Title of monograph: Uncertainty and Imprecision in Decision Making and Decision Support: New Challenges, Solutions and Perspectives

Title of chapter: Decomposition Method for Calculations on Intuitionistic Fuzzy Numbers

Author/Authors: Marek Landowski

Year: 2021

Keywords: Intuitionistic fuzzy number, Intuitionistic fuzzy arithmetic, Multidimensional arithmetic, Decomposition method, RDM arithmetic

Abstract: 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

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

Author/Authors: Aleksandra Łapko, Aleksander Panasiuk, Roma Strulak-Wójcikiewicz, Marek Landowski

Place of publication: Sustainability, vol. 12, no. 4, pp. 1466

Year: 2020

Keywords: city tourism, tourist attractiveness, tourism management, air pollution, sustainable tourism

Abstract: 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.

Title: Attitudes of Palestinian and Polish Medical Students Towards Death

Author/Authors: Krzysztof Zdziarski, Mariam S. Awad, Marek Landowski, Paulina Zabielska, Beata Karakiewicz

Place of publication: OMEGA-JOURNAL OF DEATH AND DYING, vol. #, pp. #

Year: 2020

Keywords: acceptance of death, avoidance of death, escape from death, fear of death, medical students

Abstract: 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.

Title: Shadowed numbers and their standard and multidimensional arithmetic

Author/Authors: Marek Landowski

Place of publication: INFORMATION SCIENCES, vol. 507, pp. 485-502

Year: 2020

Keywords: Shadowed number, Granular computing

Abstract: 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.

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

Author/Authors: Marek Landowski, Anna Landowska

Place of publication: Transportation Research Procedia, vol. 39, pp. 270-279

Year: 2019

Keywords: vehicle traffic volume, data mining, statistical methods, congestion

Abstract: 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.

Title of monograph: Advances in Soft and Hard Computing

Title of chapter: Horizontal Fuzzy Numbers for Solving Quadratic Fuzzy Equation

Author/Authors: Marek Landowski

Year: 2019

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

Abstract: 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

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

Author/Authors: Marek Landowski

Place of publication: SOFT COMPUTING, vol. 23, no. 12, pp. 3921-3933

Year: 2019

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

Abstract: 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.

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

Author/Authors: Aleksandra Łapko, Roma Strulak-Wójcikiewicz, Marek Landowski, Radosław Wieczorek

Place of publication: Sustainability, vol. 11, no. 1, pp. 121

Year: 2019

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

Abstract: 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.

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

Author/Authors: Marek Landowski, Anna Landowska

Place of publication: Transportation Research Procedia, vol. 39, pp. 260-269

Year: 2019

Keywords: rough sets, decision rules, transport, vehicle traffic volume

Abstract: 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.

Title of monograph: Theory and Application of Fuzzy Systems and Soft Computing

Title of chapter: Why Multidimensional Fuzzy Arithmetic?

Author/Authors: Andrzej Piegat, Marek Landowski

Year: 2019

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

Abstract: 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

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

Author/Authors: Andrzej Piegat, Marek Landowski

Place of publication: Granular Computing, vol. 3, no. 1, pp. 39-48

Year: 2018

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

Abstract: 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.

Title of monograph: Advances in Fuzzy Logic and Technology 3

Title of chapter: Is Fuzzy Number the Right Result of Arithmetic Operations on Fuzzy Numbers?

Author/Authors: Adnrzej Piegat, Marek Landowski

Year: 2018

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

Abstract: 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

Title of monograph: Advances in Fuzzy Logic and Technology 2

Title of chapter: Usage of RDM Interval Arithmetic for Solving Cubic Interval Equation

Author/Authors: Marek Landowski

Year: 2018

Keywords: Interval arithmetic, RDM arithmetic, Cubic equation, Multidimensional solution, Uncertainty theory

Abstract: 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

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

Author/Authors: Marek Landowski

Place of publication: SADHANA-ACADEMY PROCEEDINGS IN ENGINEERING SCIENCES, vol. 43, no. 12, pp. 205

Year: 2018

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

Abstract: 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.

Title: RDM interval method for solving quadratic interval equation

Author/Authors: Marek Landowski

Place of publication: Przegląd Elektrotechniczny, vol. 93, no. 1, pp. 65-68

Year: 2017

Keywords: standard interval arithmetic, RDM interval arithmetic, quadratic interval equation, uncertainty theory

Abstract: 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.

Title of monograph: Hard and Soft Computing for Artificial Intelligence, Multimedia and Security

Title of chapter: Comparison of RDM Complex Interval Arithmetic and Rectangular Complex Arithmetic

Author/Authors: Marek Landowski

Year: 2017

Keywords: Complex variable, RDM complex interval arithmetic, Rectangular complex arithmetic, Uncertainty theory

Abstract: 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

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

Author/Authors: Andrzej Piegat, Marek Landowski

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

Year: 2017

Keywords: interval arithmetic, one-dimensional interval arithmetic, multi-dimensional interval arithmetic, RDM interval arithmetic

Abstract: 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.

Title of monograph: Uncertainty Modeling. Studies in Computational Intelligence

Title of chapter: Fuzzy Arithmetic Type 1 with Horizontal Membership Functions

Author/Authors: Andrzej Piegat, Marek Landowski

Year: 2017

Keywords: Fuzzy arithmetic, Fuzzy mathematics, Uncertainty theory, Granular computing, Soft computing

Abstract: 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

Title of monograph: Hard and Soft Computing for Artificial Intelligence, Multimedia and Security

Title of chapter: On Fuzzy RDM-Arithmetic

Author/Authors: Andrzej Piegat, Marek Landowski

Year: 2017

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

Abstract: 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