Linear Programming Problem with Interval Type 2 Fuzzy Coefficients and an Interpretation for Its Constraints
Interval type 2 fuzzy numbers are a special kind of type 2 fuzzy numbers. These numbers can be described by triangular and trapezoidal shapes. In this paper, first, perfectly normal interval type 2 trapezoidal fuzzy numbers with their left-hand and right-hand spreads and their core have been introdu...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2016/8496812 |
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| author | A. Srinivasan G. Geetharamani |
| author_facet | A. Srinivasan G. Geetharamani |
| author_sort | A. Srinivasan |
| collection | DOAJ |
| description | Interval type 2 fuzzy numbers are a special kind of type 2 fuzzy numbers. These numbers can be described by triangular and trapezoidal shapes. In this paper, first, perfectly normal interval type 2 trapezoidal fuzzy numbers with their left-hand and right-hand spreads and their core have been introduced, which are normal and convex; then a new type of fuzzy arithmetic operations for perfectly normal interval type 2 trapezoidal fuzzy numbers has been proposed based on the extension principle of normal type 1 trapezoidal fuzzy numbers. Moreover, in this proposal, linear programming problems with resources and technology coefficients are perfectly normal interval type 2 fuzzy numbers. To solve this kind of fuzzy linear programming problems, a method based on the degree of satisfaction (or possibility degree) of the constraints has been introduced. In this method the fulfillment of the constraints can be measured with the help of ranking method of fuzzy numbers. Optimal solution is obtained at different degree of satisfaction by using Barnes algorithm with the help of MATLAB. Finally, the optimal solution procedure is illustrated with numerical example. |
| format | Article |
| id | doaj-art-f88d75103b074c9ab4ae638db0aebdb0 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-f88d75103b074c9ab4ae638db0aebdb02025-02-03T01:03:33ZengWileyJournal of Applied Mathematics1110-757X1687-00422016-01-01201610.1155/2016/84968128496812Linear Programming Problem with Interval Type 2 Fuzzy Coefficients and an Interpretation for Its ConstraintsA. Srinivasan0G. Geetharamani1Department of Mathematics, Anna University, Bharathidasan Institute of Technology (BIT) Campus, Tiruchirappalli, Tamilnadu 620 024, IndiaDepartment of Mathematics, Anna University, Bharathidasan Institute of Technology (BIT) Campus, Tiruchirappalli, Tamilnadu 620 024, IndiaInterval type 2 fuzzy numbers are a special kind of type 2 fuzzy numbers. These numbers can be described by triangular and trapezoidal shapes. In this paper, first, perfectly normal interval type 2 trapezoidal fuzzy numbers with their left-hand and right-hand spreads and their core have been introduced, which are normal and convex; then a new type of fuzzy arithmetic operations for perfectly normal interval type 2 trapezoidal fuzzy numbers has been proposed based on the extension principle of normal type 1 trapezoidal fuzzy numbers. Moreover, in this proposal, linear programming problems with resources and technology coefficients are perfectly normal interval type 2 fuzzy numbers. To solve this kind of fuzzy linear programming problems, a method based on the degree of satisfaction (or possibility degree) of the constraints has been introduced. In this method the fulfillment of the constraints can be measured with the help of ranking method of fuzzy numbers. Optimal solution is obtained at different degree of satisfaction by using Barnes algorithm with the help of MATLAB. Finally, the optimal solution procedure is illustrated with numerical example.http://dx.doi.org/10.1155/2016/8496812 |
| spellingShingle | A. Srinivasan G. Geetharamani Linear Programming Problem with Interval Type 2 Fuzzy Coefficients and an Interpretation for Its Constraints Journal of Applied Mathematics |
| title | Linear Programming Problem with Interval Type 2 Fuzzy Coefficients and an Interpretation for Its Constraints |
| title_full | Linear Programming Problem with Interval Type 2 Fuzzy Coefficients and an Interpretation for Its Constraints |
| title_fullStr | Linear Programming Problem with Interval Type 2 Fuzzy Coefficients and an Interpretation for Its Constraints |
| title_full_unstemmed | Linear Programming Problem with Interval Type 2 Fuzzy Coefficients and an Interpretation for Its Constraints |
| title_short | Linear Programming Problem with Interval Type 2 Fuzzy Coefficients and an Interpretation for Its Constraints |
| title_sort | linear programming problem with interval type 2 fuzzy coefficients and an interpretation for its constraints |
| url | http://dx.doi.org/10.1155/2016/8496812 |
| work_keys_str_mv | AT asrinivasan linearprogrammingproblemwithintervaltype2fuzzycoefficientsandaninterpretationforitsconstraints AT ggeetharamani linearprogrammingproblemwithintervaltype2fuzzycoefficientsandaninterpretationforitsconstraints |