Similarity Measures of Sequence of Fuzzy Numbers and Fuzzy Risk Analysis
We present the methods to evaluate the similarity measures between sequence of triangular fuzzy numbers for making contributions to fuzzy risk analysis. Firstly, we calculate the COG (center of gravity) points of sequence of triangular fuzzy numbers. After, we present the methods to measure the degr...
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2015-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2015/724647 |
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| author | Zarife Zararsız |
| author_facet | Zarife Zararsız |
| author_sort | Zarife Zararsız |
| collection | DOAJ |
| description | We present the methods to evaluate the similarity measures between sequence of triangular fuzzy numbers for making contributions to fuzzy risk analysis. Firstly, we calculate the COG (center of gravity) points of sequence of triangular fuzzy numbers. After, we present the methods to measure the degree of similarity between sequence of triangular fuzzy numbers. In addition, we give an example to compare the methods mentioned in the text. Furthermore, in this paper, we deal with the (t1,t2) type fuzzy number. By defining the algebraic operations on the (t1,t2) type fuzzy numbers we can solve the equations in the form x+u(t1,t2)=v(t1,t2), where u(t1,t2) and v(t1,t2) are fuzzy number. By this way, we can build an algebraic structure on fuzzy numbers. Additionally, the generalized difference sequence spaces of triangular fuzzy numbers [l∞(Ft)]B(r^,s^), [c(Ft)]B(r^,s^), and [c0(Ft)]B(r^,s^), consisting of all sequences u∗=(u(t1,t2)k) such that Br^,s^u∗ is in the spaces l∞(Ft), c(Ft), and c0(Ft), have been constructed, respectively. Furthermore, some classes of matrix transformations from the space cFtB(r^,s^) and μ(Ft) to μ(Ft) and cFtB(r^,s^) are characterized, respectively, where μ(Ft) is any sequence space. |
| format | Article |
| id | doaj-art-3e3742b4eb094473a223a113953c751d |
| institution | OA Journals |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-3e3742b4eb094473a223a113953c751d2025-08-20T02:08:24ZengWileyAdvances in Mathematical Physics1687-91201687-91392015-01-01201510.1155/2015/724647724647Similarity Measures of Sequence of Fuzzy Numbers and Fuzzy Risk AnalysisZarife Zararsız0Department of Mathematics, Faculty of Art and Science, University of Nevşehir Hacı Bektaş Veli, 50300 Nevşehir, TurkeyWe present the methods to evaluate the similarity measures between sequence of triangular fuzzy numbers for making contributions to fuzzy risk analysis. Firstly, we calculate the COG (center of gravity) points of sequence of triangular fuzzy numbers. After, we present the methods to measure the degree of similarity between sequence of triangular fuzzy numbers. In addition, we give an example to compare the methods mentioned in the text. Furthermore, in this paper, we deal with the (t1,t2) type fuzzy number. By defining the algebraic operations on the (t1,t2) type fuzzy numbers we can solve the equations in the form x+u(t1,t2)=v(t1,t2), where u(t1,t2) and v(t1,t2) are fuzzy number. By this way, we can build an algebraic structure on fuzzy numbers. Additionally, the generalized difference sequence spaces of triangular fuzzy numbers [l∞(Ft)]B(r^,s^), [c(Ft)]B(r^,s^), and [c0(Ft)]B(r^,s^), consisting of all sequences u∗=(u(t1,t2)k) such that Br^,s^u∗ is in the spaces l∞(Ft), c(Ft), and c0(Ft), have been constructed, respectively. Furthermore, some classes of matrix transformations from the space cFtB(r^,s^) and μ(Ft) to μ(Ft) and cFtB(r^,s^) are characterized, respectively, where μ(Ft) is any sequence space.http://dx.doi.org/10.1155/2015/724647 |
| spellingShingle | Zarife Zararsız Similarity Measures of Sequence of Fuzzy Numbers and Fuzzy Risk Analysis Advances in Mathematical Physics |
| title | Similarity Measures of Sequence of Fuzzy Numbers and Fuzzy Risk Analysis |
| title_full | Similarity Measures of Sequence of Fuzzy Numbers and Fuzzy Risk Analysis |
| title_fullStr | Similarity Measures of Sequence of Fuzzy Numbers and Fuzzy Risk Analysis |
| title_full_unstemmed | Similarity Measures of Sequence of Fuzzy Numbers and Fuzzy Risk Analysis |
| title_short | Similarity Measures of Sequence of Fuzzy Numbers and Fuzzy Risk Analysis |
| title_sort | similarity measures of sequence of fuzzy numbers and fuzzy risk analysis |
| url | http://dx.doi.org/10.1155/2015/724647 |
| work_keys_str_mv | AT zarifezararsız similaritymeasuresofsequenceoffuzzynumbersandfuzzyriskanalysis |