sets theory
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2022 ◽  
Author(s):  
Besma Belhadj

Abstract Poverty is recently considered to be a multidimensional one. That is to say the poor can suffer multiple disadvantages at the same time. This paper aims to further develop and refine the multidimensional poverty measure using Fuzzy Sets Theory (FST). The application of FST starts with the choice of membership functions and the rules to manipulate to integrate attributes inequality in multidimensional poverty measure. An application based on individual well-being data from Tunisian households in 2015 is presented to illustrate use proposed concepts. JEL classification: P46; I32; D81; C00;


2021 ◽  
Vol 14 (12) ◽  
pp. 590
Author(s):  
Katarzyna Boratyńska

The consequences of COVID-19 will aggravate existing multidimensional risks and reveal new ones. The research gap allows contributing to recognizing the exogenous risk factors of corporate bankruptcy during the COVID-19 pandemic in EU countries. This study aims at revealing how to evaluate the risk of corporate bankruptcy phenomenon in the COVID-19 times. The question arises as to whether Schumpeter’s creative destruction approach is still accurate. The article concentrates on implementing the fsQCA (fuzzy set Qualitative Comparative Analysis) method to identify and evaluate the main exogenous drivers of corporate bankruptcy in EU countries based on Fragile States Index data. This new approach focuses on fuzzy sets theory. The fsQCA method is a globally recognized alternative to quantitative analysis (in which the causal complexity is ignored) and qualitative methods for examining individual cases (which do not have the tools to generalize on their basis). The research indicates and examines the main external factors that would increase the risk of corporate bankruptcy in EU countries: namely, economic decline, uneven economic development, unemployment rate, demographic pressure, and government debt. The study discusses the influence of zombie companies on economies during the COVID-19 pandemic. Identifying risk factors that determine the threat of corporate bankruptcy may constitute practical recommendations for business and restructuring practitioners, financial institutions, and banking and public sector representatives in creating warning and recovery measures during the COVID-19 pandemic.


2021 ◽  
Vol 27 (4) ◽  
pp. 78-81
Author(s):  
Mladen Vassilev-Missana

In the paper, the inequality \frac{\mu^{\frac{1}{\nu}}}{\nu} + \frac{\nu^{\frac{1}{\mu}}}{\mu} \leq \frac{1}{2\mu\nu} - 1 is introduced and proved. The same inequality is valid for \mu = \mu_A(x), \nu = \nu_A(x), where \mu_A and \nu_A are the membership and the non-membership functions of an arbitrary intuitionistic fuzzy set A over a fixed universe E and x \in E.


2021 ◽  
Vol 2131 (3) ◽  
pp. 032007
Author(s):  
O Chislov ◽  
N Lyabakh ◽  
M Kolesnikov ◽  
M Bakalov ◽  
D Bezusov

Abstract The relevance of mechanisms and fuzzy modeling methods used in transport and logistics processes is justified. The logic of the transport and logistics chains study by their decomposition into separate economic entities with subsequent synthesis, with taking into account their conflicting interests, is presented. The task of managing transport and logistics processes is set within the framework of the conceptual positions of the fuzzy sets theory: the use of linguistic variables, the concept of a fuzzy set, fuzzy inference, implemented on the basis of fuzzy sets operations. In this study, the fuzzy modeling on the bottom-up conclusions from the premises to the conclusion was used. Various methods of implication and defuzzification have been analyzed. An iterative procedure for managing transport and logistics chains and their links has been proposed, which ensures the adaptation of the process to the specified performance indicators. A calculated example is given for a marshalling yard as a link in the transport and logistics chain.


Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2938
Author(s):  
Rully Charitas Indra Prahmana ◽  
Afit Istiandaru

Some countries have puppet culture in various forms, terms, and ways, including Indonesia. As a country with a diverse culture, it has detailed and comprehensive characteristics and stories related to puppets, especially the Javanese shadow puppet. Some experts have explored its characteristics and found out that it contains many mathematical elements which could be used as a starting point to learn mathematics. The elements, however, still focus on the exploration of geometry material. We hardly find any other material that has been explored as deep as the geometry material in the context of the Javanese shadow puppet. Therefore, this study aims to explore the other elements of mathematics potentially found in this context which—for this example—is the sets material. Besides, this study also discusses the righteous life values that the students could internalize during mathematics learning through shadow puppet culture. We used ethnography to explore it through literature study, documentation, and field notes. We found some interesting elements, characteristics, and patterns in the Javanese shadow puppet, which can be used as a starting point to learn the sets concept. Furthermore, the values and philosophy of the shadow puppet culture harbor the potential to foster the students’ good character and behavior.


