Выявление аномального поведения системами обнаружения атак при интервально-значном представлении данных

В статье рассмотрен метод обнаружения аномального поведения пользователей распределенной компьютерной сети при интервально-значном представлении данных, основанный на построении устойчивой кластерной структуры с помощью эвристического метода возможностной кластеризации. Предложенный метод иллюстрируется результатами вычислительного эксперимента.У статті розглянуто метод виявлення аномальної поведінки користувачів розподіленої комп’ютерної мережі при інтервально-значному зображенні даних, що заснований на побудові стійкої кластерної структури за допомогою евристичного методу можливісної кластеризації. Запропонований метод ілюструється результатами обчислювального експерименту.A method of detecting anomalous user behavior in a distributed computational network for a case of interval-valued data is considered in the article. The method is based on constructing stable clustering structure using a heuristic method of possibilistic clustering. The proposed method is illustrated by the results of numerical experiment

On Intuitionistic Fuzzy Entropy of Order-α

Using the idea of Rènyi’s entropy, intuitionistic fuzzy entropy of order-α is proposed in the setting of intuitionistic fuzzy sets theory. This measure is a generalized version of fuzzy entropy of order-α proposed by Bhandari and Pal and intuitionistic fuzzy entropy defined by Vlachos and Sergiadis. Our study of the four essential and some other properties of the proposed measure clearly establishes the validity of the measure as intuitionistic fuzzy entropy. Finally, a numerical example is given to show that the proposed entropy measure for intuitionistic fuzzy set is reasonable by comparing it with other existing entropies

Atanassov’s intuitionistic fuzzy index of hypergroupoids

In this work we introduce the concept of Atanassov’s intuitionistic fuzzy index of a hypergroupoid based on the notion of intuitionistic fuzzy grade of a hypergroupoid. We calculate it for some particular hypergroups, making evident some of its special properties

Data granulation by the principles of uncertainty

Researches in granular modeling produced a variety of mathematical models, such as intervals, (higher-order) fuzzy sets, rough sets, and shadowed sets, which are all suitable to characterize the so-called information granules. Modeling of the input data uncertainty is recognized as a crucial aspect in information granulation. Moreover, the uncertainty is a well-studied concept in many mathematical settings, such as those of probability theory, fuzzy set theory, and possibility theory. This fact suggests that an appropriate quantification of the uncertainty expressed by the information granule model could be used to define an invariant property, to be exploited in practical situations of information granulation. In this perspective, a procedure of information granulation is effective if the uncertainty conveyed by the synthesized information granule is in a monotonically increasing relation with the uncertainty of the input data. In this paper, we present a data granulation framework that elaborates over the principles of uncertainty introduced by Klir. Being the uncertainty a mesoscopic descriptor of systems and data, it is possible to apply such principles regardless of the input data type and the specific mathematical setting adopted for the information granules. The proposed framework is conceived (i) to offer a guideline for the synthesis of information granules and (ii) to build a groundwork to compare and quantitatively judge over different data granulation procedures. To provide a suitable case study, we introduce a new data granulation technique based on the minimum sum of distances, which is designed to generate type-2 fuzzy sets. We analyze the procedure by performing different experiments on two distinct data types: feature vectors and labeled graphs. Results show that the uncertainty of the input data is suitably conveyed by the generated type-2 fuzzy set models.Comment: 16 pages, 9 figures, 52 reference

A Fuzzy-Set Qualitative Comparative Analysis of Publications on the Fuzzy Sets Theory

