Abstract
The Maclaurin symmetric mean (MSM) can capture the interrelationship among the multi-input arguments and it also can generalize most of the existing operators. Now MSM has been extended to intuitionistic fuzzy sets (IFSs) which can easily express the vague information. However, the operational rules of IFSs used in the extended MSM operator didn’t consider the interaction between the membership function and non-membership function, so there are some weaknesses. In this paper, in order to combine the advantages of the MSM and interaction operational rules of IFSs, we propose the intuitionistic fuzzy interaction Maclaurin symmetric mean (IFIMSM) operator, the intuitionistic fuzzy weighted interaction Maclaurin symmetric mean (IFWIMSM) operator, respectively. Furthermore, we research some desirable properties and some special cases of them. Further, we develop a new method to deal with some multi-attribute group decision-making (MAGDM) problems under intuitionistic fuzzy environment based on these operators. Finally, an illustrative example is given to testify the availability of the developed method by comparing with the other existing methods.
Highlights
multi-attribute group decision-making (MAGDM) has been applied in all kind of fields more and more widely (Celik, Gumus, & Alegoz, 2014; Gürbüz & Albayrak, 2014; Mulliner, Malys, & Maliene, 2015; Rabbani, Zamani, Yazdani-Chamzini, & Zavadskas, 2014; Zhang, & Guo, 2016; Wu, Cao, & Li, 2016; Tian, Wang, & Wang, 2017), the goal of these decision-makings is to select the best one from the finite alternatives according to some attributes
In order to overcome the limitation of intuitionistic fuzzy interaction Maclaurin symmetric mean (IFIMSM) operator, we develop the intuitionistic fuzzy weighted interaction Maclaurin symmetric mean (IFWIMSM) operator as follows
We extended the Maclaurin symmetric mean (MSM) operator to intuitionistic fuzzy numbers (IFNs) based on the interaction operations for the IFNs and proposed some interaction MSM operators for IFNs, such as the IFIMSM and IFWIMSM operators, we discussed some desirable characteristics of them, such as idempotency and commutativity
Summary
MAGDM has been applied in all kind of fields more and more widely (Celik, Gumus, & Alegoz, 2014; Gürbüz & Albayrak, 2014; Mulliner, Malys, & Maliene, 2015; Rabbani, Zamani, Yazdani-Chamzini, & Zavadskas, 2014; Zhang, & Guo, 2016; Wu, Cao, & Li, 2016; Tian, Wang, & Wang, 2017), the goal of these decision-makings is to select the best one from the finite alternatives according to some attributes.
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