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Mathematics
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Advanced Fuzzy Models in Economics
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Advanced Fuzzy Models in Economics

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Fuzzy Sets, Systems and Decision Making".

Deadline for manuscript submissions: closed (31 January 2021) | Viewed by 8591

Special Issue Editors

Prof. Dr. Ewa Roszkowska

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Guest Editor
Faculty of Economics and Finance, University of Bialystok, 15-062 Bialystok, Poland
Interests: negotiation; negotiation support; multicriteria decision making; fuzzy multicriteria decision making
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Krzysztof Piasecki

E-Mail Website
Guest Editor
Institute of Economy and Finance, WSB University in Poznań, ul. Powstańców Wielkopolskich 5, 61-895 Poznań, Poland
Interests: mathematics for fuzzy systems; quantified behavioral finance; operations research; financial mathematics
Special Issues, Collections and Topics in MDPI journals
Dr. Aleksandra Wójcicka-Wójtowicz

E-Mail Website
Guest Editor
Department of Operations Research, Poznan University of Economics and Business, 61-875 Poznan, Poland
Interests: credit risk; debtors’ evaluation; fuzzy systems supporting credit risk decision making; multicriteria decision making

Special Issue Information

Dear Colleagues,

In economic theory as well as in business practice, we encounter many imprecise concepts. Imprecise data are the premises which serve the specification of economic models and, consequently, the decision-making process. All this requires the utilization of the imprecise interference rule. In the second half of the 20th century, we witnessed the development of the behavioral economy. The world of economic concepts and models became even more imprecise.

Lofti Zadeh addressed the arising needs by proposing a concept of a fuzzy set defined as “a class of objects whose memberships are not precisely defined”. Fuzzy set theory is an extension of Boolean set theory. The multivalued logic and the lattice are the theoretical background of fuzzy set theory. Fuzzy sets provide a better representation of the reality than the classical mathematical representation based on two-valued logic. Fuzzy set theory laid the foundations for vital modeling uncertainty, vagueness, and imprecision. The theory of fuzzy sets noted a great progress in economics in both theoretical and practical studies. This theory can be especially successfully used when combined with multicriteria decision making, behavioral finance, mathematical economics, MCDM methods for handling imprecision, and vagueness in real decision-making problems in several different areas.

Since the pioneering paper of Zadeh, a number of extensions of the fuzzy set theory with practical applications in different areas have also been proposed: intuitionistic fuzzy sets, interval-valued fuzzy sets, interval-valued intuitionistic fuzzy sets, rough sets, bipolar fuzzy sets, grey sets, hesitant fuzzy sets, fuzzy numbers, and oriented fuzzy sets, among others.

The objective of this Special Issue is to gather a collection of papers reflecting the latest developments in practical applications of the fuzzy mathematical tools. We invite authors to submit original research and review articles which give a deeper insight into the applications of fuzzy set theory in economics. 
The proposed papers should present the advanced fuzzy systems related to the following directions of quantified economics development:

  • Behavioral quantitative finance;
  • Economic diagnosis;
  • Economic forecasting;
  • Financial mathematics;
  • Mathematical economics;
  • Multicriteria decision making;
  • Negotiation and group decisions.

We will also take into consideration justified proposals of other significant directions of development of fuzzy mathematics which may be applied in economics. We are motivated by the overriding aim to indicate the connections between fuzzy systems and real economics.

Prof. Dr. Ewa Roszkowska
Prof. Dr. Krzysztof Piasecki
Dr. Aleksandra Wójcicka-Wójtowicz
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Fuzzy analysis
  • Fuzzy numbers
  • Fuzzy reasoning
  • Fuzzy sets
  • Fuzzy systems
  • Mathematics for fuzzy systems

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Published Papers (4 papers)

