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.
Highlights
To represent inconsistent and indeterminate information in the real world, Smarandache [1]introduced the neutrosophic set (NS) concept as the extension of the fuzzy set and intuitionistic fuzzy sets
To develop new measures in simplified neutrosophic decision-making problems, this study proposes asymmetry measures of simplified neutrosophic set (SNS) and their normalized symmetry measure of SNSs for the first time, and develops a multiple attribute decision-making (MADM) method by using the weighted symmetry measure of SNSs
A practical example about selecting the manufacturing schemes in the flexible manufacturing system is provided in SNS (SVNS and interval neutrosophic set (INS)) environments to show the applications of the weighted symmetry measure-based MADM method in realistic scenarios, and a comparative example with existing relative measures for single-valued neutrosophic set (SVNS) is given to show the feasibility and effectiveness of the proposed method
Summary
To represent inconsistent and indeterminate information in the real world, Smarandache [1]. As the subclass of NS, Ye [2] presented a simplified neutrosophic set (SNS), where its indeterminacy-membership, truth-membership, and falsity-membership functions are in the real standard interval [0, 1] to conveniently apply in engineering fields. To develop new measures in simplified neutrosophic decision-making problems, this study proposes asymmetry measures of SNSs and their normalized symmetry measure of SNSs for the first time, and develops a MADM method by using the weighted symmetry measure of SNSs. this paper is presented as the following frame.
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