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Automatic image detection is one of the most im- portant areas in computing due to its potential application in numerous real-world scenarios. One important tool to deal with that is called overlap indices. They were introduced as a procedure to provide the maximum lack of knowledge when comparing two fuzzy objects. They have been successfully applied in the following fields: image processing, fuzzy rule-based systems, decision making and computational brain interfaces. This notion of overlap indices is also necessary for applications in which type-2 fuzzy sets are required. In this paper we introduce the notion of type-(2, k) overlap index (k 0, 1, 2) in the setting of type-2 fuzzy sets. We describe both the reasons that have led to this notion and the relationships that naturally arise among the algebraic underlying structures. Finally, we illustrate how type- (2, k) overlap indices can be employed in the setting of fuzzy rule-based systems when the involved objects are type-2 fuzzy sets. This manuscript has been partially supported by Junta de Andalucía by Projects A-FQM-170-UGR20 (Program FEDER Andalucía 2014-2020) and FQM-365 (Andalusian CICYE), and also by Projects PID2020-119478GBI00 and PID2019-108392GB-I00 (AEI/10.13039/501100011033, Ministerio de Ciencia e Innovación), by CNPq (301618/2019-4), FAPERGS (19/2551- 0001660) and grant VEGA 1/0267/21.

Unmanned Aerial Vehicles (UAVs) are increasingly used in the military field. Especially in recent years, UAVs have been a very effective instrument in gaining airspace superiority and military success. Many countries compete with each other to develop better UAV technology or improve the technical features of UAVs. Therefore, it is critical to determine which UAV has the best performance, considering technical and operational characteristics, because the vehicles with more advanced performance can provide countries with strategic superiority. The purpose of this study is to investigate the technical, cost, and operational performance of Medium Altitude Long Endurance UAVs (MALE UAVs). In the study, as a result of a wide literature review, we determined a performance criterion for this type of vehicle. The model presented here uses an Interval Type-2 Fuzzy Analytical Hierarch Process (IT2FAHP) and an Interval Type-2 Fuzzy Technique for Order of Preference by Similarity to an Ideal Solution (IT2FTOPSIS) hybrid method. The findings indicate that some MALE UAVs have superior technical and operational performance over others and demonstrate that range, max take-off weight, and payload are important criteria in determining the performance and superiority of these vehicles.

Graph theory has been a useful tool for logic programming in many aspects. In this paper, we propose an equivalent representation of multi-adjoint logic programs using hypergraphs, which are a generalization of classical graphs that allows the use of hypergraph theory in logic programming. Specifically, this representation has been considered in this paper to increase the level and flexibility of different termination results of the computation of the least model of fuzzy logic programs via the immediate consequence operator. Consequently, the least model of more general and versatile fuzzy logic programs can be obtained after finitely many iterations, although infinite programs or programs with loops and general aggregators will be considered Agencia Estatal de Investigación PID2019-108991GB-I00 Junta de Andalucía FEDER-UCA18-108612 European Union COST Action CA17124

The use of solar photovoltaic (PV) panels is one of the most promising ways to generate electricity. However, the complex technical parameters associated with them make the choice between different PV panels a complicated task. The aim of the article is the analysis and multi-criteria evaluation of PV panels available on the Polish market and to indicate the optimal solar PV panels according to the adopted technical criteria. The practical goal was achieved using a fuzzy approach, taking into account the uncertainty of operational parameters. Based on the applied approach and multi-criteria NEAT F-PROMETHEE method, a fuzzy decision model was built for the evaluation of PV panels. The results of this model were compared with the results of an analogous model that did not take into account the uncertainty of the data. As a result of the research, it was found that the results of the fuzzy model should be considered more reliable, because fuzzy numbers allow for capturing more data than real numbers, which translates into greater reliability of the results of the fuzzy model.

International audience; This work is devoted to an sliding-mode control for nonlinear singularly perturbed system under a network control framework. Aiming at describing the nonlinearities with parameter uncertainties in the studied system, the idea of interval type-2 (IT2) fuzzy method is employed in the system modeling. A disturbance observer is developed to acquire the unknown disturbance, and the estimated value is implemented into the controller for neutralizing the influence of the disturbance. To further reduce the occupation of network resources, an event-triggered communication protocol with a dynamic threshold parameter is adopted, where the triggered condition can be adjusted adaptively as the evolution of the system states. Then, an appropriate fuzzy integral sliding motion is constructed based on the constructed system model and disturbance estimation. It is worth noting that the constructed fuzzy controller follows the idea of nonparallel distribution compensation, which improves the designed flexibility. In terms of fuzzy processing, by introducing the membership functions dependent method into the stability analysis, a series of relaxed criteria are established to ensure the global asymptotic stability for the closed-loop systems with performance level. Finally, two classical examples of circuit model and inverted pendulum model are extended to IT2 fuzzy idea, showing the rationality of the proposed approach.

The pandemic period has made remote work a reality in many organizations. Despite the possible negative aspects of this form of work, many employers and employees appreciate its flexibility and effectiveness. Therefore, employers are looking for the most optimal tools to support this form of work. However, this may be difficult due to their complexity, different functionality, or different conditions of the company’s operations. Decisions on the choice of a given solution are usually made in a group of decision makers. Often their subjective assessments differ from each other, making it even more difficult to make a decision. The aim of this article is to propose a methodological solution supporting the assessment of the most popular teleconferencing systems and generating their ranking. The feature of this solutions is the combination of two important methodological aspects facilitating the selection process. The first one concerns the possibility of taking into account quantitative and qualitative criteria expressed linguistically and of an uncertain nature in the assessment (NEAT F-PROMETHEE method). The second one is related to the possibility of taking into account the assessments of many experts, including the consensus study between them (PROSA GDSS method). The use of these combined methods to assess teleconferencing platforms made it possible to create their ranking and indicate the solution that best meets the adopted criteria (based on experts’ opinions). The Microsoft Teams system turned out to be this solution, whose functionality, usability, multi-platform aspect and other elements turned out to be crucial in the context of the overall assessment. The results obtained may be a guideline for managers and decision makers facing the choice of a tool supporting remote work.

Cities of the 21st century are buffeted with challenges, leaving potentially serious consequences on the future of urban living. Smartening development in cities has reinvented hopes of melting down predicaments in the early 2000s'. However, perplexed by the intensifying complexities of smart cities, urban living in smart cities needs to be evaluated with multiple conflicting criteria. Multi-criteria-based evaluations have been an answer to this case when attempting to gauge the composite performance of multiple decision-making entities. Several multi-criteria assessment techniques exist when dealing with selection problems. Nonetheless, the vagueness associated with the methodologies accompanied by uncertainties and complexities is inevitable in multi-attribute assessments. Fuzzy-based multi-criteria models are often an answer to such uncertainties when modelling real-world problems. The study thus presents a novel fuzzy expert-based multi-criteria decision support model, where the Analytical Hierarchy Process (AHP) is combined with the Evaluation based on Distance from Average Solution (EDAS) approach under a spherical fuzzy environment to create a composite index for comprehensive performance monitoring. The case of 35 high-tech European cities was used to empirically validate the proposed novel approach and thus construct a composite index. The composite index considers the intricate facet of integrating the concept of smart cities with sustainability, urban resilience, and livability under a unified framework. The fuzzy c-means partitioning technique was then used to segment smart cities into high, medium, and low-performing classes. A comparative analysis considering several distance-based approaches under a fuzzy environment with the SF-AHP and EDAS methodology is conducted to validate the robustness and stability of the proposed novel decision support model. The results revealed London as the top-ranked smart city that promotes sustainability, resilience, and livability in its current urban development model. Dusseldorf, Zurich, Munich, Oslo, Dublin, Amsterdam, Hamburg, Rome, Moscow, and Stockholm were no exemption from addressing the tritactic goals of sustainability, urban resilience, and livability well into their urban development plan and were placed in the high-performance cluster. The proposed model is efficient to express decision makers' preferences in a larger space and modelling functional parameters including hesitancy independently in the 3-dimensional domain. The model supports decision-makers and relocation analysts to assess the performance of smart cities and set targets to improve performance to remodel urban development to a more sustainable, resilient, and livable pattern.