[EN] The publication opportunities in science require knowing the existing gaps in the academic debate. In recent decades, scholars specializing in fuzzy theory and applied methodologies have experienced an unprecedented evolution of the field. The Sustainable Development Goals (SDGs) have shaped the way socio-technical transitions use fuzzy methodologies to solve environmental problems. This study conducts a systematic literature review of articles published in the Journal Citations Report on these specific fields. The Web of Science (Core Collection) was used and a database was assembled (N = 1956) that allowed the evaluation of the evolution of the research agenda and detecting high-impact publication opportunities. A model of analysis of successful strategies in academic influence is proposed. The model is tested with a configurational methodology through fuzzy-set Qualitative Comparative Analysis (fsQCA). The conditions used are: number of authors, underlying interest of the researchers, standardized citations per year, age of the articles and link of the research with sustainability. The results are solid and inform five paths that ensure the success of academic publications in high-impact journals. The robustness of the model allows its extrapolation to other fields of research. The contribution of this article allows knowledge of the academic conversation and its research opportunities. In addition, it clarifies the different paths that guarantee high impact research articles. This article offers important recommendations for academics and journal editors, allowing them to guide and advise academic production in the scholarly debate of the future.This research was funded by ESIC Business and Marketing School under grant number 1-V-2021 and is part of the SEDDeS Research Group (Society, Digital Economy and Sustainable Development).Castello-Sirvent, F. (2022). A Fuzzy-Set Qualitative Comparative Analysis of Publications on the Fuzzy Sets Theory. Mathematics. 10(8):1-23. https://doi.org/10.3390/math1008132212310

Multi-Criteria Decision-Making Model using Intuitionistic Fuzzy Entropy and Variable Weight Theory

The aim of this research is to develop a new multi-criteria decision-making method that integrates an intuitionistic fuzzy entropy measure and variable weight theory to be implemented in different fields to provide a solution for MCDM problems when the available information is incomplete. A limited number of studies have considered determining decision maker’s weights by performing objective techniques, and almost all of these researches detected a constant weights for the decision makers. In addition, most of the MCDM studies were not formulated to perform sensitivity analysis. The new method is based on the TOPSIS model with an intuitionistic fuzzy entropy measure in the exponential-related function form and the engagement of the variable weight theory to determine weights for the decision-makers that vary as per attibutes. Lastly, a mathematical model was developed in this research to be as an input for developing the mobile-aplication based method in future for virtual use of the new MCDM method

3-tuple Bézier surface interpolation model for data visualization

In this paper, the 3-tuple Bézier surface interpolation model is introduced. The 3-tuple control net relation is defined through intuitionistic fuzzy concept. Later, the control net is blended with Bernstein basis function to obtain surface blending function and to produce 3-tuple Bézier surface. The 3-tuple Bézier surface model is illustrated through the interpolation method by using data point with intuitionistic features. Some numerical example is shown. Lastly, the 3-tuple Bézier surface properties is also discussed

Medical Pattern Recognition: Applying an Improved Intuitionistic Fuzzy Cross-Entropy Approach

One of the toughest challenges in medical diagnosis is the handling of uncertainty. Since medical diagnosis with respect to the symptoms uncertain, they will be assumed to have an intuitive nature. Thus, to obtain the uncertain optimism degree of the doctor, fuzzy linguistic quantifiers will be used. The aim of this article is to provide an improved nonprobabilistic entropy approach to support doctors examining the work of the preliminary diagnosing. The proposed entropy measure is based on intuitionistic fuzzy sets, extrainformation regarding hesitation degree, and an intuitive and mathematical connection between the notions of entropy in terms of fuzziness and intuitionism has been revealed. An illustrative example for medical pattern recognition demonstrates the usefulness of this study. Furthermore, in order to make computing and ranking results easier and to increase the recruiting productivity, a computer-based interface system has been developed to support doctors in making more efficient judgments

New Entropy-Based Similarity Measure between Interval-Valued Intuitionstic Fuzzy Sets

In this paper we propose a new approach to construct similarity measures using the entropy measure for Interval-Valued Intuitionistic Fuzzy Sets. In addition, we provide several illustrative examples to demonstrate the practicality and effectiveness of the proposed formula. Finally, we use the new proposed similarity measure to develop new approach for solving problems of pattern recognition and multi-criteria fuzzy decision making