon situations, has undoubtfully a fuzzy content. We propose, first, to show i...

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 defuzzifi...

The central moments of a random variable are extensively used to understand the characteristics of distributions in classical statistics. It is well known that the second central moment of a given random variable is simply its variance. When fuzziness in data occurs, the situation becomes much more complicated. The central moments of a fuzzy random...

Testing hypotheses could sometimes benefit from the fuzzy context of data or from the lack of precision in specifying the hypotheses. A fuzzy approach is therefore needed for reflecting the right decision regarding these hypotheses. Different methods of testing hypotheses in a fuzzy environment have already been presented. On the basis of the class...

Nous présentons une approche d'ANOVA simple étendue à l'environnement flou. Sachant que le calcul d'un produit flou s'avère compliqué, une approximation de ce produit est requise. Notre contribution est d'approximer la différence entre deux nombres flous par une méthode intitulée méthode de la ”signed distance”. Le but est alors de réduire la compl...

This synthetic dataset composed of 500 observations is used in Example 2 of Section 6 - Paper submitted to the "27èmes rencontres francophones sur la logique floue et ses applications, Arras, France", November 2018

Fuzzy statistical methods appear to be well suited to situations where the data we are collecting are exposed to fuzziness and uncertainty. Calculating for instance analytically or numerically the fuzzy variance could be advantageous. Yet, this task is not simple, especially regarding the difficulties in measuring the multiplication of two fuzzy se...

We extend the classical approach of hypothesis testing to the fuzzy environment. We propose a method based on fuzziness of data and on fuzziness of hypotheses at the same time. The fuzzy p-value with its α-cuts is provided and we show how to defuzzify it by the signed distance method. We illustrate our method by numerical applications where we trea...

Considering our interest in studying questionnaires composed by linguistic variables e.g. categorical variables using fuzzy logic and applying it in real life data, we show how to compute and analyse this type of data in a fuzzy perspective. We propose an individual and global evaluations of the so-called ”linguistic questionnaires” using the signe...

Dans ce travail, nous présentons une nouvelle méthode d’auto-apprentissage du langage de programmation R, un langage utile pour les statisticiens comme pour tout autre chercheur désirant faire des analyses statistiques. Le Notebook Jupyter est une application Web innovatrice utilisée fondamentalement pour l’enseignement de langage de programmation....

PurposeDue to sedentarity-associated disease risks, there is much interest in methods to increase low-intensity physical activity. In this context, it is widely assumed that altering posture allocation can modify energy expenditure (EE) to impact body-weight regulation and health. However, we have recently shown the existence of two distinct phenot...

Having in mind the evaluation of linguistic questionnaires, we aim to present a comparison in terms of statistical measures between on one side a relative recent defuzzification method, known as the signed distance method, and on the other side, other well-known traditional methods. The distribution’s properties of data resulting from the defuzzifi...

Linguistic questionnaires are one of the very challenging keys in the world of surveys, in particular considering their fuzziness and imprecision. Many approaches have been used to evaluate them. In this paper, we show the individual and global evaluations of a linguistic questionnaire using fuzzy logic, and the relation between these two evaluatio...

La situation de travail des entrepreneurs, dirigeants de PME, travailleurs indépendants, est souvent présenté comme caractérisée par une large autonomie de décision, une liberté dans le choix des activités, une flexibilité au niveau de la gestion du temps, la possibilité de développer ses connaissances et ses compétences. C’est par exemple ainsi qu...

## Projects

Project (1)