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Generalized trapezoidal hesitant fuzzy numbers and their applications to multi criteria decision-making problems

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Abstract

Generalized hesitant trapezoidal fuzzy number whose membership degrees are expressed by several possible trapezoidal fuzzy numbers, is more adequate or sufficient to solve real-life decision problem than real numbers. Therefore, in this paper, to model the some multi-criteria decision-making (MCDM) problems, we define concept of generalized trapezoidal hesitant fuzzy (GTHF) number, whose membership degrees of an element to a given set are expressed by several different generalized trapezoidal fuzzy numbers in the set of real numbers R. Then, we introduce some basic operational laws of GTHF-numbers and some properties of them. Also, we propose a decision-making method to solve the MCDM problems in which criteria values take the form of GTHF information. To use in proposed decision-making method, we first give definitions of some concepts such as score, standard deviation degree, deviation degree of GTHF-numbers. We second develop some GTHF aggregation operators called the GTHF-number weighted geometric operator, GTHF-number weighted arithmetic operator, GTHF-number weighted geometric operator, GTHF-number weighted arithmetic operator. Finally, we give a numerical example for proposed MCDM to validate the reasonable and applicable of the proposed method.

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Authors and Affiliations

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

    Irfan Deli

  2. Department of Mathematics, Faculty and Sciences, Çankırı Karatekin University, 18100, Çankırı, Turkey

    Faruk Karaaslan

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  1. Irfan Deli
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  2. Faruk Karaaslan
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Correspondence to Irfan Deli.

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Deli, I., Karaaslan, F. Generalized trapezoidal hesitant fuzzy numbers and their applications to multi criteria decision-making problems. Soft Comput 25, 1017–1032 (2021). https://doi.org/10.1007/s00500-020-05201-2

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