Power engineering is one of the most dynamic industries in the modern world; it applies specific production and management technologies and also assumes a complex structural transformation of power systems and transition of power engineering business to a qualitatively new level providing sustainable power supply. Within the context of existing situation, the electric power industry, which is currently actively developing, is an important element of power infrastructure that requires a long-term and continuous solution of the challenges the industry faces. These are the circumstances of the development of methodological tools and decision-making procedures based on multi-criteria analysis, since the tasks of developing energy systems in modern conditions represent the most typical class of tasks where the problem of taking into account multi-criteria and uncertainty is most acute. The purpose of the study is to develop methods for the formation and comparison of options for the development of electric power systems in conditions of uncertainty and multi-criteria. The use of fuzzy set reporting models and new decision-making procedures based on fuzzy relations are proposed to address the development challenges. When addressing them, a considerable room for applying multi-criteria analysis algorithms to various aspects of the problem of power systems development in the fuzzy information environment was demonstrated. The results of the study are presented in the form of an analysis of the rational concentration of power plant capacities, which made it possible to identify the most effective way to reduce the plant’s installed capacity while increasing the role of environmental criteria. The work was supported Russian Foundation for Basic Research (RFBR), contract № 20-010-00886.

Urban freight transportation requires wise management considerations since it is one of the most challenging issues cities face to attain sustainability. To help with the challenging decision process, an integrated two-stage decision analysis approach is proposed. In the first stage, the Defining Interrelationships Between Ranked criteria (DIBR) method is used to consolidate the experts’ opinions to compute the weights of the predetermined decision criteria. In the second stage, a novel approach that integrates Combined Compromise Solution (CoCoSo) with the context of type-2 neutrosophic numbers is used to identify the most optimal management decision alternative. A case study is developed to show the viability and practicability of the proposed methodology. The results indicated that “building a logistics center (for fast and cheap delivery)” is the highest-ranked decision alternative, followed by “optimized and integrated operation of urban logistics,” and “zero-emission zone implementation,” respectively. The proposed methodology can be used as a decision analysis framework for urban city authorities while selecting the most optimal policies and related solution alternatives towards achieving and sustaining low-emission urban freight transportation. © 2022 Elsevier Inc.

Nowadays, most fuzzy clustering algorithms are sensitive to the initialization results of clustering algorithms and have a weak ability to handle high-dimensional data. To solve these problems, we developed the viewpoint-driven subspace fuzzy c-means (VSFCM) algorithm. Firstly, we propose a new cut-off distance. Based on this, we establish the cut-off distance-induced clustering initialization (CDCI) method and use it as a new strategy for cluster center initialization and viewpoint selection. Secondly, by taking the viewpoint obtained by CDCI as the entry point of knowledge, a new fuzzy clustering strategy driven by knowledge and data is formed. Based upon these, we put forward the VSFCM algorithm combined with viewpoints, separation terms, and subspace fuzzy feature weights. Moreover, compared with the symmetric weights obtained by other subspace clustering algorithms, the weights of the VSFCM algorithm exhibit significant asymmetry. That is, they assign greater weights to features that contribute more, which is validated on the artificial dataset DATA2 in the experimental section. The experimental results compared with multiple advanced clustering algorithms on the three types of datasets validate that the proposed VSFCM algorithm has the best performance in five indicators. It is demonstrated that the initialization method CDCI is more effective, the feature weight allocation of VSFCM is more consistent with the asymmetry of experimental data, and it can achieve better convergence speed while displaying better clustering efficiency.

There are a sufficient number of works devoted to modeling crushing machines. Nevertheless, the fact that there are a large number of working conditions, and the ongoing development of science and technology, require continuous improvement and specification of the models intended for crushing processes and those of the devices concerned. However, there are few studies related to single-roll gyratory crushers. Such crushers are promising for use in mines to crush rocks laid in the developed space. Mathematical modeling and optimization of the design parameters of the working chamber and the executive body (roll) of a single-roll gyratory shaft crusher, designed for crushing strong rocks, was performed in this paper. A differential equation was derived. As a result of its solution, the rational shape of the working chamber cheek of the single-roll gyratory crusher was established, representing a logarithmic spiral arc. Analytical expressions were derived to determine the rational rotation speed and productivity of the crusher under consideration. Expressions for calculating the kinematic load components acting on the roll were formulated. They are the periodic functions of the shaft rotation angle. The Fourier series expansion showed that the loads contained harmonics of the first, second, third and fourth orders. Using the concept of fuzzy sets, a multi-criteria optimization of the design parameters of the working chamber was performed, including the values of the eccentricity and the central angle of the beginning of the cheek profile. The variation coefficients of the kinematic components of the loads acting on the working body reduced, due to the optimal choice of the working chamber profile and the angular coordinates of the installation of the fixed cheeks. The torque reduced 1.67 times, while the radial load decreased 1.2 times.

Masonry is a widespread construction system, but it is very prone to seismic damage. In Italy, almost 60% of residential buildings are constructed in masonry, and 85% of them were built before 1980 without specific design regulation; thus, there is the need for large-scale vulnerability assessment. When large stocks of residential buildings (>50–100) are involved, also in historical centers, seismic vulnerability analysis must resort to simplified and computer-aided methods. Among these, the best known analyze (i) the overall shear strength normalized to the weight; (ii) the activation coefficient of local mechanisms; and (iii) dimensionless indexes obtained from the weighted sum of scores associated with a set of vulnerability factors. The Vulnus procedure proposes a vulnerability function in the 3D space defined by these factors, namely VIP, VOP and VV. The ‘mechanical’ indexes VIP and VOP determine the capacity of the building (in-plane and out-of-plane, respectively), whereas the ‘empirical’ index VV sets the pace at which this capacity is reached and the uncertainty in its final value. The procedure considers the confidence level of the indexes by means of fuzzy set theory, which enables expression of the vulnerability in linguistic terms (e.g., ‘high’ or ‘low’), as well as through a fragility curve. In this paper, a web toolbox based on the Vulnus procedure, namely, Vulnus Web, is proposed. It enables the central archiving of data, improved interaction with the program code and a wider dissemination. The new procedure was applied to a masonry building hit by the Central Italy 2016 earthquake; both the vulnerability level assessed numerically and the damage prediction were in good accordance with the actual seismic performance of the building.

The paper is dedicated to modeling electricity spot prices and pricing forward contracts on energy markets. The underlying dynamics of electricity spot prices is governed by a stochastic mean reverting diffusion with jumps having mixed-exponential distribution. Application of financial mathematics and stochastic methods enabled the derivation of the analytical formula for the forward contract’s price in a crisp case. Since the model parameters’ incertitude is considered, their fuzzy counterparts are introduced. Utilization of fuzzy arithmetic enabled deriving an analytical expression for the futures price and proposing a modified method for decision-making under uncertainty. Finally, numerical examples are analyzed to illustrate our pricing approach and the proposed financial decision-making method.

Computation intelligence techniques are important for making decisions in an agile-based offshore software development paradigm. Offshore development faces additional challenges, such as trust, communication and coordination, and socio-cultural and knowledge transfer. There is a need to determine the rankings of challenges considering their criticality concerning practitioners working in agile-based offshore software development. This paper aims to identify and rank agile challenges in offshore software development by applying computational intelligence techniques. From the systematic literature review, we identified 30 communication and coordination challenges. The distributed agile pattern catalog consists of 15 patterns, from which eight were used to solve communication and collaboration challenges. Many researchers have used fuzzy logic to quantify their results. We further applied the fuzzy analytical technique to determine the priority order concerning the criticality of the identified agile pattern catalog. The results showed that Central Code Repository Pattern ranked the most significant for solving communication and coordination challenges. Global Scrum Board Pattern and Synchronous Communication Pattern ranked second.

Este artículo analiza los resultados de las elecciones a la Alcaldía de Santiago de Cali en 2003, 2007, 2011 y 2015. Con base en premisas del modelo sociológico del comportamiento electoral y mediante la utilización de conjuntos difusos (fuzzy sets) y de geo-referenciación, se hacen estimaciones acerca de las conductas electorales según el estrato socioeconómico y los niveles de fragmentación exhibidos por los distintos segmentos de candidaturas (élite-no élite). De esta manera, se identifican configuraciones causales que, como condiciones suficientes, contribuyen a desmitificar percepciones generalizadas sobre el impacto de algunos sectores de la ciudad en la elección del alcalde. This article analyzes the election results for the mayoralty of Santiago de Cali in 2003, 2007, 2011 and 2015. Based on premises of the sociological model of voting behavior and through the use of fuzzy sets and geo-referencing, it makes estimates regarding electoral behavior in relation to socio-economic status and levels of fragmentation exhibited by the different types of candidacy (elite–non-elite). Causal configurations are thus identified which, as sufficient conditions, contribute to demystifying widespread perceptions about the impact of some sectors of the city on the election of the mayor. Este artigo analisa os resultados das eleições para a Prefeitura de Santiago de Cali em 2003, 2007, 2011 e 2015. Com base em princípios do modelo sociológico do comportamento eleitoral e mediante a utilização de conjuntos difusos (fuzzy sets) e de georreferenciamento, fazem-se estimativas sobre os comportamentos eleitorais segundo a classe socioeconômica e os níveis de fragmentação exigidos pelos diferentes segmentos de candidaturas (elite-não elite). Dessa maneira, identificam-se configurações causais que, como condições suficientes, contribuem para desmitificar percepções generalizadas sobre o impacto de alguns setores da cidade na seleção do prefeito.

