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neutrosophic set is characterized by three independent degrees namely the truth-membership degree (T), indeterminacy-membership degree (I), and falsity-membership degree (F). In this paper, we present an extension of the VIKOR method for the solution of multi-criteria decision-making problems, namely neutrosophic set-VIKOR (NS-VIKOR) in a refined neutrosophic environment. The weight of each decision-maker is considered a singlevalued neutrosophic number. The criteria for the weight of every decision-maker are also considered neutrosophic numbers. An aggregation operator is used to combine all decision-makers’ opinions into a single opinion for a rating between criteria and alternatives. Euclidean distances from the positive and negative ideal solutions are calculated to construct relative closeness coefficients. Lastly, an illustrative example of tablet selection is provided to show the applicability of the proposed VIKOR approach.
supplier industry, analysis is concentrated on the Cooper Standard company, one of the world’s most prominent component suppliers. The study was conducted with the management team of the Cooper Standard branch in Serbia. Triangular fuzzy numbers are employed to effectively evaluate the critical areas of production management and overall competitiveness over time. The findings of the empirical survey confirmed the usability and usefulness of the proposed approach. Also, the longitudinal character of this case study provided an opportunity to follow the patterns of change over a period of 5 years (2019–2024).
constitute a key methodology for addressing data uncertainty and imprecision. We discuss various techniques within the field of fuzzy sets, including fuzzy classification, outlier detection, and missing data imputation, emphasizing their significance across various fields of science and social life. The presented results indicate the potential for innovative research and further development in this field. The academic community at Lublin University of Technology plays a significant role in promoting and advancing fuzzy set theory, which is crucial for future scientific and technological research.
brakujących danych. Zbiory rozmyte stanowią kluczową metodologię do rozwiązywania problemów związanych z niepewnością i nieprecyzyjnością danych. Omawiamy różne techniki w dziedzinie zbiorów rozmytych, w tym klasyfikację rozmytą, wykrywanie wartości odstających oraz imputację brakujących danych, podkreślając ich znaczenie w różnych dziedzinach nauki i życia społecznego. Przedstawione wyniki wskazują na potencjał innowacyjnych badań i dalszego rozwoju w tej dziedzinie. Społeczność akademicka Politechniki Lubelskiej odgrywa istotną rolę w promowaniu i rozwijaniu teorii zbiorów rozmytych, co jest kluczowe dla przyszłych badań naukowych i technologicznych.
problem. The research problem was identified: the time buffer size in a critical path programme does not guarantee a 90 % probability of timely project execution. A new model was then elaborated to estimate the buffer size; it was applied in a technical production preparation project. An additional comparative analysis was performed using the following methods to verify the model more accurately: half of the time total of a path, the sum of squares (SSQ), and the root square error method (RSEM). The application of the fuzzy model to estimate the buffer size in a critical chain programme offers can shorten the total planned project duration. It has a higher probability of timely project execution than other methods for estimating the buffer size. It guarantees a 90 % probability of timely project execution, keeping aggressive task times, which eliminates unwanted situations such as student syndrome, Parkinson’s law, overestimating task duration, and multitasking. Project programming is an inherent part of the project planning stage in project management. Recently, project management has been increasingly developing, which has been confirmed by the article’s source literature analysis. The analysis revealed a research gap in models estimating project buffer size, which might guarantee a 90 % probability of timely project execution. Thus, a fuzzy model for estimating time buffer size in a critical chain was developed, constituting added value to the science of management and quality of production engineering (currently, mechanical engineering). The fuzzy model for estimating time buffer size was applied in one Polish enterprise in a project for a new product’s technical production preparation. The fuzzy model for estimating time buffer size permits the shortening of the duration of tasks to aggressive times, guaranteeing a 90 % probability of project timely execution. The elaborated model for estimating time buffer size may be applied further in practice in projects programmed using the critical chain method.
proposed model based on simulation methods and Gauss or Clayton copulas, it is possible to calculate the value of risk in the production of ready-mixed concrete with underestimated quality. Exposure to risk in assessing the quality of concrete can be measured as the product of the level of risk and the consequences of embedding under-quality concrete in a structure, and the developed matrix makes it possible to determine the level of risk and contribute not only to its quantification during the various phases of its production, but can affect the final quality of the concrete produced. Using the proposed model, the article calculates the level of risk in the production of ready-mixed concrete with underperformance.
