Tytuł: The Opinions of Poles about the Need to Provide Humanitarian Aid to Refugees from the Area Covered by the Russian–Ukrainian War

Autor/Autorzy: Karakiewicz - Krawczyk K., Zdziarski K., Landowski M., Nieradko-Heluszko A., Kotwas A., Szumilas P., Knyszyńska A., Karakiewicz B.

Miejsce publikacji: International Journal of Environmental Research and Public Health, 2022, vol 19, issue 20

Rok: 2022

Abstrakt: The armed conflict in Ukraine has caused a lot of emotions around the world. Many countries have been involved in helping brutally attacked people, especially mothers and children. The versatile involvement of large powers is monitored and noticeable by the media. Active help from Poland is a very visible sign of human solidarity with the suffering Ukrainian nation. Open hearts, houses and institutions and humanitarian and medical aid are elements of Polish kindness and empathy. The aim of the research was to collect Poles’ opinions about the need to provide humanitarian aid to Ukrainians from the territories of the Russian–Ukrainian war. Capturing feelings of Poles towards Ukrainians during the war is an interesting issue that shows subjective opinions about the existential situation perceived in the space of mutual personal interactions. The results showing opinions on help were collected from a group of 1012 people throughout Poland with the help of an authorial questionnaire. The obtained data shows a positive attitude of Poles to Ukrainians. The most willing to help are people over 49 years old, more often with a good and very good financial situation. Respondents believe that general assistance from other countries and the European Parliament is not sufficient. Military support is accepted the most by the oldest participants of research, and less by the age group up to 30 years who support medical help more. More concerned about the ongoing conflict are respondents under the age of 30 and the least wealthy, including, more often, women. The richest respondents are least afraid of the effects of the ongoing Russian–Ukrainian conflict. The conducted research confirms the openness of Polish society to refugees and brings opinions about existential solidarity with the suffering Ukrainian nation.

Tytuł: Attitudes of Palestinian and Polish Medical Students Towards Death

Autor/Autorzy: Zdziarski K., Awad M.S., Landowski M., Zabielska P., Karakiewicz B.

Miejsce publikacji: Omega (2022), USA, 86(1), pp. 241-254

Rok: 2022

Słowa kluczowe: acceptance of death; avoidance of death; escape from death;

Abstrakt:

Tytuł: Are multidimensional RDM interval arithmetic and constrained interval arithmetic one and the same?

Autor/Autorzy: Andrzej Piegat, Marek Landowski

Miejsce publikacji: Iranian Journal of Fuzzy Systems , tom 19, zeszyt 5, str. 17 – 34, (2022)

Rok: 2022

Słowa kluczowe: Multidimensional fuzzy arithmetic; RDM fuzzy arithmetic; RDM interval arithmetic; constraint fuzzy arithmetic; constraint interval arithmetic;

Tytuł: Subjective Feelings of Polish Doctors after Receiving the COVID-19 Vaccine

Autor/Autorzy: Marek Landowski, Krzysztof Zdziarski, Paulina Zabielska, Beata Karakiewicz

Miejsce publikacji: International Journal of Environmental Research and Public Health 18, no. 12: 6291.

Rok: 2021

Słowa kluczowe: COVID-19; vaccine; doctor; subjective feelings; psychosocial condition; attitude; behaviour

Abstrakt: 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.

Tytuł monografii: Uncertainty and Imprecision in Decision Making and Decision Support: New Challenges, Solutions and Perspectives

Tytuł rozdziału monografii: Decomposition Method for Calculations on Intuitionistic Fuzzy Numbers

Autor/Autorzy: Marek Landowski

Rok: 2021

Słowa kluczowe: Intuitionistic fuzzy number, Intuitionistic fuzzy arithmetic, Multidimensional arithmetic, Decomposition method, RDM arithmetic

Abstrakt: In this paper the definition of a multidimensional trapezoidal horizontal intuitionistic fuzzy number (TrHIFN) and multidimensional decomposition method (TrHIFN arithmetic) for calculations on TrHIFNs are presented. Till now, for intuitionistic fuzzy numbers (IFN) only low-dimensional approaches have been considered. The proposed arithmetic is based on multidimensional rdm interval arithmetic (RDMIA) and its extension horizontal fuzzy arithmetic (HFA). A direct result obtained with TrHIFN arithmetic is described in multidimensional space as a granule of information about the solution. From the direct solution, IFN as an indicator (a span) of the direct solution can be calculated. Moreover, in the paper the examples with basic operations on TrHIFN and the solution of intuitionistic fuzzy linear system (IFLS) are considered.

