On Uniform Convergence of Sequences and Series of Fuzzy-Valued Functions
The class of membership functions is restricted to trapezoidal one, as it is general enough and widely used. In the present paper since the utilization of Zadeh’s extension principle is quite difficult in practice, we prefer the idea of level sets in order to construct for a fuzzy-valued function vi...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2015/870179 |
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| _version_ | 1849398519806296064 |
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| author | Uğur Kadak Hakan Efe |
| author_facet | Uğur Kadak Hakan Efe |
| author_sort | Uğur Kadak |
| collection | DOAJ |
| description | The class of membership functions is restricted to trapezoidal one, as it is general enough and widely used. In the present paper since the utilization of Zadeh’s extension principle is quite difficult in practice, we prefer the idea of level sets in order to construct for a fuzzy-valued function via related trapezoidal membership function. We derive uniform convergence of fuzzy-valued function sequences and series with some illustrated examples. Also we study Hukuhara differentiation and Henstock integration of a fuzzy-valued function with some necessary inclusions. Furthermore, we introduce the power series with fuzzy coefficients and define the radius of convergence of power series. Finally, by using the notions of H-differentiation and radius of convergence we examine the relationship between term by term H-differentiation and uniform convergence of fuzzy-valued function series. |
| format | Article |
| id | doaj-art-a1cd2bc4b8c74c9c939b267b2709340b |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-a1cd2bc4b8c74c9c939b267b2709340b2025-08-20T03:38:35ZengWileyJournal of Function Spaces2314-88962314-88882015-01-01201510.1155/2015/870179870179On Uniform Convergence of Sequences and Series of Fuzzy-Valued FunctionsUğur Kadak0Hakan Efe1Department of Mathematics, Faculty of Sciences, Gazi University, 06500 Ankara, TurkeyDepartment of Mathematics, Faculty of Sciences, Gazi University, 06500 Ankara, TurkeyThe class of membership functions is restricted to trapezoidal one, as it is general enough and widely used. In the present paper since the utilization of Zadeh’s extension principle is quite difficult in practice, we prefer the idea of level sets in order to construct for a fuzzy-valued function via related trapezoidal membership function. We derive uniform convergence of fuzzy-valued function sequences and series with some illustrated examples. Also we study Hukuhara differentiation and Henstock integration of a fuzzy-valued function with some necessary inclusions. Furthermore, we introduce the power series with fuzzy coefficients and define the radius of convergence of power series. Finally, by using the notions of H-differentiation and radius of convergence we examine the relationship between term by term H-differentiation and uniform convergence of fuzzy-valued function series.http://dx.doi.org/10.1155/2015/870179 |
| spellingShingle | Uğur Kadak Hakan Efe On Uniform Convergence of Sequences and Series of Fuzzy-Valued Functions Journal of Function Spaces |
| title | On Uniform Convergence of Sequences and Series of Fuzzy-Valued Functions |
| title_full | On Uniform Convergence of Sequences and Series of Fuzzy-Valued Functions |
| title_fullStr | On Uniform Convergence of Sequences and Series of Fuzzy-Valued Functions |
| title_full_unstemmed | On Uniform Convergence of Sequences and Series of Fuzzy-Valued Functions |
| title_short | On Uniform Convergence of Sequences and Series of Fuzzy-Valued Functions |
| title_sort | on uniform convergence of sequences and series of fuzzy valued functions |
| url | http://dx.doi.org/10.1155/2015/870179 |
| work_keys_str_mv | AT ugurkadak onuniformconvergenceofsequencesandseriesoffuzzyvaluedfunctions AT hakanefe onuniformconvergenceofsequencesandseriesoffuzzyvaluedfunctions |