problemu. W artykule przedstawiono zagadnienia związane ze zbiorami rozmytymi oraz podano przykłady. Ponadto zaprezentowano metody adaptacji systemów wiedzy opartej na zbiorach rozmytych takie jak algorytmy genetyczne, programowanie ewolucyjne, algorytmy uczące się, uczenie przez wzmacnianie oraz adaptację online.
problem domain. In this paper, the issues related to fuzzy sets are presented and examples are given. In addition, methods for adaptation of fuzzy set-based knowledge systems such as genetic algorithms, evolutionary programming, learning algorithms, reinforcement learning and online adaptation are presented.
handle potentially inconsistent data inside information systems. In Pawlak's original proposal, this is achieved by providing a lower and upper approximation of a concept, using the equivalence classes of an indiscernibility relation as building blocks. Noting the highly complementary characteristics of fuzzy sets and rough sets, Dubois and Prade proposed the first working definition of a fuzzy rough set, and thus paved the way for a flourishing hybrid theory with numerous theoretical and practical advances. In this tutorial, we will explain how fuzzy rough sets may be successfully applied to a variety of machine learning problems. After a brief discussion of how the hybridization between fuzzy sets and rough sets may be achieved, including an extension based on ordered weighted average operators, we will focus on the following practical applications: 1. Fuzzy-rough nearest neighbor (FRNN) classification, along with its adaptations for imbalanced datasets and multi-label datasets 2. Fuzzy-rough feature selection (FRFS) 3. Fuzzy-rough instance selection (FRIS) and Fuzzy-rough prototype selection (FRPS) We will also demonstrate software implementations of all of these algorithms in the Python library fuzzy-rough-learn.
sandy land of Daji Khan in northern Shaanxi Province is one of the serious desertification areas in China. The phenomenon of soil erosion and ecological deterioration is extremely serious. Therefore, it is urgent to strengthen to pay attention to the research of Mu Us sandy land, to help the restoration of damaged soil, and to build a powerful soil ecosystem. In this paper, the soil quality in the process of development and utilization of the Mu Us sandy land was evaluated based on fuzzy sets for the purpose of sustainable utilization of compound soil. Based on soil structure and soil fertility, 16 evaluation indexes of soil quality in Mu Us sandy land were screened, and then the evaluation index system of soil quality was constructed. The fuzzy multi-objective decision-making model based on fuzzy sets was used to comprehensively evaluate the soil quality from 2013 to 2019. We calculated that the year-on-year growth rates of soil quality from 2013 to 2019 are 13.56, 0.16, 12.81, 33.84, 9.68, and 14.80%, respectively. The results showed that the overall soil quality in the study area showed a trend of increasing year by year, and the year-on-year increase was the largest in 2017. Meanwhile, the reasons for the sudden increase in soil quality in typical years were analyzed. The results showed that the dominant factor of this phenomenon was the comprehensive influence of soil fertility. Furthermore, the relationship between soil fertility and cultivated horizon in typical years was analyzed one by one, and the specific factors affecting soil fertility were discussed.
przeglądu ważniejszych metod informatycznego rozwiązywania problemów, zaliczanych do sztucznej inteligencji. Omówiono także kierunki rozwoju owych metod, wskazując, że nie stanowią one zwartej metodologii, lecz są kolekcją różnych rozwiązań, zmierzających do uzyskania inteligentnego działania maszyn, co zasygnalizowano mówiąc o archipelagu sztucznej inteligencji. Skupiono także uwagę na problemie zagrożeń potencjalnie niesionych przez rozwój sztucznej inteligencji i wskazano na sposoby ograniczania tych zagrożeń.
popularity and reviews the more important methods of IT problem-solving, classified as artificial intelligence. The directions of development of these methods were also discussed, indicating that they do not constitute a coherent methodology, but are a collection of various solutions aimed at achieving intelligent operation of machines, which was indicated when talking about the archipelago of artificial intelligence. Attention was also focused on the problem of threats potentially brought by the development of artificial intelligence and indicated ways of reducing these threats.
energooszczędny okazał się mniej korzystny od tradycyjnego. Największą przewagę budynku energooszczędnego nad tradycyjnym widać w przypadku metody zaproponowanej w rozporządzeniu.
energy-saving variant turned out to be less favorable than the traditional one. The greatest advantage of an energy-saving building over a traditional one can be seen using the method proposed in the regulation.