Non-additive measures, also known as fuzzy measures, capacities, and monotonic games, are increasingly used in different fields. Applications have been built within computer science and artificial intelligence related to e.g. decision making, image processing, machine learning for both classification, and regression. Tools for measure identification have been built. In short, as non-additive measures are more general than additive ones (i.e., than probabilities), they have better modeling capabilities allowing to model situations and problems that cannot be modeled by the latter. See e.g. the application of non-additive measures and the Choquet integral to model both Ellsberg paradox and Allais paradox. Because of that, there is an increasing need to analyze non-additive measures. The need for distances and similarities to compare them is no exception. Some work has been done for defining $f$-divergence for them. In this work we tackle the problem of defining the optimal transport problem for non-additive measures. Distances for pairs of probability distributions based on the optimal transport are extremely used in practical applications, and they are being studied extensively for their mathematical properties. We consider that it is necessary to provide appropriate definitions with a similar flavour, and that generalize the standard ones, for non-additive measures. We provide definitions based on the M\"obius transform, but also based on the $(\max, +)$-transform that we consider that has some advantages. We will discuss in this paper the problems that arise to define the transport problem for non-additive measures, and discuss ways to solve them. In this paper we provide the definitions of the optimal transport problem, and prove some properties.

Range query processing is a common edge computing and service in the Internet of Things, which can extract user-interest information from distributed edge devices. How to design lightweight privacy-preserving range query processing methods remains a challenging task. Existing secure range query approaches suffer from both high communication cost and long response time, which makes them unsuitable for edge computing over resource-constrained edge devices. In this paper, we propose two privacy-aware fuzzy query processing schemes based on fuzzy theory. Linguistic range variables, fuzzy overlap information and its recovery mechanism are introduced respectively. In addition, two distributed privacy-aware fuzzy range query processing algorithms are devised. Our approaches not only serve for privacy protection, but also aim to provide other optimal performances in terms of reliability, energy efficiency, and real-time response. Theoretical analysis and experimental evaluations based on real-world data sets validated our motivation.

This paper investigates the dissipativity-based filtering problem for the nonlinear systems subject to both uncertainties and time-varying delay in the time-delay interval type-2 (IT2) polynomial fuzzy framework. Filter design is a challenging issue for complex nonlinear systems especially when uncertainties and time delay exist. IT2 polynomial fuzzy model is an effective and powerful approach to analyze and synthesize uncertain nonlinear systems. This is the first attempt to design both the full-order and reduced-order IT2 polynomial fuzzy filter to ensure that the filtering error system is asymptotically stable under the dissipativity constraint. The design of filtering is based on the imperfect premise matching scheme where the number of fuzzy rules and shapes of membership functions of the designed fuzzy filter can differ from those of IT2 polynomial fuzzy model, to provide greater design flexibility and lower implementation burden. By utilizing the Lyapunov-Krasovskii functional based approach, the information of membership functions, time delay and system states is taken into account in the design process to develop the relaxed membership-function-dependent (MFD) and delay-dependent filtering existence criteria. Finally, simulation results are presented to illustrate the effectiveness of the filtering algorithm reported in this paper.

Automated brain tumor segmentation of MR image is a very challenging task in a medical point of view. As the nature of the tumor, it can appear anywhere in the brain region with any size, shape, and contrast, that makes the segmentation process more difficult. In order to handle such issues, present work proposes an automated brain tumor segmentation method using rough-fuzzy C-means (RFCM) and shape based topological properties. In rough-fuzzy C-means, overlapping partition is efficiently handled by fuzzy membership and uncertainty in the datasets is resolved by lower and upper bound of the rough set. Fuzzy boundary and crisp lower approximation in RFCM play an effective contribution in brain tumor segmentation on MR images. Initial centroids selection is a major issue in C-means algorithms. Present work has introduced a method for initial centroids selection by which the execution time of RFCM is reduced as compared to random initial centroids. A patch based K-means method is also implemented for skull stripping as a preprocessing step. The proposed method was tested on MRI standard benchmark datasets. Experimental results show that the proposed method has achieved better performance based on statistical volume metrics than previous state-of-the-art algorithms with respect to ground truth (manual segmentation). It is also experimentally noticed that RFCM method achieves most promising results with higher accuracy than HCM (hard C-means) and FCM (fuzzy C-means).

The crypto and digital assets ecosystems have attracted investment, regulators, and speculators to their environment. As the blockchain-based framework can reduce transaction costs, generate distributed trust, and enable decentralized platforms, it has become a potential new base for decentralized business models. Previous studies have highlighted the advantages and drawbacks of each platform, such as interest rates, cost concerns, transparency issues, hacking issues, and hazards. Consequently, it is challenging for investors to evaluate the cryptocurrency trading system which determines the optimum exchanges and crucial aspects. Therefore, in order to rank the optimal digital token trading system, this paper develops an evaluation architecture to determine the various token trading systems. The developed architecture integrates fuzzy theory and the best-worst method (BWM) into the decision-making process to assess decision behaviors regarding preference for digital token trading systems in investors in Taiwan. First, this work establishes the views and parameters by modifying the Delphi method based on a literature review and survey. Second, the fuzzy-BWM is applied to obtain the fuzzy weights of the views and parameters. Then, defuzzification and BWM are used to rank the optimal alternatives of the digital token trading systems for investors. The results indicate that the optimal digital token trading system is the decentralized platform, and the critical parameters are gas fees, interest rates, and the mechanism of savings under fuzzy uncertain scenarios. This means that when considering the uncertain and ambiguous characteristics of the expert decision process in digital token trading systems, the evaluation is decentralized and the gas fees are the most important parameter in the digital token investment platform. Academically, the fuzzy BWM-based decision-making architecture can provide corporations and investors with valuable guidance to rank the optimal digital token trading systems based on fuzzy uncertain scenarios. Commercially, the proposed architecture could provide corporations and investors with a useful model to measure the optimal digital token trading system.

The health and productivity of animals, as well as farmers’ financial well-being, can be significantly impacted by cattle illnesses. Accurate and timely diagnosis is therefore essential for effective disease management and control. In this study, we consider the development of models and algorithms for diagnosing diseases in cattle based on Sugeno’s fuzzy inference. To achieve this goal, an analytical review of mathematical methods for diagnosing animal diseases and soft computing methods for solving classification problems was performed. Based on the clinical signs of diseases, an algorithm was proposed to build a knowledge base to diagnose diseases in cattle. This algorithm serves to increase the reliability of informative features. Based on the proposed algorithm, a program for diagnosing diseases in cattle was developed. Afterward, a computational experiment was performed. The results of the computational experiment are additional tools for decision-making on the diagnosis of a disease in cattle. Using the developed program, a Sugeno fuzzy logic model was built for diagnosing diseases in cattle. The analysis of the adequacy of the results obtained from the Sugeno fuzzy logic model was performed. The processes of solving several existing (model) classification and evaluation problems and comparing the results with several existing algorithms are considered. The results obtained enable it to be possible to promptly diagnose and perform certain therapeutic measures as well as reduce the time of data analysis and increase the efficiency of diagnosing cattle. The scientific novelty of this study is the creation of an algorithm for building a knowledge base and improving the algorithm for constructing the Sugeno fuzzy logic model for diagnosing diseases in cattle. The findings of this study can be widely used in veterinary medicine in solving the problems of diagnosing diseases in cattle and substantiating decision-making in intelligent systems.

In this paper, we provide several Arzelà–Ascoli-type results on the space of all continuous functions from a Tychonoff space X into the fuzzy sets of Rn, (FUSCB(Rn),Hend), which are upper semi-continuous and have bounded support endowed with the endograph metric. Namely, we obtain positive results when X is considered to be a kr-space and C(X,(FUSCB(Rn),Hend)) is endowed with the compact open topology, as well as when we assume that X is pseudocompact and C(X,(FUSCB(Rn),Hend)) is equipped with the uniform topology.