ISBN: 978-3-030-47023-4

Tytuł: Shadowed numbers and their standard and multidimensional arithmetic

Autor/Autorzy: Marek Landowski

Miejsce publikacji: INFORMATION SCIENCES, vol. 507, pp. 485-502

Rok: 2020

Słowa kluczowe: Shadowed number, Granular computing

Abstrakt: A shadowed set was introduced by W. Pedrycz as a concept of modeling vagueness. There are methods and algorithms for obtaining a shadowed set on the basis of a fuzzy set; a shadowed number can also be obtained from a fuzzy number. This article presents definitions of a shadowed number and two concepts of its arithmetic. The first arithmetic is called standard shadowed arithmetic (SSA) and relies on standard interval arithmetic (SIA), while the second is called multidimensional RDM shadowed arithmetic (RDMSA) and is based on multidimensional relative distance measure interval arithmetic (RDMIA). This paper presents the basic properties of operations on shadowed numbers with SSA and RDMSA. It also provides examples that show the difference between the results obtained with SSA and those obtained with multidimensional RDMSA. RDMSA introduces a multidimensional approach to the concept of uncertainty calculation results. Theories and examples presented in this paper will help to develop three-way decision methods and models, and can be applied in granular computing.

Tytuł: The State of Air Pollution as a Factor Determining the Assessment of a City’s Tourist Attractiveness—Based on the Opinions of Polish Respondents

Autor/Autorzy: Aleksandra Łapko, Aleksander Panasiuk, Roma Strulak-Wójcikiewicz, Marek Landowski

Miejsce publikacji: Sustainability, vol. 12, no. 4, pp. 1466

Rok: 2020

Słowa kluczowe: city tourism, tourist attractiveness, tourism management, air pollution, sustainable tourism

Abstrakt: 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.

Tytuł: Attitudes of Palestinian and Polish Medical Students Towards Death

Autor/Autorzy: Krzysztof Zdziarski, Mariam S. Awad, Marek Landowski, Paulina Zabielska, Beata Karakiewicz

Miejsce publikacji: OMEGA-JOURNAL OF DEATH AND DYING, vol. #, pp. #

Rok: 2020

Słowa kluczowe: acceptance of death, avoidance of death, escape from death, fear of death, medical students

Abstrakt: Attitudes of students of health-related subjects towards the death are an important issue showing the behaviour and values ​​that guide young people in everyday interactions. The study was conducted using the Questionnaire About Attitudes Against Death (DAP-R-PL) among 309 students, including 150 Palestinian from the Faculty of Nursing and Health Sciences and 159 Polish from the Faculty of Health Sciences. It was noticed that the attitude of Death Avoidance is higher in Palestinians than in Poles. The biggest difference between correlation indicators is for the factors fear of death and death avoidance (FD and DA). This value is positive for Palestinian respondents and negative for Polish respondents. The study confirms that the attitudes of students towards death from both universities in the perspective of 5 factors are positive and in future contacts with dying patients they will cope with this challenge.

Tytuł: Knowledge extraction from the experimental data of the vehicle traffic volume

Autor/Autorzy: Marek Landowski, Anna Landowska

Miejsce publikacji: Transportation Research Procedia, vol. 39, pp. 270-279

Rok: 2019

Słowa kluczowe: vehicle traffic volume, data mining, statistical methods, congestion

Abstrakt: The problem of urban traffic is very important because of the ever-increasing growth of vehicles, which is one of the reasons for the congestion in urban areas. The article presents knowledge extraction with the use of the statistical methods. The characteristics of vehicle traffic volume are determined. The data come from an experiment carried out in Szczecin as part of the Green and Sustainable Freight Transport Systems in Cities (GRASS) project. On the basis of the data, vehicle traffic volume characteristics were calculated at selected points taking into account the type of vehicles, time of the day, day of the week and the speed of vehicles.

