Symmetry Measures of Simplified Neutrosophic Sets for Multiple Attribute Decision-Making Problems

Abstract

A simplified neutrosophic set (containing interval and single-valued neutrosophic sets) can be used for the expression and application in indeterminate decision-making problems because three elements in the simplified neutrosophic set (including interval and single valued neutrosophic sets) are characterized by its truth, falsity, and indeterminacy degrees. Under a simplified neutrosophic environment, therefore, this paper firstly defines simplified neutrosophic asymmetry measures. Then we propose a normalized symmetry measure and a weighted symmetry measure of simplified neutrosophic sets and develop a simplified neutrosophic multiple attribute decision-making method based on the weighted symmetry measure. All alternatives can be ranked through the weighted symmetry measure between the ideal solution/alternative and each alternative, and then the best one can be determined. Finally, an illustrative example on the selection of manufacturing schemes (alternatives) in the flexible manufacturing system demonstrates the applicability of the proposed method in a simplified (interval and single valued) neutrosophic setting, and then the decision-making method based on the proposed symmetry measure is in accord with the ranking order and best choice of existing projection and bidirectional projection-based decision-making methods and strengthens the resolution/discrimination in the decision-making process corresponding to the comparative example.

Bidirectional projection measure of linguistic neutrosophic numbers and their application to multi-criteria group decision making

“…Example 5.3 will show the advantages of the proposed method based on the bidirectional projection by comparing with projection of LNNs and the method based on TOPSIS model proposed by Liang et al (2017). Example 5.4 will show the advantages of the proposed method with LNNs by comparing with bidirectional projection of SVNs in Ye (2017b) and the weighted symmetry measure of SVNs in Tu et al (2018). with the criteria C j ( 1, 2, 3, 4, 5) j = by LNNs based on the LTs: G g extremely bad g pretty bad g bad g a little bad g medium g a little good g good = × is listed in Table 12.…”

“…In this section, we will illustrate the proposed MCGDM method in detail by some examples, and further prove its effectiveness and advantages by comparing with the existing MCGDM methods (Fang & Ye, 2017;Liang et al, 2017;Tu, Ye, & Wang, 2018;Ye, 2017b).…”

“…Normalized decision matrix R 3 by DM D 3 . Table 7 Collective decision matrix R. (Tu et al, 2018). In the following, we give analysis about this experimental result as follows:…”

“…When comparing the proposed method with the Tu et al's method (Tu et al, 2018), there exist different evaluation information and measurement of two methods. Obviously, we have known linguistic evaluation can better describe the imprecise cognition and be closer to presentative judgement of human by comparing the Ye's MCDM method (Ye, 2017b) with our proposed method.…”

“…Section 5 describes a numerical example and makes a comparison between the proposed method with those presented approaches in Fang and Ye (2017), Liang et al (2017), Tu et al (2018) and Ye (2017b). Section 6 concludes this paper.…”