En la presente Memoria estudiamos dos problemas abiertos en el contexto de los conjuntos difusos, introducidos por L.A. Zadeh en 1965 como una forma matemática de expresar la incertidumbre que nos rodea en el mundo real. Por un lado, presentamos un operador de aproximación que asocia un único número difuso normal a cada conjunto difuso del intervalo [0, 1]. La necesidad y la enorme aplicabilidad de este operador viene justificada por el hecho de que las principales técnicas matemáticas y estadísticas que se han propuesto hasta el momento (regresión, distancias, etc.) hacen uso exclusivamente de números difusos. Dichas técnicas no pueden ser aplicadas en general en contextos en los que los datos de entrada son conjuntos difusos arbitrarios, pues requieren de las especiales propiedades algebraicas y geométricas que verifican concretamente los números difusos. De esta forma, el operador propuesto es capaz de tomar los datos difusos de entrada y transformarlos, de una forma razonable, en n´umeros difusos con los que poder trabajar después. Este operador depende de una amplia colección de parámetros iniciales que le aportan gran ductilidad desde su propia concepción. Adicionalmente, se muestran las principales propiedades que satisface este operador, entre las que destacamos el estudio de sus puntos fijos y la propiedad minimizante que verifica. Por otro lado, presentamos un definición de índice de solapamiento en el marco de los conjuntos difusos de tipo 2. Habíamos observado que, tras la introducción de las funciones de solapamiento y su posterior éxito al ser aplicadas a distintos problemas de investigación, algunos autores habían tratado de extender esta noción al campo de los conjuntos difusos de tipo 1, lo cual se había conseguido a la luz del índice de consistencia de Zadeh. De esta forma, era interesante abordar el caso de los conjuntos difusos de tipo 2, que son capaces de modelizar situaciones de incertidumbre a través de una estructura algebraica más fina donde los propios conjuntos difusos de tipo 1 no alcanzan. De esta forma, introducimos las principales condiciones que ha de verificar un índice de solapamiento sobre conjuntos difusos de tipo 2, estudiamos sus primeras propiedades y mostramos amplias familias de ejemplos de esta clase de índices, relacionando los diferentes niveles de estructuras difusas. Ademas, discutimos la condición de normalidad para esta clase de índices y mostramos alternativas a la que aquí se presenta. Finalmente, ilustramos como emplear los índices de solapamiento de tipo (2, 0) y (2, 1) para implementar algoritmos inferenciales para sistemas interpolativos difusos de tipo 2, de tal forma que se pueda extraer una conclusión a partir de unas premisas y un hecho, todos ellos expresados con conjuntos difusos de tipo 2., In this Memory we study two open problems in the context of fuzzy sets, introduced by L.A. Zadeh in 1965 as a mathematical way of expressing the uncertainty that surrounds us in the real world. On the one hand, we present an approximation operator that associates a unique normal fuzzy number to each fuzzy set in the interval [0, 1]. The need and the great applicability of this operator is justified by the fact that the main mathematical and statistical techniques that have been proposed up to now (regression, distances, etc.) make exclusively use of fuzzy numbers. Such techniques cannot be applied in general contexts where the input data are arbitrary fuzzy sets, since they require the special algebraic and geometric properties that, concretely, fuzzy numbers verify. In this way, the proposed operator is able to transform the fuzzy input data, in a reasonable way, into fuzzy numbers to work with afterwards. This operator depends on a wide collection of initial parameters that give it great ductility from its very conception. Additionally, the main properties that this operator satisfies are shown, among which we highlight the study of its fixed points and the minimizing property that it verifies. On the other hand, we introduce a definition of overlap index in the framework of type-2 fuzzy sets. We had observed that, after the introduction of overlap functions and their subsequent success in applications to different research problems, some authors had tried to extend this notion to the field of type-1 fuzzy sets, which had been achieved inspired by Zadeh’s consistency index. Thus, it was interesting to address the case of type-2 fuzzy sets, which are able to model uncertainty situations through a finer algebraic structure where type-1 fuzzy sets themselves do not reach. In this way, we introduce the main conditions to be verified by an overlap index on type-2 fuzzy sets, we study its first properties and we show large families of examples of this class of indices, relating the different levels of fuzzy structures. Furthermore, we discuss the normality condition for this class of indices and we show alternatives to the one presented here. Finally, we illustrate how to employ overlap indices of type (2, 0) and (2, 1) to implement inferential algorithms for type-2 fuzzy interpolative fuzzy systems, such that a conclusion can be drawn from fuzzy rules and a fact, all of them expressed as type-2 fuzzy sets., Tesis Univ. Granada.

Данная статья посвящена разработке методики оценки удовлетворенности клиентов предприятия, которое предоставляет населению услуги медицинского характера с учетом эмоционально окрашенной информации, поступающей от клиентов. Авторами проведен анализ нескольких связанных публикаций на данную тему. На основе этого анализа выявлены существующие недостатки рассмотренных методик. С целью устранить вышеописанные недостатки предложено усовершенствование одного из рассмотренных методов. Усовершенствование заключается в добавлении в математическую модель дополнительного параметра, который характеризует эмоциональный отклик клиента медицинской организации в качестве обратной связи. Выбрана модель оценки удовлетворенности пациентов с учетом эмоций клиентов с использованием нечетких классификаторов и приведена общая схема расчета интегрального показателя. Предложенная методика описана поэтапно. Каждый этап методики также рассмотрен более детально. В процессе одного из этапов экспертами определен набор показателей для дальнейшей работы, в состав которого входит параметр, описывающий эмоциональную реакцию пациента. Проведен численный эксперимент, реализующий предложенную методику, а также описаны его результаты. На основе результатов расчетного эксперимента сформированы выводы по работе., This article is devoted to development of a methodology for assessing customer satisfaction of an enterprise that provides medical services to population taking into consideration emotionally charged information coming from customers. Authors analyzed several related publications on this issue. Based on that, the existing shortcomings of the methods under review were identified. To eliminate them, it is proposed to improve one of these methods. The improvement consists in adding an additional parameter to the mathematical model which characterizes emotional response of a client of a medical organization as feedback. A model for assessing patient satisfaction was chosen with due regard for customers’ emotions using fuzzy classifiers. A general scheme for calculating the integral indicator was given. The proposed methodology is described step by step. Each stage of the methodology was also studied in greater detail. During one of the stages, the experts determined a set of indicators for further research, which includes a parameter that describes a patient's emotional reaction. A numerical experiment was carried out that implements the proposed method and its results are described. Following on from the results of the computational experiment, conclusions were drawn., МОДЕЛИРОВАНИЕ, ОПТИМИЗАЦИЯ И ИНФОРМАЦИОННЫЕ ТЕХНОЛОГИИ, Выпуск 2 (41) 2023, Pages 1-2

Tamamen ikili değerlendirmeye dayanan bir matematiksel modelleme olan klasik mantıkta her değer için sadece iki durum vardır, 1 sembolünün verildiği ve doğru anlamına gelen ilk durum ile 0 sembolünün verildiği ve yanlış anlamına gelen ikinci durum. Ancak gerçek bundan daha geniştir ve yalnızca 0 ve 1 olmak üzere iki duruma bağlı olmayabilir. Bu nedenle, yaklaşık veya spesifik olmayan bilgileri temsil etme problemini çözmek için genel çerçeveyi sağlayan yeni bir mantığa ihtiyaç duyulmuş. Bulanık mantık adı verilen bu mantık ilk olarak 1965 yılında İranlı bilim adamı Lutfi Zadeh, tarafından ortaya atılmıştır. Bulanık mantık, sıcak, soğuk, ılık, az, çok, gibi deyimler ve belirsiz ifadeler aracılığıyla tümdengelim üzerine kuruludur. Çalışma boyunca, bulanık mantığın klasik mantığın bir genişlemesi olduğu sonucuna varılmıştır. Klasik mantık, üyelik derecesi {0,1} kümesi olduğunda, bulanık mantığın özel bir durumudur, Bulanık mantık sadece kümeler teorisinde değil, yapay zekada, gelişmiş elektronik cihazlarda, endüstriyel kontrolörlerde ve hatta günlük hayatımızda büyük öneme sahiptir. Bu tezde de bulanık küme, bulanık küme türleri ve bunlarla ilgili önemli cebirsel işlemler açıklanacaktır. Sonrasında bulanık topolojik uzay tanımı verilerek bulanık topolojik uzayların toplamları üzerinde, açık kümeler, kaplı kümeler, içi, kapanış, taban, komşuluklar ve süreklilik gibi ifadeler tanımlanacaktır. Tanımlanan bu topolojik toplamlar için elde edilen bazı sonuçlardan bahsedilecektir. In classical logic, which is purely a mathematical modeling based on binary evaluation, there are only two cases for each value, the first case where the symbol 1 is given and means true, and the second case where the symbol 0 is given and means false. But the truth is broader than that and may not depend solely on two states 0 and 1. Therefore, a new logic was needed that provides the general framework to solve the problem of representing approximate or nonspecific information. This logic, called fuzzy logic, was first put forward by Iranian scientist Lutfi Zadeh in 1965. Fuzzy logic is based on deduction through idioms such as hot, cold, warm, less, more, and indefinite expressions. Throughout the study, it is concluded that fuzzy logic is an extension of classical logic. Classical logic is a special case of fuzzy logic, when the membership degree is {0,1} set, Fuzzy logic has great importance not only in set theory, but also in artificial intelligence, advanced electronic devices, industrial controllers and even in our daily life. In this thesis, fuzzy set, fuzzy set types and important algebraic operations related to them will be explained. Then, by giving the definition of fuzzy topological space, we will define open sets, covered sets, interior, closure, base, neighborhoods and continuity on the sums of fuzzy topological spaces. Some of the results obtained for these topological sums will be mentioned.

