Multi-attribute group decision-making for online education live platform selection based on linguistic intuitionistic cubic fuzzy aggregation operators

Hao Bin Liu,Saleem Abdullah,Yi Liu,Lei Xu

doi:10.1007/s40314-020-01406-1

Abstract

The purpose of this study is to propose a multi-attribute group decision-making (MAGDM) method for online education live platform selection based on proposed novel aggregation operators (AOs) under linguistic intuitionistic cubic fuzzy set (LICFS). First, the Archimedean copula and co-copula are extended to handle linguistic intuitionistic cubic fuzzy information (LICFI) and the operational law of linguistic intuitionistic cubic fuzzy variables (LICFVs) based on extended copula (EC) and extended co-copula (ECC) are given. In addition, linguistic intuitionistic cubic fuzzy copula weighted average (LICFCWA) operator and linguistic intuitionistic cubic fuzzy copula weighted geometric (LICFCWG) operator are proposed based on EC and ECC under LICFI; meanwhile, some special forms of LICFCWA and LICFCWG have been obtained by different types generators of ECs and ECCs. Third, a novel MAGDM approach based on proposed LICFCWA (LICFCWG) is constructed to solve the selection problem of the online education live platform in the period of the COVID-19, and a detailed parameter analysis was carried out. Fourthly, LICFS will degenerate into linguistic intuitionistic fuzzy set and intuitionistic cubic fuzzy set, respectively, in different cases. Finally, some comparisons are carried out with other existing proposed MAGDM approaches. By comparing different types of experiments, the effectiveness and flexibility of the proposed approach are also showed.

Highlights

To solve the uncertain information in practical decision-making problems (DMPs), Zadeh (1965) proposed the fuzzy set (FS) in 1965
Some extended LFSs are widely used in complex DMPs, such as linguistic hesitation fuzzy set (LHFS) (Gou et al 2018), linguistic neutrosophic set (LNS) (Jin et al 2019), linguistic intuitionistic fuzzy set (LIFS) (Chen et al 2015; Arora and Garg 2019; Verma and Sharma 2013; Verma 2014), linguistic Pythagoras fuzzy set (LPFS) (Garg 2018), and so on
Linguistic membership degree (MD) is the collection of two terms one is interval-valued fuzzy set while other is fuzzy set. linguistic non-membership degree (NMD) is described in the same manner

Summary

Introduction

To solve the uncertain information in practical decision-making problems (DMPs), Zadeh (1965) proposed the fuzzy set (FS) in 1965. To improve the performance of FS, Atanassov (1986) proposed intuitionistic fuzzy set (IFS) by adding a non-membership degree (NMD). In some practical DMPs, it is difficult for decision-makers (DMs) to give their preference information in quantitative form, but they are easy to describe DMs’ opinions with linguistic variables (LVs) (Zadeh 1975; Herrera and Martinez 2000). In the development of LFSs, Chen et al (2015) proposed to combine LTS and IFS, and put forward LIFS. He expressed membership degree (MD) and NMD by LTS, and received extensive attention. Some AOs based on CFS are proposed and applied in practice (Fahmi et al 2017, 2018c, d, 2019; Qiyas and Abdullah 2020)

Objectives

Methods

Conclusion