Tytuł monografii: Advances in Soft and Hard Computing

Tytuł rozdziału monografii: Horizontal Fuzzy Numbers for Solving Quadratic Fuzzy Equation

Autor/Autorzy: Marek Landowski

Rok: 2019

Słowa kluczowe: Fuzzy quadratic equation, Fuzzy number, Horizontal fuzzy number, Fuzzy arithmetic, RDM arithmetic, Uncertainty theory, Artificial intelligence

Abstrakt: The paper presents method for solving the quadratic equation with fuzzy coefficients. Based on the horizontal fuzzy numbers the solution of fuzzy quadratic equation can be obtained. Solutions with horizontal fuzzy numbers are multidimensional. Obtained solutions are compared with results of standard fuzzy arithmetic. In examples was shown that results with standard fuzzy arithmetic are overestimated or underestimated. Method with horizontal fuzzy numbers generates the granule of information about the solution. Obtained granule gives full information about the solution. Moreover, the granule of information gives possibility to indicate the crisp quadratic equation for crisp value of the solution.

ISBN: 978-3-030-03313-2

Tytuł monografii: Theory and Application of Fuzzy Systems and Soft Computing

Tytuł rozdziału monografii: Why Multidimensional Fuzzy Arithmetic?

Autor/Autorzy: Andrzej Piegat, Marek Landowski

Rok: 2019

Słowa kluczowe: Fuzzy arithmetic, RDM fuzzy arithmetic, Horizontal membership function, Granular computing, Multidimensional fuzzy arithmetic

Abstrakt: In the paper authors try to convince readers that application of multidimensional fuzzy arithmetic (MFAr) is useful because this arithmetic delivers more precise solutions of uncertain problems than low-dimensional fuzzy arithmetic, which is mostly used at present.

ISBN: 978-3-030-04163-2

Tytuł: Usage of the rough set theory for generating decision rules of number of traffic vehicles

Autor/Autorzy: Marek Landowski, Anna Landowska

Miejsce publikacji: Transportation Research Procedia, vol. 39, pp. 260-269

Rok: 2019

Słowa kluczowe: rough sets, decision rules, transport, vehicle traffic volume

Abstrakt: Often, it is difficult to interpret and use the large size of data obtained from the experiment. In addition, the generated information can be unprecise. The rough set theory besides probability theory, fuzzy set theory and many others in recent years is very often used by scientists to solve problems of data mining. In the paper the data mining of the traffic vehicles with rough set theory was made. With this theory it was shown that it is possible to generate the decision rules of the number of vehicles at the specific points in the city. On the basis of 120 examples 16 well-defined linguistic decision rules were obtained.

Tytuł: Method with horizontal fuzzy numbers for solving real fuzzy linear systems

Autor/Autorzy: Marek Landowski

Miejsce publikacji: SOFT COMPUTING, vol. 23, no. 12, pp. 3921-3933

Rok: 2019

Słowa kluczowe: Fuzzy number, Horizontal fuzzy number, Fuzzy linear system, Fuzzy arithmetic, RDM arithmetic, Uncertainty theory, Artificial Intelligence, Granular computing

Abstrakt: 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.

Tytuł: Management of Waste Collection from Yachts and Tall Ships from the Perspective of Sustainable Water Tourism

Autor/Autorzy: Aleksandra Łapko, Roma Strulak-Wójcikiewicz, Marek Landowski, Radosław Wieczorek

Miejsce publikacji: Sustainability, vol. 11, no. 1, pp. 121

Rok: 2019

Słowa kluczowe: sustainable tourism, water tourism, waste management, The Tall Ships Races, statistical analysis

Abstrakt: 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.