Restricted equivalence functions are well-known functions to compare two numbers in the interval between 0 and 1. Despite the numerous works studying the properties of restricted equivalence functions and their multiple applications as support for different similarity measures, an extension of these functions to an n-dimensional space is absent from the literature. In this paper, we present a novel contribution to the restricted equivalence function theory, allowing to compare multivalued elements. Specifically, we extend the notion of restricted equivalence functions from L to L n and present a new similarity construction on L n . Our proposal is tested in the context of color image anisotropic diffusion as an example of one of its many applications. The authors gratefully acknowledge the financial support of the grant PID2019-108392GB-I00 funded by MCIN/AEI/10.13039/50110001103, as well as grant VEGA 1/0545/20. Also, the financial support of Consellería d’Innovacio, Universitats, Ciencia i Societat Digital from Comunitat Valenciana (APOSTD/2021/227) and the European Social Fund (Investing In Your Future) and to Tracasa Instrumental and the Immigration Policy and Justice Department of the Government of Navarre.

Анализируются вопросы приоритетности выбора энергоисточников для Ненецкого автономного округа на основе использования экспертной процедуры и аппарата нечеткой математики. Предложен специальный алгоритм для обоснования решений в нечеткой логике в условиях многокритериальности и неопределенности. При проведении исследований выбраны пять базовых вариантов энергоисточников для обеспечения энергоснабжения территорий НАО, дано их сравнение и выбран наилучший вариант., The priority ranking of the choice of energy sources for the Nenets Autonomous Okrug (NAO) are analyzed using the expert procedure and fuzzy mathematics method. A special algorithm is proposed for substantiating solutions in fuzzy logic under conditions of multicriteria and uncertainty. A comparison of five basic options of energy sources selected for the research that can provide the energy supply of the territories of the NAO revealed the best one to be selected., Промышленная энергетика, Выпуск 4 2023, Pages 10-15

Following the second wave of Covid-19 infections in India, individuals are now arriving to hospitals with a variety of symptoms, not simply for mucormycosis, a fungal infection. The most common symptoms are extreme tiredness, drowsiness, body and joint pain, mental fog, and fever, but pneumonia, collapsed lungs, heart attacks, and strokes have all been reported. Pythagorean fuzzy sets (PFSs) proposed by Yager [40] offers a novel technique to characterize uncertainty and ambiguity with greater precision and accuracy. The idea was developed specifically to describe uncertainty and ambiguity mathematically and to provide a codified tool for dealing with imprecision in real-world circumstances. This article addresses novel logarithmic entropy measures under PFSs. Additionally, numerical illustration is utilized to ascertain the strength and validity of the proposed entropy measures. Application of the measures is used in detecting diseases related to Post COVID 19 implications through TOPSIS method. Comparison of the suggested measures with the existing ones is also demonstrated.&nbsp

An operator is a special symbol for performing a specific function. Several operators like modal operators, topological operators, level operators, etc. have been defined over intuitionistic fuzzy sets. At the same time, so many operations were introduced and studied. The key objective of this paper is to study those operations over intuitionistic fuzzy sets and to investigate their properties. Some new results are obtained and proved.

Since its beginning, Fuzzy logic has shown its usefulness in different areas of knowledge; forthe particular case of process control, from the construction of process models to the design of advanced controllers, it has proven its effectiveness and importance on industrial applications. This work presents a guide for studying systems based on fuzzy logic for process control,startingfrom the origins, theoretical foundations, and a guide for constructingsome loop controllers implemented on a benchmark plant

The study presents a mathematical model for the development of an optimal wagon transport plan in conditions of relative uncertainty. It describes an algorithm that allows searching for an optimal railroad-blocking plan in an environment of approximate initial data. The algorithm is based on the branch-and-bound method and fuzzy intervals. An example is provided of how an optimal transport plan for wagon flows given in this way can be determined.

By using a class of aggregation control functions, we introduce the concept of multiple-HU-OS1-stability and get an optimum approximation for a nonlinear single fractional differential equation (NS-ABC-FDE) with a Mittag–Leffler kernel. We apply an alternative fixed-point theorem to prove the existence of a unique solution and the multiple-HU-OS1-stability for the NS-ABC-FDE in the symmetric matrix-valued FBS. Finally, with an example, we show the application of the obtained results.

Let X be a compact metric space and a continuous map f:X→X which defines a discrete dynamical system (X,f). The map f induces two natural maps, namely f¯:K(X)→K(X) on the hyperspace K(X) of non-empty compact subspaces of X and the Zadeh’s extension f^:F(X)→F(X) on the space F(X) of normal fuzzy set. In this work, we analyze the interaction of some orbit tracing dynamical properties, namely the specification and shadowing properties of the discrete dynamical system (X,f) and its induced discrete dynamical systems (K(X),f¯) and (F(X),f^). Adding an algebraic structure yields stronger conclusions, and we obtain a full characterization of the specification property in the hyperspace, in the fuzzy space, and in the phase space X if we assume that the later is a convex compact subset of a (metrizable and complete) locally convex space and f is a linear operator.

We propose a Mamdani-Type Fuzzy Inference based posterior decision-making approach to multi-objective diet optimization problem. We optimize the multi-objective diet problem with evolutionary algorithms that result in tens/hundreds of non-dominated solutions which is too large to pick one of them by the decision-maker. Even though all the solutions are optimized for all the objectives simultaneously, not all objective functions may be equally important to a user and, also their importance may change for that user over time. Our main goal is to develop an applicable method for representing and incorporating a decision maker's (DM) instant preferences for objectives into decision-making stage. The FIS based decision making can guide users to decide on the most suitable menus. User's instant preferences for each objective form rule sets. Using Mamdani type FIS in the post-decision process of the multi-objective diet problem is a novel contribution. A desirability measure is calculated by using rule sets and membership functions considering the objective values, and based on the desirability measure the most preferred menu(s) are provided to the user. Our method can direct the DM to the region of interest in the search space of the multi-objective diet problem. Thus, the daily menu suggestions become more applicable, practical, and desirable for the users., Çok amaçlı diyet optimizasyonu problemine Mamdani Tipi Bulanık Çıkarım tabanlı sonradan karar verme yaklaşımı öneriyoruz. Çok amaçlı diyet problemini, onlarca/yüzlerce baskılanamayan çözüm ile sonuçlanan Evrimsel Algoritmalarla optimize ediyoruz. EA’lar ile önerilen günlük menü sayısı, bunlardan birini seçmek için çok fazladır. Tüm çözümler aynı anda tüm amaçlar için optimize edilmiş olsa da, tüm amaç fonksiyonları bir kullanıcı için eşit derecede önemli olmayabilir ve ayrıca zaman içinde o kullanıcı için önemleri değişebilir. Ana hedefimiz, bir karar vericinin hedefler için anlık tercihlerini temsil edebileceği ve çok amaçlı diyet optimizasyon probleminin karar verme aşamasına dahil edebileceği için uygulanabilir bir yöntem geliştirmektir. Bulanık çıkarım tabanlı karar verme, kullanıcılara yüzlerce uygulanabilir çözüm arasından en uygun menüleri seçme konusunda rehberlik edebilir. Her amaç için kullanıcının anlık tercihlerini alarak yeni kural setleri oluştururuz. Mamdani tipi Bulanık Çıkarım Sistemi'nin çok amaçlı diyet probleminin karar sonrası sürecinde kullanılması yeni bir katkıdır. Amaç değerleri dikkate alınarak kural kümeleri ve üyelik fonksiyonları kullanılarak bir tercih edilirlik ölçüsü hesaplanır ve istenirlik ölçüsüne göre kullanıcıya en çok tercih edilen menü/menüler sunulur. KV’nin sözlü ifadeleriyle, yöntemimiz KV'yi çok amaçlı diyet probleminin optimizasyonu ile oluşturulan çözüm kümesinin arama uzayında ilgili bölgeye yönlendirebilir. Böylece günlük menü önerileri kullanıcılar için daha uygulanabilir, pratik ve arzu edilir hale gelmektedir.