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Research

14 pages, 480 KiB  
Article
On the Similarity and Dependence of Time Series
by Vilém Novák and Soheyla Mirshahi
Mathematics 2021, 9(5), 550; https://doi.org/10.3390/math9050550 - 5 Mar 2021
Cited by 8 | Viewed by 1784
Abstract
In this paper, we undertake the problem of evaluating interrelation among time series. Interrelation is measured using a similarity index. In this paper, we suggest a new one based on the known fuzzy transform (F-transform), which has been proven to remove higher frequencies [...] Read more.
In this paper, we undertake the problem of evaluating interrelation among time series. Interrelation is measured using a similarity index. In this paper, we suggest a new one based on the known fuzzy transform (F-transform), which has been proven to remove higher frequencies than a given threshold and reduce the random noise significantly. The F-transform also provides an estimation of the slope of time series in a given imprecisely delineated time. We prove some of the suggested index properties and show its ability to measure similarity (and thus the interrelation) on a selection of several real financial time series. The method is well interpretable and easy to adjust. Full article
(This article belongs to the Special Issue Advanced Fuzzy Models in Economics)
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13 pages, 338 KiB  
Article
Application of the Oriented Fuzzy Numbers in Credit Risk Assessment
by Aleksandra Wójcicka-Wójtowicz and Krzysztof Piasecki
Mathematics 2021, 9(5), 535; https://doi.org/10.3390/math9050535 - 4 Mar 2021
Cited by 7 | Viewed by 2143
Abstract
Over the years, banks have faced many difficulties, related mainly to lax credit standards for borrowers and counterparties. The goal of credit risk management is to maintain the volume of credit risk at acceptable level as it is a vital feature in risk [...] Read more.
Over the years, banks have faced many difficulties, related mainly to lax credit standards for borrowers and counterparties. The goal of credit risk management is to maintain the volume of credit risk at acceptable level as it is a vital feature in risk management. Credit analysts take into consideration factors of a wider spectrum, e.g., the prospects of the line of business, the experience of board members, credibility of suppliers, etc. Those factors are often considered on the linguistic scale, which includes such imprecise and inaccurate phrases, for instance, such as: more/less experienced, better/worse prospects, etc., which, for the experts and decision makers, are justified and result from their personal experience, preferences and human nature. The paper presents the approach of supporting methods in the credit risk decision-making process. It presents evaluation scales of imprecise phrases commonly used during the process of credit risk assessment based on experts’ preferences. Due to the imprecision, the oriented fuzzy numbers are a useful tool. For such described evaluation scales, we use a scoring function determined with the use of an adapted Simple Additive Weighting (SAW) method. Full article
(This article belongs to the Special Issue Advanced Fuzzy Models in Economics)
27 pages, 2586 KiB  
Article
Oriented Fuzzy Numbers vs. Fuzzy Numbers
by Krzysztof Piasecki and Anna Łyczkowska-Hanćkowiak
Mathematics 2021, 9(5), 523; https://doi.org/10.3390/math9050523 - 3 Mar 2021
Cited by 10 | Viewed by 1960
Abstract
A formal model of an imprecise number can be given as, inter alia, a fuzzy number or oriented fuzzy numbers. Are they formally equivalent models? Our main goal is to seek formal differences between fuzzy numbers and oriented fuzzy numbers. For this purpose, [...] Read more.
A formal model of an imprecise number can be given as, inter alia, a fuzzy number or oriented fuzzy numbers. Are they formally equivalent models? Our main goal is to seek formal differences between fuzzy numbers and oriented fuzzy numbers. For this purpose, we examine algebraic structures composed of numerical spaces equipped with addition, dot multiplication, and subtraction determined in a usual way. We show that these structures are not isomorphic. It proves that oriented fuzzy numbers and fuzzy numbers are not equivalent models of an imprecise number. This is the first original study of a problem of a dissimilarity between oriented fuzzy numbers and fuzzy numbers. Therefore, any theorems on fuzzy numbers cannot automatically be extended to the case of oriented fuzzy numbers. In the second part of the article, we study the purposefulness of a replacement of fuzzy numbers by oriented fuzzy numbers. We show that for a portfolio analysis, oriented fuzzy numbers are more useful than fuzzy numbers. Therefore, we conclude that oriented fuzzy numbers are an original and useful tool for modelling a real-world problems. Full article
(This article belongs to the Special Issue Advanced Fuzzy Models in Economics)
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17 pages, 1124 KiB  
Article
Interval-Valued Intuitionistic Fuzzy Synthetic Measure (I-VIFSM) Based on Hellwig’s Approach in the Analysis of Survey Data
by Ewa Roszkowska and Bartłomiej Jefmański
Mathematics 2021, 9(3), 201; https://doi.org/10.3390/math9030201 - 20 Jan 2021
Cited by 15 | Viewed by 1951
Abstract
Several complex phenomena are measured with the use of tools in the form of a questionnaire where the values of criteria are assessed by the respondents using ordinal scales. Therefore, a special method of construction of synthetic measure is needed which takes into [...] Read more.
Several complex phenomena are measured with the use of tools in the form of a questionnaire where the values of criteria are assessed by the respondents using ordinal scales. Therefore, a special method of construction of synthetic measure is needed which takes into account the fact that such measurement scale allows only to determine the relationship between the states of objects: diversity, equality, minority, and majority. The main goal of this study is to propose a synthetic measure based on Hellwig’s approach and the interval-valued intuitionistic fuzzy set theory which allows to measure complex social phenomena under uncertainty, including data from questionnaire surveys. First, the method of converting ordinal data from questionnaires to interval-valued intuitionistic fuzzy sets (I-VIFS) is proposed. Next, the method of constructing a synthetic measure for I-VIFS is presented. Finally, through this synthetic measure, the optimism coefficient is defined, which allows to set the limits of the intervals for I-VIFS parameters. The usefulness of the proposed approach is showed using the results of a questionnaire survey of the subjective quality of life of inhabitants of selected communes in Poland. Results indicate that the synthetic measure is suitable and effective to evaluate complex phenomena based on ordinal data from questionnaire surveys under the conditions of measurement uncertainty. Moreover, the use of the concept of the optimism coefficient increases the flexibility of its application. Full article
(This article belongs to the Special Issue Advanced Fuzzy Models in Economics)
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