Cities are multifunctional by definition, and an increasingly significant function is the tourist function. City tourism is one of the most dynamically developing forms of tourism. Tourists' decisions regarding choosing a destination are influenced by a number of factors determining the subjective assessment of the tourist attractiveness of a given city, and one of them may be the state of air pollution, as it can have a negative impact on the health of both city dwellers and tourists. This article is an attempt to determine whether potential tourists consider information about the level of a city's air quality in the assessment of its tourist attractiveness and the impact of this information on their travel decisions. The article presents the results of surveys conducted among a group of 509 respondents from Poland. On this basis, an assessment was made of the extent to which information on the condition of air quality in a given city is relevant for persons planning a tourist trip. In the conducted research, decisions regarding both business and private trips were evaluated. In addition, information on factors that could increase the respondents' interest in the condition of air quality in the city of the intended trip (e.g., trip with children, trip length) was collected. Due to the fact that tourism is a significant source of income for many cities, the research results presented in the article may be of significant importance for entities creating the urban tourist product and responsible for its management. The article also draws attention to the fact that reducing pollution in cities can contribute to increases in their tourist attractiveness.

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For many scientists interval arithmetic (IA, I arithmetic) seems to be easy and simple. However, this is not true. Interval arithmetic is complicated. This is confirmed by the fact that, for years, new, alternative versions of this arithmetic have been created and published. These new versions tried to remove shortcomings and weaknesses of previously proposed options of the arithmetic, which decreased the prestige not only of interval arithmetic itself, but also of fuzzy arithmetic, which, to a great extent, is based on it. In our opinion, the main reason for the observed shortcomings of the present IA is the assumption that the direct result of arithmetic operations on intervals is also an interval. However, the interval is not a direct result but only a simplified representative (indicator) of the result. This hypothesis seems surprising, but investigations prove that it is true. The paper shows what conditions should be satisfied by the result of interval arithmetic operations to call it a "result", how great its dimensionality is, how to perform arithmetic operations and solve equations. Examples illustrate the proposed method of interval computations.

The COVID-19 pandemic has caused enormous confusion around the world in our daily existence. The security measures taken, such as physical distance, wearing a mask, quarantine or closing shopping malls, and even isolating large groups of the population, did not contribute to the complete overcoming of the problem. Information on the positive results of research into the COVID-19 vaccine and, finally, its administration offered hope that the pandemic would be overcome. The undertaken problem of research concerning the subjective analysis of the feelings of doctors in Poland after receiving the COVID-19 vaccine shows an important area of the medical world, which is directly responsible for their own health and the patients entrusted to them. In addition, 149 people participated in the study (8–13 February 2021), including 57% of women and 43% of men. The minimum and maximum age of the respondents are 26 and 69 years old. Furthermore, 85% of respondents took two doses of the vaccine and 15% took one. The authorial questionnaire was completed by the participants in the study online in February 2021. The results obtained indicate that the COVID-19 vaccine generates hope for stopping the pandemic. In addition, 96% of research participants think so. Doctors in middle and mature age are the most optimistic, while the youngest ones are less optimistic. In addition, 57% of respondents do not worry about side effects after taking the vaccine. Fear at the time of vaccination was experienced by over 9% of doctors. The most frequently reported post-vaccination reactions are injection site pain, fatigue and headache. Increased temperature occurred in older female respondents. From a psychosocial perspective, men are more likely to fear being infected personally with the virus, and women are more likely to be infected with their loved ones. The presented subjective assessment presents the physicians’ view captured at the moment in terms of existential and emotional. The presented feelings of the research participants reflect their personal satisfaction, responsibility for their own health, care for their relatives and patients.

The paper presents a method for solving real fuzzy systems of linear equations with the usage of horizontal fuzzy numbers (HFNs). Based on the multidimensional RDM interval arithmetic and a fuzzy number in a parametric form, the definition of a horizontal fuzzy number with nonlinear left and right borders was given. Additionally, the paper presents the properties of basic algebraic operations on these numbers. The usage of horizontal fuzzy numbers with linear and nonlinear borders was illustrated in the examples with n × n fuzzy linear systems. The obtained results are multidimensional and satisfy the fuzzy linear systems. Calculated solutions of fuzzy linear systems were compared with the results of other methods. The solution obtained with horizontal fuzzy numbers satisfies any equivalent form of fuzzy linear system, whereas the results of existing methods do not satisfy the equivalent forms of the system. The presented examples also show that the method with HFN delivers a full multidimensional solution (direct solution). The analyzed results of standard methods, which are only a part of span (indicator, indirect solution) of a full solution and/or include values that do not satisfy the fuzzy linear systems, are underestimated or overestimated. The proposed method gives a possibility to obtain a crisp solution together with a crisp system of equations; other methods do not possess these properties.

The paper presents a new (to the best of the authors' knowledge) estimator of probability called the "Ep h √ 2 completeness estimator" along with a theoretical derivation of its optimality. The estimator is especially suitable for a small number of sample items, which is the feature of many real problems characterized by data insufficiency. The control parameter of the estimator is not assumed in an a priori, subjective way, but was determined on the basis of an optimization criterion (the least absolute errors).The estimator was compared with the universally used frequency estimator of probability and with Cestnik's m-estimator with respect to accuracy. The comparison was realized both theoretically and experimentally. The results show the superiority of the Ep h √ 2 completeness estimator over the frequency estimator for the probability interval p h ∈ (0.1, 0.9). The frequency estimator is better for p h ∈ [0, 0.1] and p h ∈ [0.9, 1].

This article deals with the issue of waste collection from yachts and tall ships that is important from the perspective of sustainable tourism. There are, of course, procedures that regulate the passing of waste by vessels, which also apply to tourist vessels. However, the authors made an attempt to analyze the process of waste collection carried out under non-standard conditions, i.e., during a mass event held at the port of the Tall Ships Races final, which took place in 2017 in Szczecin. Many yachts and tall ships participated in the event, and in addition, due to the multiplicity of attractions, the event area was very popular among tourists and visitors (over one and a half million people in three days). Due to the safety of the participants, and the need to maintain high aesthetic standards, the procedures for collecting waste from vessels had to be modified. In addition to the preparation of a flowchart on which the existing procedural modifications were presented, based on the source data received from the waste collection company, quantitative and structural analyses of the waste were carried out. The conducted research showed that the waste collection required the coordination of the activities of many entities. This article also draws attention to operational problems that occurred during waste collection from vessels during the Tall Ships Races final. Statistical analysis allowed for the determination of the days where the vessels disposed the most solid and liquid waste, and how the structure of the amount of collected waste was shaped. The Tall Ships Races is the most popular and the biggest event of this type in the world—gathering the largest number of tall ships. They are carried out annually, and their route leads through various ports; however, the regatta final is the culminating point that attracts the largest number of tourists. For this reason, many cities are trying to become its organizers. In 2018, the finals took place in the Dutch port of Harlingen, and in 2019, the Danish port of Aarhus will be responsible for its organization. Two years later, in 2021, the Tall Ships Races regatta final will be hosted by Szczecin again. The results of the research conducted in this article may be helpful for appropriate preparation by subsequent ports for waste collection, which may contribute to the safety of the participants taking part in the event.