observe a lack of tools al- lowing one to derive the set of non-dominated trading opportunities considered in the multicriteria space. This article focuses on multicriteria analysis, in which several different market indicators describe a single instrument on the forex market (currency pair), leading to definite criteria. Thus, for a given time horizon, we consider a set of currency pairs described by a group of technical market indicators in every trading session. However, instead of deriving crisp information, based on the buy-no buy binary logic, we use concepts from the fuzzy sets theory, in which each criterion for a single variant takes a value from the h0, 1i interval. We select only the non-dominated variants from such a set, which will be used as elements of the portfolio of currency pairs on the forex market. We test our idea on the real-world data covering more than ten years, several technical market indicators, and over twenty different currency pairs. The preliminary results show that the proposed idea can be treated as a promising concept for deriving a portfolio of currency pairs instead of focusing on only a single currency pair.
controller, various counts and configurations of fuzzy sets were defined, whereby the relevant results were achieved by their application on controlled system.
attempts to test system reliability with the benefit of membership function. Within this context, specific problems of reasoning-based approaches are studied, explored and correlated with standard reliability approaches. In this paper Generalized Trapezoidal Fuzzy numbers (GTrFN) are used to assess the structure's fuzzy reliability. The reliability of each event is assigned with different level of satisfaction and some improved operations on the generalized trapezoidal fuzzy numbers (GTrFN) are used to calculate the fuzzy boundaries for the resultant reliability of the final event along with the degree of satisfaction. Also the results are compared to demonstrate the application of the improved operations on Generalized Trapezoidal Fuzzy Numbers (GTrFN). The obtained results converge to more precise interval values as compare to the vague fuzzy number.
wynikami innych istniejących algorytmów odpowiednich do tego zadania. Uzyskane wyniki modelu analizowano. Algorytm ten może być stosowany w zadaniach rzeczywistych.
algorithms suitable for these tasks. The obtained results of the model were analysed. This algorithm can be used in real-life tasks.
whose descriptions sufficiently correspond with the current measurements taken by the device. A fuzzy assignment level for each of the potentially considered venues depends on the difference between the averaged network strengths for the venue and the signal strengths currently measured with the device for localization purposes. Ultimately, the device is assigned to the venue with the highest level of assignment.
których opis w odpowiednim stopniu pokrywa się z pomiarami dokonanymi przez urządzenie. Stopień rozmytej przynależności do każdego z wstępnie wytypowanych pomieszczeń zależy z kolei od różnicy pomiędzy uśrednionymi wartościami sygnałów sieci bezprzewodowych i aktualnie zmierzonymi do celów lokalizacji. Ostatecznie urządzeniu przypisywane jest to pomieszczenie, dla którego stopień przynależności jest największy.
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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.
of a two-stage intuitionistic fuzzy transportation problem (2-S IFTP) through the prism of index matrices (IMs). Its main objective is to find the quantities of delivery from manifacturers and resselers to buyers to maintain the supply and demand requirements at the cheapest transportation costs. The solution procedure is demonstrated by a numerical example.
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.
account, too. Both fuzzy sets and shadowed sets are used to model the impreciseness of important parameters of this HRF and the costs of maintenance services. Contrary to more classical and widely-used approaches to cost analysis (i.e. a constant yield or nominal value of money), a strictly stochastic process (i.e. the one-factor Vasicek model) of an interest rate is assumed in the analysis of maintenance costs. This approach models future behaviour of the interest rate (i.e. the future value of money) in a more realistic way. Respective algorithms together with exemplary results of numerical simulations for two setups, which are related to fuzzy and shadowed sets, are also provided.
której brana jest pod uwagę również liczba wcześniejszych uszkodzeń. Do modelowania nieprecyzyjności istotnych parametrów tej HRF oraz kosztów działań serwisowych są wykorzystywane zarówno zbiory rozmyte jak i zbiory cieniowane. W przeciwieństwie do bardziej klasycznych i szeroko wykorzystywanych podejść do analizy kosztów eksploatacji (tzn. stałej stopy procentowej lub wartości nominalnej pieniądza), założono ściśle stochastyczny proces (tzn. jednoczynnikowy model Vasicka) dla stopy procentowej. Podejście to modeluje przyszłe zachowanie stopy procentowej (czyli przyszłej wartości pieniądza) w bardziej realistyczny sposób. Zaprezentowano również odpowiednie algorytmy wraz z przykładowymi wynikami symulacji numerycznych dla dwóch zestawów parametrów, związanych ze zbiorami rozmytymi i cieniowanymi.
outbreak situation in a given region up to one month in advance.
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