fuzzy set theory
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Ongoing global COVID-19 pandemic is not only health crisis but the economic challenge. The future of society depends on how successfully the authorities find a balance between imposition of stringent restrictions and economic development. Tax policies play a role in reducing losses caused by the COVID-19 lockdowns. All countries are taking tax measures to mitigate the impact of the effects of COVID-19 pandemic on society. While the COVID-19 pandemic has not yet been defeated, it is too early to draw conclusions about which tax measures against the effects of COVID-19 are efficient. On the other hand, correct trajectory of economic recovery can be missed if not to analyze the other countries experience. The object of this study is tax measures in the European countries against the effects of COVID-19. The subject of the study is the fuzzy set theory to assess the efficiency of tax measures in the European countries against the effects of COVID-19. The aim of the study is to find out which European countries have been more succeeded in tax measures implementing and type of their immediate crisis response. The analysis is carried out in 29 European countries. The result of the study allows to state that the number of tax measures against the effects of COVID-19 does not affect their efficiency and the most popular type of immediate crisis response has been the business cash-flow enhances.

<abstract> <p>One of the most dominant and feasible technique is called the PHF setting is exist in the circumstances of fuzzy set theory for handling intricate and vague data in genuine life scenario. The perception of PHF setting is massive universal is compared to these assumptions, who must cope with two or three sorts of data in the shape of singleton element. Under the consideration of the PHF setting, we utilized some SM in the region of the PHF setting are to diagnose the PHFDSM, PHFWDSM, PHFJSM, PHFWJSM, PHFCSM, PHFWCSM, PHFHVSM, PHFWHVSM and demonstrated their flexible parts. Likewise, a lot of examples are exposed under the invented measures based on PHF data in the environment of medical diagnosis to demonstrate the stability and elasticity of the explored works. Finally, the sensitive analysis of the presented works is also implemented and illuminated their graphical structures.</p> </abstract>

Real-time data stream mining algorithms are largely based on binary datasets and do not handle continuous quantitative data streams, especially in medical data mining field. Therefore, this paper proposes a new weighted sliding window fuzzy frequent pattern mining algorithm based on interval type-2 fuzzy set theory over data stream (WSWFFP-T2) with a single scan based on the artificial datasets of medical data stream. The weighted fuzzy frequent pattern tree based on type-2 fuzzy set theory (WFFPT2-tree) and fuzzy-list sorted structure (FLSS) is designed to mine the fuzzy frequent patterns (FFPs) over the medical data stream. The experiments show that the proposed WSWFFP-T2 algorithm is optimal for mining the quantitative data stream and not limited to the fragile databases; the performance is reliable and stable under the condition of the weighted sliding window. Moreover, the proposed algorithm has high performance in mining the FFPs compared with the existing algorithms under the condition of recall and precision rates.

Abstract. Several alternatives have been proposed to shift the paradigms of water management under uncertainty from predictive to decision-centric. An often-mentioned tool is the response surface mapping system performance with a large sample of future hydroclimatic conditions through a stress test. Dividing this exposure space between acceptable and unacceptable states requires a criterion of acceptable performance defined by a threshold. In practice, however, stakeholders and decision-makers may be confronted with ambiguous objectives for which the acceptability threshold is not clearly defined (crisp). To accommodate such situations, this paper integrates fuzzy thresholds to the response surface tool. Such integration is not straightforward when response surfaces also have their own irreducible uncertainty from the limited number of descriptors and the stochasticity of hydroclimatic conditions. Incorporating fuzzy thresholds, therefore, requires articulating categories of imperfect knowledge that are different in nature, i.e., the irreducible uncertainty of the response itself relative to the variables that describe change and the ambiguity of the acceptability threshold. We, thus, propose possibilistic surfaces to assess flood vulnerability with fuzzy acceptability thresholds. An adaptation of the logistic regression for fuzzy set theory combines the probability of an acceptable outcome and the ambiguity of the acceptability criterion within a single possibility measure. We use the flood-prone reservoir system of the Upper Saint François River basin in Canada as a case study to illustrate the proposed approach. Results show how a fuzzy threshold can be quantitatively integrated when generating a response surface and how ignoring it might lead to different decisions. This study suggests that further conceptual developments could link the reliance on acceptability thresholds in bottom-up assessment frameworks with the current uses of fuzzy set theory.

