An Efficient Ranking Technique for Intuitionistic Fuzzy Numbers with Its Application in Chance Constrained Bilevel Programming
The aim of this paper is to develop a new ranking technique for intuitionistic fuzzy numbers using the method of defuzzification based on probability density function of the corresponding membership function, as well as the complement of nonmembership function. Using the proposed ranking technique a...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Advances in Fuzzy Systems |
| Online Access: | http://dx.doi.org/10.1155/2016/6475403 |
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| _version_ | 1850160240606052352 |
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| author | Animesh Biswas Arnab Kumar De |
| author_facet | Animesh Biswas Arnab Kumar De |
| author_sort | Animesh Biswas |
| collection | DOAJ |
| description | The aim of this paper is to develop a new ranking technique for intuitionistic fuzzy numbers using the method of defuzzification based on probability density function of the corresponding membership function, as well as the complement of nonmembership function. Using the proposed ranking technique a methodology for solving linear bilevel fuzzy stochastic programming problem involving normal intuitionistic fuzzy numbers is developed. In the solution process each objective is solved independently to set the individual goal value of the objectives of the decision makers and thereby constructing fuzzy membership goal of the objectives of each decision maker. Finally, a fuzzy goal programming approach is considered to achieve the highest membership degree to the extent possible of each of the membership goals of the decision makers in the decision making context. Illustrative numerical examples are provided to demonstrate the applicability of the proposed methodology and the achieved results are compared with existing techniques. |
| format | Article |
| id | doaj-art-b46c1dccbe96413e8c9901fe1be5fb9d |
| institution | OA Journals |
| issn | 1687-7101 1687-711X |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Fuzzy Systems |
| spelling | doaj-art-b46c1dccbe96413e8c9901fe1be5fb9d2025-08-20T02:23:12ZengWileyAdvances in Fuzzy Systems1687-71011687-711X2016-01-01201610.1155/2016/64754036475403An Efficient Ranking Technique for Intuitionistic Fuzzy Numbers with Its Application in Chance Constrained Bilevel ProgrammingAnimesh Biswas0Arnab Kumar De1Department of Mathematics, University of Kalyani, Kalyani 741235, IndiaDepartment of Mathematics, Government College of Engineering and Textile Technology, Serampore 712201, IndiaThe aim of this paper is to develop a new ranking technique for intuitionistic fuzzy numbers using the method of defuzzification based on probability density function of the corresponding membership function, as well as the complement of nonmembership function. Using the proposed ranking technique a methodology for solving linear bilevel fuzzy stochastic programming problem involving normal intuitionistic fuzzy numbers is developed. In the solution process each objective is solved independently to set the individual goal value of the objectives of the decision makers and thereby constructing fuzzy membership goal of the objectives of each decision maker. Finally, a fuzzy goal programming approach is considered to achieve the highest membership degree to the extent possible of each of the membership goals of the decision makers in the decision making context. Illustrative numerical examples are provided to demonstrate the applicability of the proposed methodology and the achieved results are compared with existing techniques.http://dx.doi.org/10.1155/2016/6475403 |
| spellingShingle | Animesh Biswas Arnab Kumar De An Efficient Ranking Technique for Intuitionistic Fuzzy Numbers with Its Application in Chance Constrained Bilevel Programming Advances in Fuzzy Systems |
| title | An Efficient Ranking Technique for Intuitionistic Fuzzy Numbers with Its Application in Chance Constrained Bilevel Programming |
| title_full | An Efficient Ranking Technique for Intuitionistic Fuzzy Numbers with Its Application in Chance Constrained Bilevel Programming |
| title_fullStr | An Efficient Ranking Technique for Intuitionistic Fuzzy Numbers with Its Application in Chance Constrained Bilevel Programming |
| title_full_unstemmed | An Efficient Ranking Technique for Intuitionistic Fuzzy Numbers with Its Application in Chance Constrained Bilevel Programming |
| title_short | An Efficient Ranking Technique for Intuitionistic Fuzzy Numbers with Its Application in Chance Constrained Bilevel Programming |
| title_sort | efficient ranking technique for intuitionistic fuzzy numbers with its application in chance constrained bilevel programming |
| url | http://dx.doi.org/10.1155/2016/6475403 |
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