Nonlinear Triangular Intuitionistic Fuzzy Number and Its Application in Linear Integral Equation
In this paper we introduce the different arithmetic operations on nonlinear intuitionistic fuzzy number (NIFN). All the arithmetic operations are done by max-min principle method which is nothing but the application of interval analysis. We also define the nonlinear intuitionistic fuzzy function whi...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Advances in Fuzzy Systems |
| Online Access: | http://dx.doi.org/10.1155/2019/4142382 |
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| author | Sankar Prasad Mondal Adrijit Goswami Sujit Kumar De |
| author_facet | Sankar Prasad Mondal Adrijit Goswami Sujit Kumar De |
| author_sort | Sankar Prasad Mondal |
| collection | DOAJ |
| description | In this paper we introduce the different arithmetic operations on nonlinear intuitionistic fuzzy number (NIFN). All the arithmetic operations are done by max-min principle method which is nothing but the application of interval analysis. We also define the nonlinear intuitionistic fuzzy function which is used for finding the values, ambiguities, and ranking of nonlinear intuitionistic fuzzy number. The de-i-fuzzification of the corresponding intuitionistic fuzzy solution is done by average of (α,β)-cut method. Finally we solve integral equation with NIFN by the help of intuitionistic fuzzy Laplace transform method. |
| format | Article |
| id | doaj-art-a08dbecfb96a41288ad756c73ef884e3 |
| institution | Kabale University |
| issn | 1687-7101 1687-711X |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Fuzzy Systems |
| spelling | doaj-art-a08dbecfb96a41288ad756c73ef884e32025-02-03T06:00:06ZengWileyAdvances in Fuzzy Systems1687-71011687-711X2019-01-01201910.1155/2019/41423824142382Nonlinear Triangular Intuitionistic Fuzzy Number and Its Application in Linear Integral EquationSankar Prasad Mondal0Adrijit Goswami1Sujit Kumar De2Department of Natural Science, Maulana Abul Kalam Azad University of Technology, West Bengal, Haringhata, Nadia, West Bengal, IndiaDepartment of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur-721302, IndiaDepartment of Mathematics, Midnapore College (Autonomous), Midnapore-721101, West Bengal, IndiaIn this paper we introduce the different arithmetic operations on nonlinear intuitionistic fuzzy number (NIFN). All the arithmetic operations are done by max-min principle method which is nothing but the application of interval analysis. We also define the nonlinear intuitionistic fuzzy function which is used for finding the values, ambiguities, and ranking of nonlinear intuitionistic fuzzy number. The de-i-fuzzification of the corresponding intuitionistic fuzzy solution is done by average of (α,β)-cut method. Finally we solve integral equation with NIFN by the help of intuitionistic fuzzy Laplace transform method.http://dx.doi.org/10.1155/2019/4142382 |
| spellingShingle | Sankar Prasad Mondal Adrijit Goswami Sujit Kumar De Nonlinear Triangular Intuitionistic Fuzzy Number and Its Application in Linear Integral Equation Advances in Fuzzy Systems |
| title | Nonlinear Triangular Intuitionistic Fuzzy Number and Its Application in Linear Integral Equation |
| title_full | Nonlinear Triangular Intuitionistic Fuzzy Number and Its Application in Linear Integral Equation |
| title_fullStr | Nonlinear Triangular Intuitionistic Fuzzy Number and Its Application in Linear Integral Equation |
| title_full_unstemmed | Nonlinear Triangular Intuitionistic Fuzzy Number and Its Application in Linear Integral Equation |
| title_short | Nonlinear Triangular Intuitionistic Fuzzy Number and Its Application in Linear Integral Equation |
| title_sort | nonlinear triangular intuitionistic fuzzy number and its application in linear integral equation |
| url | http://dx.doi.org/10.1155/2019/4142382 |
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