On Approximation of Any Ordered Fuzzy Number by A Trapezoidal Ordered Fuzzy Number
In this paper, the model of imprecise quantity information is an ordered fuzzy number. The purpose of our study is to propose some methods of approximating any ordered fuzzy number using a trapezoidal ordered fuzzy number. The information ambiguity is evaluated by means of an energy measure. The inf...
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| Format: | Article |
| Language: | English |
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MDPI AG
2018-10-01
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| Series: | Symmetry |
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| Online Access: | http://www.mdpi.com/2073-8994/10/10/526 |
| _version_ | 1811279952960552960 |
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| author | Krzysztof Piasecki Anna Łyczkowska-Hanćkowiak |
| author_facet | Krzysztof Piasecki Anna Łyczkowska-Hanćkowiak |
| author_sort | Krzysztof Piasecki |
| collection | DOAJ |
| description | In this paper, the model of imprecise quantity information is an ordered fuzzy number. The purpose of our study is to propose some methods of approximating any ordered fuzzy number using a trapezoidal ordered fuzzy number. The information ambiguity is evaluated by means of an energy measure. The information indistinctness is evaluated by Kosko’s entropy measure. We discuss the problem of approximation of an arbitrary ordered fuzzy number by the nearest trapezoidal ordered fuzzy number. This way, we can simplify arithmetical operations on the linear space of ordered fuzzy numbers. The set of feasible trapezoidal ordered numbers is limited by the combination of the following conditions: invariance of energy measure, invariance of entropy measure, and invariance of information support. Evaluating the influence of individual limits combinations on the utility of given approximations, two combinations of those restraints, recommended for use, were chosen. It was also indicated that one of the recommended approximation problems can be used only for ordered fuzzy numbers characterized by a low level of entropy. The obtained results are currently used in such multi-criterial decision making models as financial portfolio management, evaluation of negotiations offers, the fuzzy TOPSIS model, and the fuzzy SAW model. |
| first_indexed | 2024-04-13T01:05:00Z |
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| id | doaj.art-07720976ddc94190ac53c39a1b5f0370 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-13T01:05:00Z |
| publishDate | 2018-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-07720976ddc94190ac53c39a1b5f03702022-12-22T03:09:21ZengMDPI AGSymmetry2073-89942018-10-01101052610.3390/sym10100526sym10100526On Approximation of Any Ordered Fuzzy Number by A Trapezoidal Ordered Fuzzy NumberKrzysztof Piasecki0Anna Łyczkowska-Hanćkowiak1Department of Investment and Real Estate, Poznan University of Economics and Business; al. Niepodleglosci 10, 61-875 Poznań, PolandDepartment of Finance, WSB University in Poznań, ul. Powstańców Wielkopolskich 5, 61-895 Poznań, PolandIn this paper, the model of imprecise quantity information is an ordered fuzzy number. The purpose of our study is to propose some methods of approximating any ordered fuzzy number using a trapezoidal ordered fuzzy number. The information ambiguity is evaluated by means of an energy measure. The information indistinctness is evaluated by Kosko’s entropy measure. We discuss the problem of approximation of an arbitrary ordered fuzzy number by the nearest trapezoidal ordered fuzzy number. This way, we can simplify arithmetical operations on the linear space of ordered fuzzy numbers. The set of feasible trapezoidal ordered numbers is limited by the combination of the following conditions: invariance of energy measure, invariance of entropy measure, and invariance of information support. Evaluating the influence of individual limits combinations on the utility of given approximations, two combinations of those restraints, recommended for use, were chosen. It was also indicated that one of the recommended approximation problems can be used only for ordered fuzzy numbers characterized by a low level of entropy. The obtained results are currently used in such multi-criterial decision making models as financial portfolio management, evaluation of negotiations offers, the fuzzy TOPSIS model, and the fuzzy SAW model.http://www.mdpi.com/2073-8994/10/10/526ordered fuzzy numbersenergy measureentropy measureinformation ambiguityinformation indistinctness |
| spellingShingle | Krzysztof Piasecki Anna Łyczkowska-Hanćkowiak On Approximation of Any Ordered Fuzzy Number by A Trapezoidal Ordered Fuzzy Number Symmetry ordered fuzzy numbers energy measure entropy measure information ambiguity information indistinctness |
| title | On Approximation of Any Ordered Fuzzy Number by A Trapezoidal Ordered Fuzzy Number |
| title_full | On Approximation of Any Ordered Fuzzy Number by A Trapezoidal Ordered Fuzzy Number |
| title_fullStr | On Approximation of Any Ordered Fuzzy Number by A Trapezoidal Ordered Fuzzy Number |
| title_full_unstemmed | On Approximation of Any Ordered Fuzzy Number by A Trapezoidal Ordered Fuzzy Number |
| title_short | On Approximation of Any Ordered Fuzzy Number by A Trapezoidal Ordered Fuzzy Number |
| title_sort | on approximation of any ordered fuzzy number by a trapezoidal ordered fuzzy number |
| topic | ordered fuzzy numbers energy measure entropy measure information ambiguity information indistinctness |
| url | http://www.mdpi.com/2073-8994/10/10/526 |
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