A comparative study on interval arithmetic operations with intuitionistic fuzzy numbers for solving an intuitionistic fuzzy multi–objective linear programming problem
In a real world situation, whenever ambiguity exists in the modeling of intuitionistic fuzzy numbers (IFNs), interval valued intuitionistic fuzzy numbers (IVIFNs) are often used in order to represent a range of IFNs unstable from the most pessimistic evaluation to the most optimistic one. IVIFNs are...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Sciendo
2017-09-01
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| Series: | International Journal of Applied Mathematics and Computer Science |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/amcs-2017-0040 |
| _version_ | 1818586809889718272 |
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| author | Vidhya Rajendran Irene Hepzibah Rajkumar |
| author_facet | Vidhya Rajendran Irene Hepzibah Rajkumar |
| author_sort | Vidhya Rajendran |
| collection | DOAJ |
| description | In a real world situation, whenever ambiguity exists in the modeling of intuitionistic fuzzy numbers (IFNs), interval valued intuitionistic fuzzy numbers (IVIFNs) are often used in order to represent a range of IFNs unstable from the most pessimistic evaluation to the most optimistic one. IVIFNs are a construction which helps us to avoid such a prohibitive complexity. This paper is focused on two types of arithmetic operations on interval valued intuitionistic fuzzy numbers (IVIFNs) to solve the interval valued intuitionistic fuzzy multi-objective linear programming problem with pentagonal intuitionistic fuzzy numbers (PIFNs) by assuming different α and β cut values in a comparative manner. The objective functions involved in the problem are ranked by the ratio ranking method and the problem is solved by the preemptive optimization method. An illustrative example with MATLAB outputs is presented in order to clarify the potential approach. |
| first_indexed | 2024-12-16T08:58:52Z |
| format | Article |
| id | doaj.art-a7da3f6f244b45f2a7aa38e81e6abcc4 |
| institution | Directory Open Access Journal |
| issn | 2083-8492 |
| language | English |
| last_indexed | 2024-12-16T08:58:52Z |
| publishDate | 2017-09-01 |
| publisher | Sciendo |
| record_format | Article |
| series | International Journal of Applied Mathematics and Computer Science |
| spelling | doaj.art-a7da3f6f244b45f2a7aa38e81e6abcc42022-12-21T22:37:14ZengSciendoInternational Journal of Applied Mathematics and Computer Science2083-84922017-09-0127356357310.1515/amcs-2017-0040amcs-2017-0040A comparative study on interval arithmetic operations with intuitionistic fuzzy numbers for solving an intuitionistic fuzzy multi–objective linear programming problemVidhya Rajendran0Irene Hepzibah Rajkumar1Research Scholar, Bharathiar University, Coimbatore641046, Tamil Nadu, IndiaResearch and Development Centre, Bharathiar University, Coimbatore641046, Tamil Nadu, IndiaIn a real world situation, whenever ambiguity exists in the modeling of intuitionistic fuzzy numbers (IFNs), interval valued intuitionistic fuzzy numbers (IVIFNs) are often used in order to represent a range of IFNs unstable from the most pessimistic evaluation to the most optimistic one. IVIFNs are a construction which helps us to avoid such a prohibitive complexity. This paper is focused on two types of arithmetic operations on interval valued intuitionistic fuzzy numbers (IVIFNs) to solve the interval valued intuitionistic fuzzy multi-objective linear programming problem with pentagonal intuitionistic fuzzy numbers (PIFNs) by assuming different α and β cut values in a comparative manner. The objective functions involved in the problem are ranked by the ratio ranking method and the problem is solved by the preemptive optimization method. An illustrative example with MATLAB outputs is presented in order to clarify the potential approach.https://doi.org/10.1515/amcs-2017-0040pentagonal intuitionistic fuzzy numberinterval valued intuitionistic fuzzy numberinterval valued intuitionistic fuzzy arithmeticmodified interval valued intuitionistic fuzzy arithmeticinterval valued intuitionistic fuzzy multi-objective linear programming problem |
| spellingShingle | Vidhya Rajendran Irene Hepzibah Rajkumar A comparative study on interval arithmetic operations with intuitionistic fuzzy numbers for solving an intuitionistic fuzzy multi–objective linear programming problem International Journal of Applied Mathematics and Computer Science pentagonal intuitionistic fuzzy number interval valued intuitionistic fuzzy number interval valued intuitionistic fuzzy arithmetic modified interval valued intuitionistic fuzzy arithmetic interval valued intuitionistic fuzzy multi-objective linear programming problem |
| title | A comparative study on interval arithmetic operations with intuitionistic fuzzy numbers for solving an intuitionistic fuzzy multi–objective linear programming problem |
| title_full | A comparative study on interval arithmetic operations with intuitionistic fuzzy numbers for solving an intuitionistic fuzzy multi–objective linear programming problem |
| title_fullStr | A comparative study on interval arithmetic operations with intuitionistic fuzzy numbers for solving an intuitionistic fuzzy multi–objective linear programming problem |
| title_full_unstemmed | A comparative study on interval arithmetic operations with intuitionistic fuzzy numbers for solving an intuitionistic fuzzy multi–objective linear programming problem |
| title_short | A comparative study on interval arithmetic operations with intuitionistic fuzzy numbers for solving an intuitionistic fuzzy multi–objective linear programming problem |
| title_sort | comparative study on interval arithmetic operations with intuitionistic fuzzy numbers for solving an intuitionistic fuzzy multi objective linear programming problem |
| topic | pentagonal intuitionistic fuzzy number interval valued intuitionistic fuzzy number interval valued intuitionistic fuzzy arithmetic modified interval valued intuitionistic fuzzy arithmetic interval valued intuitionistic fuzzy multi-objective linear programming problem |
| url | https://doi.org/10.1515/amcs-2017-0040 |
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