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A New Approach for Ranking Shadowed Fuzzy Numbers and its Application


Affiliations
1 Department of Management Information Systems, Modern Academy for Computer Science and Management Technology, Cairo, Egypt
 

In many decision situations, decision-makers face a kind of complex problems. In these decision-making problems, different types of fuzzy numbers are defined and, have multiple types of membership functions. So, we need a standard form to formulate uncertain numbers in the problem. Shadowed fuzzy numbers are considered granule numbers which approximate different types and different forms of fuzzy numbers. In this paper, a new ranking approach for shadowed fuzzy numbers is developed using value, ambiguity and fuzziness for shadowed fuzzy numbers. The new ranking method has been compared with other existing approaches through numerical examples. Also, the new method is applied to a hybrid multi-attribute decision making problem in which the evaluations of alternatives are expressed with different types of uncertain numbers. The comparative study for the results of different examples illustrates the reliability of the new method.

Keywords

Fuzzy Numbers, Intuitionistic Fuzzy Numbers, Shadowed Sets, Shadowed Fuzzy Numbers, Ranking, Fuzziness Measure.
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  • A New Approach for Ranking Shadowed Fuzzy Numbers and its Application

Abstract Views: 346  |  PDF Views: 132

Authors

Mohamed A. H. El-Hawy
Department of Management Information Systems, Modern Academy for Computer Science and Management Technology, Cairo, Egypt

Abstract


In many decision situations, decision-makers face a kind of complex problems. In these decision-making problems, different types of fuzzy numbers are defined and, have multiple types of membership functions. So, we need a standard form to formulate uncertain numbers in the problem. Shadowed fuzzy numbers are considered granule numbers which approximate different types and different forms of fuzzy numbers. In this paper, a new ranking approach for shadowed fuzzy numbers is developed using value, ambiguity and fuzziness for shadowed fuzzy numbers. The new ranking method has been compared with other existing approaches through numerical examples. Also, the new method is applied to a hybrid multi-attribute decision making problem in which the evaluations of alternatives are expressed with different types of uncertain numbers. The comparative study for the results of different examples illustrates the reliability of the new method.

Keywords


Fuzzy Numbers, Intuitionistic Fuzzy Numbers, Shadowed Sets, Shadowed Fuzzy Numbers, Ranking, Fuzziness Measure.

References