Tytuł: Solving different practical granular problems under the same system of equations

Autor/Autorzy: Andrzej Piegat, Marek Landowski

Miejsce publikacji: Granular Computing, vol. 3, no. 1, pp. 39-48

Rok: 2018

Słowa kluczowe: Granular computing, Equations under uncertainty, Interval computations, RDM interval arithmetic, One-dimensional interval arithmetic, Multidimensional interval arithmetic

Abstrakt: This paper contains discussion about the paper of Kreinovich (Granular Computing 1(3):171–179, 2016) in which the author suggests the thesis that in conditions of uncertainty “solving different practical problems we get different solutions of the same system of equations with the same granules”. Authors of the present paper are of the opinion that the above thesis is result of one-dimensional approach to interval analysis prevailing at present in scientific community and also used by Kreinovich. According to this approach the direct result of any arithmetic operation ∗∈{+,−,×,/} on intervals is also an interval. The main scientific contribution of the paper is showing that a granular problem analysis in an incomplete, low-dimensional space can lead to untrue conclusions because picture of the problem in this space is too poor and part of valuable, important information is lost. What is seen in the full-dimensional space of the problem space cannot be seen in an incomplete, low-dimensional space. The paper also shortly describes a multidimensional approach to interval arithmetic that is free of the above-described deficiencies.

Tytuł monografii: Advances in Fuzzy Logic and Technology 3

Tytuł rozdziału monografii: Is Fuzzy Number the Right Result of Arithmetic Operations on Fuzzy Numbers?

Autor/Autorzy: Adnrzej Piegat, Marek Landowski

Rok: 2018

Słowa kluczowe: Fuzzy arithmetic, Fuzzy computations, Uncertainty theory, Granular computing, Soft computing, Artificial intelligence

Abstrakt: Present versions of fuzzy arithmetic (FA) are not ideal. For some computational problems they deliver credible results. However for many other problems the results are less credible or sometimes clearly incredible. Reason of this state of matter is the fact that present FA-versions partially or fully (depending on a method) do not possess mathematical properties that are necessary for achieving correct calculation results as: distributivity law, cancellation law, neutral elements of addition and multiplication, property of restoration, possibility of decomposition of calculation in parts, ability of credible equations’ solving, property of delivering universal algebraic solutions, possibility of formula transformation, and other. Lack of above properties is, in the authors’ opinion, caused by incorrect assumption of all existing FA-versions that result of arithmetic operations on unidimensional fuzzy intervals is also a unidimensional fuzzy interval. In the paper authors show that the correct result is a multidimensional fuzzy set and present a fuzzy arithmetic based on this proposition, which possess all necessary mathematical properties and delivers credible results.

ISBN: 978-3-319-66826-0

Tytuł monografii: Advances in Fuzzy Logic and Technology 2

Tytuł rozdziału monografii: Usage of RDM Interval Arithmetic for Solving Cubic Interval Equation

Autor/Autorzy: Marek Landowski

Rok: 2018

Słowa kluczowe: Interval arithmetic, RDM arithmetic, Cubic equation, Multidimensional solution, Uncertainty theory

Abstrakt: The paper presents the usage of Relative Distance Measure (RDM) interval arithmetic with Cardano’s rule for solving the interval cubic equations. Based on the crisp Cardano’s rule the extension for interval variables was made. Also numerical examples for a real solution are given. The solutions obtained with RDM interval arithmetic satisfy the analysed cubic interval equations. The examples show that results with standard interval arithmetic are not full solutions and give values that do not satisfy solved equations.

ISBN: 978-3-319-66823-9

Tytuł: A discussion on ”On the solution of a class fuzzy system of linear equations”

Autor/Autorzy: Marek Landowski

Miejsce publikacji: SADHANA-ACADEMY PROCEEDINGS IN ENGINEERING SCIENCES, vol. 43, no. 12, pp. 205

Rok: 2018

Słowa kluczowe: Fuzzy system of linear equations, Fuzzy arithmetic, Horizontal fuzzy number, RDM arithmetic

Abstrakt: The paper is a discussion on the results obtained by D. K. Salkuyeh in the article [Sadhana 40(2): 369-377, 2015]. Salkuyeh considers the solution of the fuzzy system of linear equations (FSLE) and gives numerical examples where the results of FSLE are calculated. It was shown that the results by Salkuyeh are not full solutions and do not satisfy equivalent forms of the analyzed FSLE. The paper presents multidimensional approach to finding the solution of the FSLE. On the basis of the notation of the horizontal fuzzy number (HFN), a full solution that satisfies the FSLE and its equivalent forms was obtained.

