Ranking Fuzzy Numbers with a Distance Method using Circumcenter of Centroids and an Index of Modality
Ranking fuzzy numbers are an important aspect of decision making in a fuzzy environment. Since their inception in 1965, many authors have proposed different methods for ranking fuzzy numbers. However, there is no method which gives a satisfactory result to all situations. Most of the methods propo...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Advances in Fuzzy Systems |
| Online Access: | http://dx.doi.org/10.1155/2011/178308 |
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| author | P. Phani Bushan Rao N. Ravi Shankar |
| author_facet | P. Phani Bushan Rao N. Ravi Shankar |
| author_sort | P. Phani Bushan Rao |
| collection | DOAJ |
| description | Ranking fuzzy numbers are an important aspect of decision making in a fuzzy environment. Since their inception in 1965, many authors have proposed different methods for ranking fuzzy numbers. However, there is no method which gives a satisfactory result to all situations. Most of the methods proposed so far are nondiscriminating and counterintuitive. This paper proposes a new method for ranking fuzzy numbers based on the Circumcenter of Centroids and uses an index of optimism to reflect the decision maker's optimistic attitude and also an index of modality that represents the neutrality of the decision maker. This method ranks various types of fuzzy numbers which include normal, generalized trapezoidal, and triangular fuzzy numbers along with crisp numbers with the particularity that crisp numbers are to be considered particular cases of fuzzy numbers. |
| format | Article |
| id | doaj-art-07fba96ce27d4acfae364bd2181e5d5d |
| institution | Kabale University |
| issn | 1687-7101 1687-711X |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Fuzzy Systems |
| spelling | doaj-art-07fba96ce27d4acfae364bd2181e5d5d2025-02-03T01:07:44ZengWileyAdvances in Fuzzy Systems1687-71011687-711X2011-01-01201110.1155/2011/178308178308Ranking Fuzzy Numbers with a Distance Method using Circumcenter of Centroids and an Index of ModalityP. Phani Bushan Rao0N. Ravi Shankar1Department of Mathematics, GITAM Institute of Technology, GITAM University, Visakhapatnam 530045, IndiaDepartment of Applied Mathematics, GITAM Institute of Science, GITAM University, Visakhapatnam 530045, IndiaRanking fuzzy numbers are an important aspect of decision making in a fuzzy environment. Since their inception in 1965, many authors have proposed different methods for ranking fuzzy numbers. However, there is no method which gives a satisfactory result to all situations. Most of the methods proposed so far are nondiscriminating and counterintuitive. This paper proposes a new method for ranking fuzzy numbers based on the Circumcenter of Centroids and uses an index of optimism to reflect the decision maker's optimistic attitude and also an index of modality that represents the neutrality of the decision maker. This method ranks various types of fuzzy numbers which include normal, generalized trapezoidal, and triangular fuzzy numbers along with crisp numbers with the particularity that crisp numbers are to be considered particular cases of fuzzy numbers.http://dx.doi.org/10.1155/2011/178308 |
| spellingShingle | P. Phani Bushan Rao N. Ravi Shankar Ranking Fuzzy Numbers with a Distance Method using Circumcenter of Centroids and an Index of Modality Advances in Fuzzy Systems |
| title | Ranking Fuzzy Numbers with a Distance Method using Circumcenter of Centroids and an Index of Modality |
| title_full | Ranking Fuzzy Numbers with a Distance Method using Circumcenter of Centroids and an Index of Modality |
| title_fullStr | Ranking Fuzzy Numbers with a Distance Method using Circumcenter of Centroids and an Index of Modality |
| title_full_unstemmed | Ranking Fuzzy Numbers with a Distance Method using Circumcenter of Centroids and an Index of Modality |
| title_short | Ranking Fuzzy Numbers with a Distance Method using Circumcenter of Centroids and an Index of Modality |
| title_sort | ranking fuzzy numbers with a distance method using circumcenter of centroids and an index of modality |
| url | http://dx.doi.org/10.1155/2011/178308 |
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