Pakistan is working on two pipeline projects, namely, Iran-Pakistan-India (IPI) and Turkmenistan-Afghanistan-Pakistan-India (TAPI) gas pipelines, to meet its energy supply-demand gap. This study's aims to compare these two projects and identify the most suitable option for Pakistan. Furthermore, as the TAPI project is progressing faster than the IPI project, this study also aims to identify the critical activities associated with TAPI projects. Finally, a model is proposed to optimize the material and transportation costs related to the TAPI project. The study's contribution by using fuzzy set theory-based multi-criteria decision-making (Fuzzy MCDM) to compare two projects along with usage of the Fuzzy Critical Path Method (FCPM) for the identification of critical activities associated with the TAPI project. Finally, the Genetic Algorithm is applied to optimize the material and transportation costs of the TAPI project. The results show that IPI has advantages over TAPI in terms of power generation, transportation cost, transits fee, and gas prices. The critical path analysis of the TAPI gas pipeline shows that it will take approximately 75 to 330.5 weeks to complete. The study is useful for the managers who have to work in these projects, the policymakers considering these projects at various levels, and the researcher having an interest in applying Fuzzy set theory with MCDM, CPM, and in the context of the energy infrastructure.

The main area of this work reflects a topic for which there is little or limited reference available and is carried out to meet the needs of professional and practical floating dry dock operators. The risk of hazards in floating dry docks is evaluated using a discrete fuzzy set theory (FST) and an evidential reasoning (ER) approach in a situation where historical failure data is not available. Fuzzy set modelling is used to estimate the safety levels of the causes of basic failure events in floating dry docks due to stability concerns using the concept of linguistic variables, and provides a framework for dealing with such variables in a systematic way. The ER approach is used to synthesise the estimated safety levels of the causes of hazards/basic hazard events. The results of this work will be valuable to dry dock masters and sister maritime engineering professionals.

Abstract The aim of this article was to evaluate urbanisation processes in space using the CORINE Land Cover (CLC) databases. The study was conducted in the rural municipality of Dywity in the direct vicinity of the city of Olsztyn. Basic concepts and methods for evaluating urbanisation processes were determined based on a review of the literature. The article addresses issues related to spatial management and GIS as a data source and a tool for analysing land management activities. The search for new methods for evaluating spatial management and spatial processes plays a particularly important role in rapidly urbanising areas. The study explored the applicability of GIS as a data source and a tool for evaluating urbanisation processes in studies that rely on modern methods such as fuzzy set theory. The intensity and dynamics of urbanisation processes were evaluated based on changes in land cover with the use of CLC databases.

The rapid development of computer technology has led to the use of fuzzy set theory in the medical, financial, economic, commercial and other fields as one of the basic components of artificial intelligence. This is due to its universal mechanism designed to analyze research in the field of humanities research. The mathematical apparatus of fuzzy set theory allows them to be performed with unformalized data, and the development and improvement of information and communication technologies make it possible to automate this process. Unformalized, abstract, "blurred" statistics, which are difficult to analyze, are also common in pedagogy. But in pedagogical practice, fuzzy logic has not been widely used. The article proves the importance and expediency of teaching students, future teachers of computer science, skills in the application of fuzzy set theory. The ability to use the mechanisms of fuzzy logic in applied programs will allow future teachers in their further pedagogical activities to conduct multi-criteria analysis of various characteristics of their students, analysis of pedagogical methods, comprehensive assessment of competencies and more. The article presents the experience of teaching fuzzy set theory, the logic of teaching and its sequence, as well as the results of such training at a pedagogical university. The necessity of the step-by-step study of fuzzy set theory is proved - from acquaintance with its basic concepts, giving examples of its application in expert systems, neural networks and artificial intelligence systems to independent construction of fuzzy knowledge representation model, development of linguistic variables and use of spreadsheet or specialized programs. The results of the experimental introduction of the topic "Fuzzy model of knowledge representation" in a training course of computer disciplines are shown. Examination of learning outcomes reveals a positive attitude of the students toward mastering the skills of using fuzzy set theory and willingness to apply it in their further pedagogical activities.