Tytuł monografii: Hard and Soft Computing for Artificial Intelligence, Multimedia and Security

Tytuł rozdziału monografii: Comparison of RDM Complex Interval Arithmetic and Rectangular Complex Arithmetic

Autor/Autorzy: Marek Landowski

Rok: 2017

Słowa kluczowe: Complex variable, RDM complex interval arithmetic, Rectangular complex arithmetic, Uncertainty theory

Abstrakt: The article presents RDM complex interval arithmetic in comparison with rectangular complex arithmetic. The basic operations and the main properties of both complex interval arithmetics are described. To show the application of RDM complex interval arithmetic the examples with complex variables were solved using RDM and rectangular complex interval arithmetics. RDM means relative distance measure. RDM complex interval arithmetic is multidimensional, this property gives a possibilty to find a full solution of the problem with complex interval variables.

ISBN: 978-3-319-48428-0

Tytuł monografii: Uncertainty Modeling. Studies in Computational Intelligence

Tytuł rozdziału monografii: Fuzzy Arithmetic Type 1 with Horizontal Membership Functions

Autor/Autorzy: Andrzej Piegat, Marek Landowski

Rok: 2017

Słowa kluczowe: Fuzzy arithmetic, Fuzzy mathematics, Uncertainty theory, Granular computing, Soft computing

Abstrakt: The chapter shortly (because of the volume limitation) presents multidimensional fuzzy arithmetic based on relative-distance-measure (RDM) and horizontal membership functions which considerably facilitate calculations. This arithmetic will be denoted as MD-RDM-F one. It delivers full, multidimensional problem solutions that further enable determining, in an accurate and unique way, various representations of the solutions such as span (maximal uncertainty of the solution), cardinality distribution of possible solution values, center of gravity of the solution granule, etc. It also allows for taking into account relations and dependencies existing between variables, what is absolutely necessary e.g. in calculations with fuzzy probabilities that always should sum up to 1 or in equation system solving.

ISBN: 978-3-319-51051-4

Tytuł monografii: Hard and Soft Computing for Artificial Intelligence, Multimedia and Security

Tytuł rozdziału monografii: On Fuzzy RDM-Arithmetic

Autor/Autorzy: Andrzej Piegat, Marek Landowski

Rok: 2017

Słowa kluczowe: Fuzzy arithmetic, Granular computing, Fuzzy RDM arithmetic, Horizontal membership function, Fuzzy HMF arithmetic, Multidimensional fuzzy arithmetic

Abstrakt: The paper presents notion of horizontal membership function (HMF) and based on it fuzzy, relative distance measure (fuzzy RDM) arithmetic that is compared with standard fuzzy arithmetic (SF arithmetic). Fuzzy RDM-arithmetic possess such mathematical properties which allow for achieving complete fuzzy solution sets of problems, whereas SF-arithmetic, in general, delivers only approximate, partial solutions and sometimes no solutions of problems. The paper explains how to realize arithmetic operations with fuzzy RDM-arithmetic and shows examples of its application.

ISBN: 978-3-319-48428-0

Tytuł: Is an interval the right result of arithmetic operations on intervals?

Autor/Autorzy: Piegat A., Landowski M.

Miejsce publikacji: International Journal of Applied Mathematics and Computer Science, vol. 27, no. 3, pp. 575-590

Rok: 2017

Słowa kluczowe: interval arithmetic, one-dimensional interval arithmetic, multi-dimensional interval arithmetic, RDM interval arithmetic

Abstrakt: 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.

Tytuł: RDM interval method for solving quadratic interval equation

Autor/Autorzy: Marek Landowski

Miejsce publikacji: Przegląd Elektrotechniczny, vol. 93, no. 1, pp. 65-68

Rok: 2017

Słowa kluczowe: standard interval arithmetic, RDM interval arithmetic, quadratic interval equation, uncertainty theory

Abstrakt: The main task of uncertainty theory is to find the solution with uncertain variable. The ways of uncertainty description are probability density distribution, possibility distribution or interval. To solve the problem with uncertainty variable the calculation on interval is needed. The article presents the usage of RDM interval arithmetic for solving quadratic interval equation. The results obtained from examples are compared with Moore’s standard interval arithmetic solutions.