Розмір пояснювальної записки – 90 аркушів, містить 26 ілюстрацій, 23 таблиць, 3 додатка, 21 посилань на джерела. Актуальність теми. Математична статистика та теорія ймовірності активно використовуються у різних сферах людства: фізика, наука про дані, медицина, підприємства або сільське господарство. Для процесів аналіза і прогнозування часових рядів на основі нечітких моделей з невизначеною (стохастичною) функцією приналежності, які також відносяться до теорії ймовірності. Але на сьогоднішній день не розроблено жодного інструменту у вигляді мови програмування для автоматизації розрахунків та знаходження відповіді. Тут збігається три фактори: лінгвістичне моделювання, теорія нечітких моделей та теорія ймовірності. Мета дослідження. Створити мову програмування для описання процессів аналіза і прогнозування числових рядів на основі нечітких моделей з невизначеною функцією приналежності. Об’єкт дослідження: Лінгвістичні моделі часових рядів. Предмет дослідження: Мова програмування. Для реалізації поставленої мети сформульовані наступні завдання: — аналіз теорії та існуючих рішень; — розробка програмного забезпечення; — дослідження ефективності розробленого програмного забезпечення. Наукова новизна результатів магістерської дисертації полягає у практичних областях застосування лінгвістичного моделювання. Так званого прямого лінгвістичного перетворення. При цьому виникла задача зворотнього лінгвістичного перетворення – перехід від лінгвістичних ланцюжків до оригінального часового ряду. Задача не вирішена на цей момент. Саме для цього потрібне програмне забезпечення з гібридом ймовірнісних і нечітких множин. Результат досягнутий шляхом розробки програмного забезпечення створення програмного забезпечення на основі нечітких множин та ймовірності функцій приналежностей. Практичне значення отриманих результатів полягає в тому, що програмне забезпечення можна використовувати у етапах розробки усіх сфер, які потребують обрахування лінгвістичних моделей часових рядів. Зв’язок з науковими програмами, планами, темами. Робота виконувалась на кафедрі інформатики та програмної інженерії Національного технічного університету України "Київський політехнічний інститут імені Ігоря Сікорського". Апробація. Наукові положення дисертації пройшли апробацію на Третій Всеукраїнській науково-практичній конференції молодих вчених та студентів «ІНЖЕНЕРІЯ ПРОГРАМНОГО ЗАБЕЗПЕЧЕННЯ І ПЕРЕДОВІ ІНФОРМАЦІЙНІ ТЕХНОЛОГІЇ» (SoftTech-2022 осінь) – м. Київ. Публікації. Наукові положення дисертації опубліковані в: 1. ХІЛЬЧЕНКО Є.А. РОЗРОБКА ПРОГРАМНОГО ЗАБЕЗПЕЧЕННЯ ДЛЯ СТВОРЕННЯ ЛІНГВІСТИЧНИХ МОДЕЛЕЙ / Є.А. Хільченко, І.В. Баклан // Матеріали Третьої Всеукраїнської науково-практичної конференції молодих вчених та студентів «ІНЖЕНЕРІЯ ПРОГРАМНОГО ЗАБЕЗПЕЧЕННЯ І ПЕРЕДОВІ ІНФОРМАЦІЙНІ ТЕХНОЛОГІЇ» (SoftTech-2022 осінь) – м. Київ: НТУУ «КПІ ім. Ігоря Сікорського», 23-25 листопада 2022 р. Розмір пояснювальної записки – 90 аркушів, містить 26 ілюстрацій, 23 таблиць, 3 додатка, 21 посилань на джерела. Актуальність теми. Математична статистика та теорія ймовірності активно використовуються у різних сферах людства: фізика, наука про дані, медицина, підприємства або сільське господарство. Для процесів аналіза і прогнозування часових рядів на основі нечітких моделей з невизначеною (стохастичною) функцією приналежності, які також відносяться до теорії ймовірності. Але на сьогоднішній день не розроблено жодного інструменту у вигляді мови програмування для автоматизації розрахунків та знаходження відповіді. Тут збігається три фактори: лінгвістичне моделювання, теорія нечітких моделей та теорія ймовірності. Мета дослідження. Створити мову програмування для описання процессів аналіза і прогнозування числових рядів на основі нечітких моделей з невизначеною функцією приналежності. Об’єкт дослідження: Лінгвістичні моделі часових рядів. Предмет дослідження: Мова програмування. Для реалізації поставленої мети сформульовані наступні завдання: — аналіз теорії та існуючих рішень; — розробка програмного забезпечення; — дослідження ефективності розробленого програмного забезпечення. Наукова новизна результатів магістерської дисертації полягає у практичних областях застосування лінгвістичного моделювання. Так званого прямого лінгвістичного перетворення. При цьому виникла задача зворотнього лінгвістичного перетворення – перехід від лінгвістичних ланцюжків до оригінального часового ряду. Задача не вирішена на цей момент. Саме для цього потрібне програмне забезпечення з гібридом ймовірнісних і нечітких множин. Результат досягнутий шляхом розробки програмного забезпечення створення програмного забезпечення на основі нечітких множин та ймовірності функцій приналежностей. Практичне значення отриманих результатів полягає в тому, що програмне забезпечення можна використовувати у етапах розробки усіх сфер, які потребують обрахування лінгвістичних моделей часових рядів. Зв’язок з науковими програмами, планами, темами. Робота виконувалась на кафедрі інформатики та програмної інженерії Національного технічного університету України "Київський політехнічний інститут імені Ігоря Сікорського". Апробація. Наукові положення дисертації пройшли апробацію на Третій Всеукраїнській науково-практичній конференції молодих вчених та студентів «ІНЖЕНЕРІЯ ПРОГРАМНОГО ЗАБЕЗПЕЧЕННЯ І ПЕРЕДОВІ ІНФОРМАЦІЙНІ ТЕХНОЛОГІЇ» (SoftTech-2022 осінь) – м. Київ. Публікації. Наукові положення дисертації опубліковані в: 1. ХІЛЬЧЕНКО Є.А. РОЗРОБКА ПРОГРАМНОГО ЗАБЕЗПЕЧЕННЯ ДЛЯ СТВОРЕННЯ ЛІНГВІСТИЧНИХ МОДЕЛЕЙ / Є.А. Хільченко, І.В. Баклан // Матеріали Третьої Всеукраїнської науково-практичної конференції молодих вчених та студентів «ІНЖЕНЕРІЯ ПРОГРАМНОГО ЗАБЕЗПЕЧЕННЯ І ПЕРЕДОВІ ІНФОРМАЦІЙНІ ТЕХНОЛОГІЇ» (SoftTech-2022 осінь) – м. Київ: НТУУ «КПІ ім. Ігоря Сікорського», 23-25 листопада 2022 р. Explanatory note size – 90 pages, contains 26 illustrations, 23 tables, 4 applications, 21 references. Topicality. Mathematical statistics and probability theory are actively used in various fields of humanity: physics, data science, medicine, business or agriculture. For the processes of analysis and forecasting of time series based on fuzzy models with an undefined (stochastic) membership function, which also refer to probability theory. But to date, no tool has been developed in the form of a programming language for automating calculations and finding the answer. Three factors converge here: linguistic modeling, fuzzy model theory, and probability theory. The aim of the study. Create a programming language for describing the processes of analysis and forecasting of numerical series based on fuzzy models with undefined functional affiliation. The object of research: Linguistic models of time series. The subject of research: Programming language. To achieve this goal, the following tasks were formulated: — analysis of theory and existing solutions; — software development; — study of the effectiveness of the developed software. The scientific novelty of the results of the master's thesis lies in the practical areas of application of linguistic modeling. The so-called direct linguistic transformation. At the same time, the problem of reverse linguistic transformation arose – the transition from linguistic chains to the original time series. The problem is not solved at this moment. This is exactly what you need software with a hybrid of probabilistic and fuzzy sets. The result is achieved by developing software based on fuzzy sets and probabilistic membership functions. The practical significance of the obtained results is that the software can be used in the stages of development of all areas that require the calculation of linguistic models of time series. Relationship with working with scientific programs, plans, topics. Work was performed at the Department of Informatics and Software Engineering of the National Technical University of Ukraine «Kyiv Polytechnic Institute. Igor Sikorsky». Approbation. The scientific provisions of the dissertation were tested at the Third All-Ukrainian scientific and practical conference of young scientists and students "SOFTWARE ENGINEERING AND ADVANCED INFORMATION TECHNOLOGIES" (SoftTech-2022 autumn) - Kyiv. Publications. The scientific provisions of the dissertation were published in: 1. Khilchenko Y.K. DEVELOPMENT OF SOFTWARE FOR THE CREATION OF LINGUISTIC MODELS/ Y.K. Khilchenko, I.V. Baklan // Materials of the Third All-Ukrainian scientific and practical conference of young scientists and students "SOFTWARE ENGINEERING AND ADVANCED INFORMATION TECHNOLOGIES" (SoftTech-2022 autumn) - Kyiv: National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", November 23-25, 2022. Explanatory note size – 90 pages, contains 26 illustrations, 23 tables, 4 applications, 21 references. Topicality. Mathematical statistics and probability theory are actively used in various fields of humanity: physics, data science, medicine, business or agriculture. For the processes of analysis and forecasting of time series based on fuzzy models with an undefined (stochastic) membership function, which also refer to probability theory. But to date, no tool has been developed in the form of a programming language for automating calculations and finding the answer. Three factors converge here: linguistic modeling, fuzzy model theory, and probability theory. The aim of the study. Create a programming language for describing the processes of analysis and forecasting of numerical series based on fuzzy models with undefined functional affiliation. The object of research: Linguistic models of time series. The subject of research: Programming language. To achieve this goal, the following tasks were formulated: — analysis of theory and existing solutions; — software development; — study of the effectiveness of the developed software. The scientific novelty of the results of the master's thesis lies in the practical areas of application of linguistic modeling. The so-called direct linguistic transformation. At the same time, the problem of reverse linguistic transformation arose – the transition from linguistic chains to the original time series. The problem is not solved at this moment. This is exactly what you need software with a hybrid of probabilistic and fuzzy sets. The result is achieved by developing software based on fuzzy sets and probabilistic membership functions. The practical significance of the obtained results is that the software can be used in the stages of development of all areas that require the calculation of linguistic models of time series. Relationship with working with scientific programs, plans, topics. Work was performed at the Department of Informatics and Software Engineering of the National Technical University of Ukraine «Kyiv Polytechnic Institute. Igor Sikorsky». Approbation. The scientific provisions of the dissertation were tested at the Third All-Ukrainian scientific and practical conference of young scientists and students "SOFTWARE ENGINEERING AND ADVANCED INFORMATION TECHNOLOGIES" (SoftTech-2022 autumn) - Kyiv. Publications. The scientific provisions of the dissertation were published in: 1. Khilchenko Y.K. DEVELOPMENT OF SOFTWARE FOR THE CREATION OF LINGUISTIC MODELS/ Y.K. Khilchenko, I.V. Baklan // Materials of the Third All-Ukrainian scientific and practical conference of young scientists and students "SOFTWARE ENGINEERING AND ADVANCED INFORMATION TECHNOLOGIES" (SoftTech-2022 autumn) - Kyiv: National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", November 23-25, 2022.