Entropy ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 1485
Author(s):  
Pavel Sevastjanov ◽  
Ludmila Dymova ◽  
Krzysztof Kaczmarek

In this short paper, a critical analysis of the Neutrosophic, Pythagorean and some other novel fuzzy sets theories foundations is provided, taking into account that they actively used for the solution of the decision-making problems. The shortcomings of these theories are exposed. It is stated that the independence hypothesis, which is a cornerstone of the Neutrosophic sets theory, is not in line with common sense and therefore leads to the paradoxical results in the asymptotic limits of this theory. It is shown that the Pythagorean sets theory possesses questionable foundations, the sense of which cannot be explained reasonably. Moreover, this theory does not completely solve the declared problem. Similarly, important methodological problems of other analyzed theories are revealed. To solve the interior problems of the Atanassov’s intuitionistic fuzzy sets and to improve upon them, this being the reason most of the criticized novel sets theories were developed, an alternative approach based on extension of the intuitionistic fuzzy sets in the framework of the Dempster–Shafer theory is proposed. No propositions concerned with the improvement of the Cubic sets theory and Single-Valued Neutrosophic Offset theory were made, as their applicability was shown to be very dubious. In order to stimulate discussion, many statements are deliberately formulated in a hardline form.


2021 ◽  
Vol 2 ◽  
pp. 81-87
Author(s):  
Eva Rakovská

Today, businesses depend strongly on data and the opinion of customers or the experience of managers or experts. The large databases contain non-heterogeneous data, which is the ground for further decisions. Business uses multicriterial decisions in more areas (e.g., customer care, marketing, product development, risk management, HR, etc.) and often it is based on assessment. One of the assessment methods is the ranking, which can be done by crisp values of data where the sharp borders between evaluated entities do not give the adequate ranking result. On the other hand, the ranking process is based on the qualitative assessment, which has linguistic expression. It is more familiar and understandable for people. The article shows how to treat non-heterogeneous data to prepare them for a ranking process using fuzzy sets theory. The article aims at offering several types of ranking methods based on different inputs and preferences of the user and describes appropriate fuzzy aggregations for solving the ranking problem.


2021 ◽  
Vol 8 (4) ◽  
pp. 238
Author(s):  
Claudio Molina Salinas

This article shows the application of an ethnographical method (lexical availability method) and diverse strategies for lexical documentation (documentation of terminology in gray literature and other published documents) to the compilation and validation of the terminology of folk-art in Mexico, a knowledge area with scarcely written tradition. As one can foresee, the result obtained from the lexicon through the different methods and strategies of documentation applied allows registering several terminological lists. From these lists and by determining the intersection of two or more lexical sets, principle obtained from the set theory, one can obtain a group that contains the most frequent elements or the common terminology of a domain. In addition to the above, the article explains how a facets system for the basic organization of this terminology can be created from the lexical documentation obtained.


2021 ◽  
Author(s):  
Jerome A. Adepoju

The Chapter presents diverse but related results to the theory of the proper and generalized Goncarov polynomials. Couched in the language of basic sets theory, we present effectiveness properties of these polynomials. The results include those relating to simple sets of polynomials whose zeros lie in the closed unit disk U=z:z≤1.. They settle the conjecture of Nassif on the exact value of the Whittaker constant. Results on the proper and generalized Goncarov polynomials which employ the q-analogue of the binomial coefficients and the generalized Goncarov polynomials belonging to the Dq- derivative operator are also given. Effectiveness results of the generalizations of these sets depend on whether q<1 or q>1. The application of these and related sets to the search for the exact value of the Whittaker constant is mentioned.


Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 2000
Author(s):  
Alina Alb Lupaş ◽  
Georgia Irina Oros

The present paper deals with notions from the field of complex analysis which have been adapted to fuzzy sets theory, namely, the part dealing with geometric function theory. Several fuzzy differential subordinations are established regarding the operator Lαm, given by Lαm:An→An, Lαmf(z)=(1−α)Rmf(z)+αSmf(z), where An={f∈H(U),f(z)=z+an+1zn+1+…,z∈U} is the subclass of normalized holomorphic functions and the operators Rmf(z) and Smf(z) are Ruscheweyh and Sălăgean differential operator, respectively. Using the operator Lαm, a certain fuzzy class of analytic functions denoted by SLFmδ,α is defined in the open unit disc. Interesting results related to this class are obtained using the concept of fuzzy differential subordination. Examples are also given for pointing out applications of the theoretical results contained in the original theorems and corollaries.


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