Abstract
Although a single-valued neutrosophic multi-valued set (SVNMVS) can reasonably and perfectly express group evaluation information and make up for the flaw of multi-valued/hesitant neutrosophic sets in group decision-making problems, its information expression and group decision-making methods still lack the ability to express and process single- and interval-valued hybrid neutrosophic multi-valued information. To overcome the drawbacks, this study needs to propose single- and interval-valued hybrid neutrosophic multi-valued sets (SIVHNMVSs), correlation coefficients of consistency interval-valued neutrosophic sets (CIVNSs), and their multi-attribute group decision-making (MAGDM) method in the setting of SIVHNMVSs. First, we propose SIVHNMVSs and a transformation method for converting SIVHNMVSs into CIVNSs based on the mean and consistency degree (the complement of standard deviation) of truth, falsity and indeterminacy sequences. Then, we present two correlation coefficients between CIVNSs based on the multiplication of both the correlation coefficient of interval-valued neutrosophic sets and the correlation coefficient of neutrosophic consistency sets and two weighted correlation coefficients of CIVNSs. Next, a MAGDM method is developed based on the proposed two weighted correlation coefficients of CIVNSs for performing MAGDM problems under the environment of SIVHNMVSs. At last, a selection case of landslide treatment schemes demonstrates the application of the proposed MAGDM method under the environment of SIVHNMVSs. By comparative analysis, our new method not only overcomes the drawbacks of the existing method, but also is more extensive and more useful than the existing method when tackling MAGDM problems in the setting of SIVHNMVSs.
Highlights
In recent decades, neutrosophic decision-making theories and methods [1, 2] have aroused general interest in indeterminate and inconsistent situations
Motivated by the new challenging ideas, the targets of this study are (1) to propose a single- and interval-valued hybrid neutrosophic multivalued set/element (SIVHNMVS/(SIVHNMVE) and a transformation method that converts SIVHNMVS/SIVHNMVE into a consistency interval-valued neutrosophic set/element (CIVNS/CIVNE) based on the average value and consistency degree of the truth, falsity and indeterminacy sequences, (2) to present two correlation coefficients between consistency interval-valued neutrosophic sets (CIVNSs) based on the multiplication of both the correlation coefficient of interval-valued neutrosophic sets (IVNS) and the correlation coefficient of neutrosophic consistency sets (NCSs) in the setting of SIVHNMVSs and two weighted correlation coefficients of CIVNSs, and (3) to develop a multi-attribute group decision-making (MAGDM) method by the proposed two weighted correlation coefficients of CIVNSs for performing MAGDM problems under the environment of SIVHNMVSs
We propose SIVHNMVS for representing the hybrid information of single-valued neutrosophic multi-valued set (SVNMVS) and an interval-valued neutrosophic multi-valued set (IVNMVS) simultaneously and introduce a transformation method for converting SIVHNMVS into CIVNS based on the mean and consistency degree of the truth, falsity and indeterminacy sequences in SIVHNMVS
Summary
Neutrosophic decision-making theories and methods [1, 2] have aroused general interest in indeterminate and inconsistent situations. All the assessed values can be constructed as the decision matrix of SIVHNMVEs D (hij )t×n (i 1, 2, ..., t; j 1, 2, ..., n) In this MAGDM problem, a MAGDM method is presented by using the weighted correlation coefficients of CIVNSs to resolve group decision-making problems under the environment of SIVHNMVSs, its decision process is detailed below: Step 1: Based on Eqs. In this MAGDM problem, the proposed MAGDM method is applied to the selection case of landslide treatment schemes under the environment of SIVHNMVSs. its decision process is detailed below: Step 1: Based on Eqs. Under the application environments of SIVHNMVSs and SVNMVSs, this section compares our new MAGDM method with existing MAGDM method [24] to show the superiority of the new method over the existing method
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