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Trapezoidal fuzzy multi-number and its application to multi-criteria decision-making problems

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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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Authors and Affiliations

  1. Muallim Rıfat Faculty of Education, Kilis 7 Aralık University, 79000, Kilis, Turkey

    Irfan Deli

  2. Department of Mathematics, Gaziantep University, 27310, Gaziantep, Turkey

    Vakkas Uluçay & Mehmet Şahin

Authors
  1. Vakkas Uluçay
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  2. Irfan Deli
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  3. Mehmet Şahin
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Correspondence to Vakkas Uluçay.

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Uluçay, V., Deli, I. & Şahin, M. Trapezoidal fuzzy multi-number and its application to multi-criteria decision-making problems. Neural Comput & Applic 30, 1469–1478 (2018). https://doi.org/10.1007/s00521-016-2760-3

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