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

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.