This study uniquely employs a fuzzy-set qualitative comparative analysis (fsQCA) technique to account for complex relationships in consumption. The fsQCA technique assumes that relationships are based on a set–subset relationship. This assumption is fundamental when decision-makers are affected by information asymmetry and are, thus, required to jointly evaluate the credibility and reliability of a range of external signals. This issue also affects consumers in markets for cultural goods, where the quality of products is not known with certainty in advance of the purchase decision. Our study uses fsQCA to establish the effect of different quality signals on consumption in the US market for video game software. Our results show that reviews from professional critics alongside brand extension and multi-platform release strategies act as signals of product quality and, therefore, lead to high sales performance.

The aim of this study is to determine the degree of importance of criteria affecting site selection of solar photovoltaic (PV) projects using a decision-making model. This study consists of four consecutive stages, as follows: criteria identification, questionnaire (survey), statistical analyses, and degree of importance of criteria. In the first stage, the criteria are determined by reviewing the scientific literature on solar PV projects. Secondly, we conduct a questionnaire to identify the importance of the criteria for solar PV project site selection. We received responses from 33 internationally renowned experts from 22 countries, including academia and industry, using an international evaluation method. Thirdly, statistical analysis is performed in SPSS regarding each criterion, comparing the averages between the groups who filled out the questionnaire. Finally, a novel logarithmic additive estimation of weight coefficients (LAAW) under fuzzy environment is proposed to determine the degree of importance of each criterion for solar PV site selection. The results show that the most important criteria for solar PV site selection are solar radiation, economic performance indicators (net present value (NPV), internal rate of return (IRR), and return on investment (ROI)), carbon emission savings, and policy support.

IF=1.46; International audience; This paper describes a new approach to analyse the way both hands are placed in relation to the steering wheel. The study is based on a 2D-tracking task, in which the stimulus is a steering wheel angle signal recorded while driving on 7 road geometries in real situations at 30 km/h. Hand movements are measured using a 3D-motion capture system. Data analysis is based on the segmentation of the hand angular position using 8 fuzzy angle windows (labelled as approximately 0°, approximately 45°, etc.), when the hand rests on the steering wheel, one window, else. To obtain information about the coordination aspect, 9 × 9 bivariate windows are considered for each time sample (recorded at 25 Hz); then, the average membership values are computed for each individual driving situation. The individual membership value sets related to the road geometries are studied via Correspondence Analysis, allowing to displaying both the inter- and intra-individual differences and the most discriminating bivariate windows. The methodology with 9 × 9 windows is more complex but implies less information loss than alternative ones e.g. when the two hands are separately analysed, which constitutes 9 + 9 windows and contains no information about the coordination aspect.

Increasingly frequent changes in demand for products, reducing product life cycles, changes in the business environment during a crisis, the innovative nature of projects, the complexity of forecasting external and internal conditions, the impact of the human factor lead to increased uncertainty and inability to plan team activities with a given degree of accuracy. In this regard, the subject matter of the article is the task of creating an adaptive project team that can work effectively in the mentioned above conditions. This task is especially relevant for the sphere of software development. The sphere is dynamic and characterized by frequent changes in product requirements, technologies, working conditions, and restrictions on project implementation. Agile approaches are used to manage such projects, which can help the team respond to uncertainties and frequent changes. To date, there are many agile approaches to project management, but the issue of selecting team members in such approaches is insufficiently covered. Therefore, this work formalizes the task of deciding on the selection of software development team members, considering the uncertainty and subjectivity of the information that affects the selection of candidates for the team. The task of the work is to create a decision-making model based on the use of the mathematical apparatus of fuzzy sets and methods of operations research. Such a model should allow considering the uncertainty of estimates of project requirements and the level of competence of team candidates. The result is a mathematical model of a two-criterion constrained optimization problem. The first objective function is aimed at finding a team composition that maximizes the maximum competencies of its members. The second criterion is aimed at forming a team with the maximum sum of competencies for all indicators, considering the weight of each indicator. The first constraint assumes that at least one team member meets the competency requirements expressed by a specific indicator. Additionally, it is required that the available time fund of the team members allows the project to be completed on time. It considers the limitation on the salary of the team. Conclusions. Solving the problem in accordance with the proposed mathematical model will allow making a team as readily as possible to meet the existing and new requirements for the project staff. The last circumstance is especially important when implementing a software development projects.

The approach of dealing with uncertainty is enhancing day-by-day with new rudiments and tools which possess their specific qualities. Usually, aggregation operators can easily manage the information in an exact manner. But each operator has different specifications in each problem. In recent few years, aggregation operators on intuitionistic fuzzy soft sets (IFSSs) or generalized intuitionistic fuzzy soft sets (GIFSSs) have been investigated but a lot of improvement is needed to obtain more accurate results. In this research, we defined new aggregation operators on GIFSSs which are used to aggregate our multi-criteria decision-making method. Reasonably, we assigned the weights with both intuitionistic fuzzy values of IFSS and intuitionistic fuzzy values of extra input in a GIFSS, and then by establishing new aggregation operators we appraised the computation in a more precise way. We defined the necessary properties of new aggregation operators and preparatory work of decision making in an algorithm. Then we expressed a real-life application by dint of the proposed methodology. Finally, we presented the comparisons of our work with already existing methods and techniques comprising aggregation operators.

The present article aims to describe the design of a fuzzy controller used for automated control of the thickness of the extruded polyethylene film effected by the adjustment of the actuator in the cooling ring. In order to determine whether the designed controller operates properly, a model extruder was created and a simulation study was carried out. The Simulink programming environment integrated with Matlab was used for the development of the fuzzy controller and the simulation. The conducted simulation study demonstrated that the implementation of the designed controller would enable the adjustment of thickness on the perimeter of the film tube and quick reaction to possible departure in the assumed film thickness in mass production.

