Trapezoidal fuzzy multi-number and its application to multi-criteria decision-making problems |
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Authors: | Uluçay Vakkas Deli Irfan Şahin Mehmet |
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Affiliation: | 1.Muallim Rıfat Faculty of Education, Kilis 7 Aralık University, 79000, Kilis, Turkey ;2.Department of Mathematics, Gaziantep University, 27310, Gaziantep, Turkey ; |
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Abstract: | In this paper, the concept of trapezoidal fuzzy multi-number (TFM-number) is proposed and some desired operational laws with properties are introduced. In the TFM-number, the occurrences are more than one with the possibility of the same or the different membership functions and the TFM-number is an extension of both fuzzy number set and fuzzy set, allowing the repeated occurrences of any element. Also, aim of this paper is to investigate a multiple criteria decision-making (MCDM) method under TFM-number environment. To construct this method, we first introduce some operational laws on TFM-number based on t-norm and s-norm. Then, TFM-number arithmetic and geometric operators are proposed. Finally, we develop an MCDM method and apply to an MCDM problem to verify the introduced decision-making methods. |
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