In recent years, q-rung orthopair fuzzy sets (q-ROFSs), a novel and rigorous generalization of the fuzzy set (FS) coined by Yager in 2017, have been used to manage inexplicit and indefinite information in daily life with a high precision and greater accuracy than intuitionistic fuzzy sets (IFSs) and Pythagorean fuzzy sets (PFSs). The characterization of a measure of similarity between q-ROFSs is important, as they have applications in different areas, including pattern recognition, clustering, image segmentation and decision making. Therefore, this article is dedicated to the construction of a measure of similarity between q-ROFSs based on the Hausdorff metric. This is a very useful tool for establishing the similarity between two objects. Furthermore, some axiomatic definitions of the distances and similarity measures of q-ROFSs are also presented. In this article, we first present a novel method to calculate the distance between q-ROFSs based on the Hausdorff metric. We then utilize our proposed distance measure to construct the degree of similarity between q-ROFSs. We provide some properties for the proposed similarity measures. We offer several numerical examples related to pattern recognition and characterization linguistic variables to demonstrate the usefulness of the proposed similarity measures. We construct an algorithm for orthopair fuzzy TODIM (interactive and multi-criteria decision making, in Portuguese) based on our proposed methods. Finally, we use the constructed orthopair fuzzy TODIM method to address problems related to daily life settings involving multi-criteria decision making (MCDM). The numerical results show that the proposed similarity measures are suitable, applicable and well-suited to the contexts of pattern recognition, queries with fuzzy linguistic variables and MCDM.

Geothermal potential is a significant advantage in terms of renewable energy for countries located on the Pacific Ring of Fire. Studies on geothermal energy sources show that Malaysia is one of the countries possessing this inexhaustible and stable energy source. This on-site energy source is a promising solution to the problem of energy security during emergencies where the energy supply chain is disrupted. To exploit this advantage, this study proposes a novel tri-layer framework to prioritize locations for direct-use geothermal energy location (DGL) in Malaysia. First, the proposed locations are screened for feasibility to limit the impact on other natural conservation areas and stable residential areas. In the second layer, locations are evaluated for efficiency using the data envelopment analysis (DEA) model based on quantitative indicators. In the third layer, the spherical fuzzy extended combination of the analytic hierarchy process (SF AHP) and the combined compromise solution (SF CoCoSo) methods are introduced and applied to prioritize high-efficiency locations. According to the findings, costs, social acceptance, and noise impacts are the qualitative criteria of most concern for DGLs. Through the tri-layer framework, the suggested concordant locations for DGLs in Malaysia are Marudi of Sarawak, Tawau of Sabah, Serian of Sarawak, and Jeram of Selangor.

R&D investments are becoming increasingly important in the developing world. Companies withlimited resources should make the most favorable investments for their own strategies. It is crucial that theseinvestments are transferred to the right projects. It is difficult to make decisions in an environment where thereare technical difficulties as well as uncertainties. At this point, it is necessary to decide which projects should bedone and which projects should not be done. In this study, project portfolio selection that seeks a systematicsolution to this decision, is covered. To solve this problem, data envelopment analysis that can evaluate theparameters without the need to build precedence relationship, is used. Parameters were set after a detailedresearch. Vagueness that is associated with difficulty of making precise judgment, was included in the model byintroducing linguistic variables. Ambiguity that characterizes the situation where there are two or morealternatives, is defined with triangular fuzzy sets and α cut method. Different models are constructed fordifferent extreme cases to solve the ambiguity. The models provide the optimal value regardless of the α value.A sample dataset of 30 projects is created to test the models and observe the results. Optimal parameters weightsare found in the models. Full pairwise comparisons are considered while examining the interdependencies.These parameters weights are recalculated according to interdependencies. Using these weights, the efficiencyscore of each project is calculated for each model. Projects are prioritized for different strategies by usingdecision making under uncertainty.

International audience; This paper highlights the challenges of representing uncertain geospatial information in knowledge graphs. We propose to use Real Estate advertisements since professionals use a lot of vernacular and vague places in order to promote a house to their target audience. Then, we suggest to model local place names using fuzzy set theory. Finally, we discuss how to build a knowledge graph that represents extracted geospatial objects and their uncertainty. CCS CONCEPTS • Information systems → Geographic information systems.

International audience; Geocoding a spatial description is challenging since vernacular place names and vague spatial expressions give uncertainty and ambiguity to the description. Usually, digital gazetteers are used to match geospatial objects to their boundaries. However, gazetteers do not contain all places. Therefore, a number of studies have proposed to enrich gazetteers by estimating and representing the vernacular places. Nevertheless, only a few approaches have taken into account vague spatial expressions such as "nearby", and have represented geospatial objects as sharp boundaries. In this work, we present an automatic workflow to retrieve a location approximation of vague spatial description. We propose a model to estimate a fuzzy representation of each mentioned geospatial information and spatial expressions. Then, we perform information fusion to find a location approximation of a property. Lastly, we demonstrate our proposed method by applying it to the case of French Real Estate advertisements with two real-world datasets in Nice and Paris. Real Estate advertisements allow us to deal with uncertain geospatial objects since a vague and exaggerated property location's description is usually provided. Our results show that our proposed method is promising and able to correctly approximate a location from uncertain spatial descriptions.

Conformance checking techniques are widely used to monitor the execution of organization processes and to pinpoint possible violations of the prescribed behavior. State-of-the-art approaches adopt a crisp evaluation of deviations: namely, every step in the execution which is not perfectly compliant with the procedural rules is marked as deviant. However, many real-world processes are driven by decisions taken by human actors, which are often characterized by uncertainty. As a consequence, deviations are often tolerated, within some boundaries. In these contexts, assessing small violations at the same level as significant ones hampers the accuracy of the provided diagnostics. In this work, we propose a novel conformance checking approach which allows to consider actors’ tolerance to violations when assessing the magnitude of detected deviations, taking into account different kinds of deviating behaviors. Experiments conducted on two real-life clinical data sets have shown that taking the extent of deviations into account leads to more fine-grained diagnostics, thus illustrating the value of the approach.

One of the most important factors affecting the success of today’s armed forces of countries is the logistics activities that ensure the supply of the required machinery, equipment and weapon systems at the right place and time, with the appropriate quantity and financial conditions. If the logistics activities are not planned and executed effectively and continuously, it would not be possible to sustain success no matter how successful it is on the front line. Until the beginning of the 2000s, the logistics support of the armed forces in the world was tried to be met with traditional methods, namely the armed forces own resources. However, since the 2000’s, as the private sector logistics support companies have started to develop themselves, the traditional methods begun to be abandoned and replaced with the performance-based logistics system for the support of the armed forces’ logistics. In this context, new processes have been initiated for the execution of the logistics activities within Turkish Armed Forces regarding this new era. This study examines the logistic activities carried out in Turkish Armed Forces with SWOT analysis in detail. In this evaluation, strengths, weaknesses, opportunities and threats were prioritized with fuzzy preference relationship method. The findings obtained in this study provided such information as which activities to be pursued with emphasis, and which weaknesses to be eliminated primarily., Günümüz ülke silahlı kuvvetlerinin başarısını etkileyen önemli unsurlardan bir tanesi de ihtiyaç duyulan makine, teçhizat ve silah sistemlerinin doğru yer ve zamanda, uygun miktar ve finansal koşullarla tedarik edilmesini sağlayan lojistik faaliyetlerdir. Eğer lojistik faaliyetler etkin ve sürekli bir şekilde planlanıp icra edilemez ise ön cephede ne kadar başarılı olunursa olunsun, başarıyı sürekli kılmak mümkün olmayacaktır. Dünyada silahlı kuvvetlerin lojistik desteği, 2000’li yılların başına kadar geleneksel yöntemlerle, yani Silahlı Kuvvetlerin kendi olanakları ile karşılanmaya çalışılmıştır. Fakat 2000’li yıllardan itibaren, özel sektör lojistik destek firmalarının kendilerini geliştirmeye başlamaları ile birlikte geleneksel yöntem terk edilmeye başlanmış ve Performansa Dayalı Lojistik Sistem (PDL) ile silahlı kuvvetlerinin lojistik desteğini sağlamaya başlamıştır. Bu kapsamda Türk Silahlı Kuvvetleri (TSK) bünyesinde lojistik faaliyetlerin icrasında bu yeni döneme yönelik süreçler başlatılmıştır. Bu çalışmada TSK bünyesinde yürütülen lojistik faaliyetler SWOT analizi ile detaylı olarak incelenmiştir. Yapılan değerlendirme ile güçlü, zayıf yönler, fırsatlar ve tehditler kendi içerisinde bulanık tercih ilişkisi yöntemi kullanılarak önceliklendirilmiştir. Çalışma ile elde edilen bulgular hangi faaliyetlere önem verilerek sürdürülmesi, zayıf yönlerden hangisinin öncelikli olarak giderilmesi gerektiği ile ilgili bilgiler sunmuştur.

We presented in this paper a new concept of sets that we launched it neutrosophic axial sets . These sets are considered as generalization of neutrosophic sets . The union relationships , intersection, union , belonging and other concepts were built on these sets , then we created two different concepts of points . Also we studied many important properties and basic theories about axial sets theory.