Search Results (4)

This paper aims to mark out new concepts of r-single valued neutrosophic sets, called r-single valued neutrosophic £-closed and £-open sets. The definition of £-single valued neutrosophic irresolute mapping is provided and its characteristic properties are discussed. Moreover, the concepts of £-single valued neutrosophic extremally disconnected and £-single valued neutrosophic normal spaces are established. As a result, a useful implication diagram between the r-single valued neutrosophic ideal open sets is obtained. Finally, some kinds of separation axioms, namely r-single valued neutrosophic ideal-$R_i$ (r-$SVNI{R}_i$, for short), where $i=\{0,1,2,3\}$, and r-single valued neutrosophic ideal-$T_j$ (r-$SVNI{T}_j$, for short), where $j=\{1,2,2\frac{1}{2},3,4\}$, are introduced. Some of their characterizations, fundamental properties, and the relations between these notions have been studied. Full article

This work indicates the insufficiency of existing symmetry measures (SMs) between asymmetry measures of simplified neutrosophic sets (SNSs) and proposes the improved normalized SMs of SNSs, including the improved SMs and weighted SMs in single-valued and interval neutrosophic settings. Then, the sine entropy measures of SNSs are presented to establish a sine entropy weight model for solving the criteria weights in decision-making. Based on the improved weighted SMs of SNSs and the sine entropy weight model, a multi-criteria decision-making (MCDM) method with unknown criteria weights (an improved MCDM method) is established in the SNS setting. In the MCDM process, corresponding to the criteria weights obtained by the sine entropy model, the ranking order of all alternatives and the best one are given by means of the improved weighted SMs between the ideal solution and each alternative. Lastly, the improved MCDM method is applied to an actual decision example in single-valued and interval neutrosophic settings to indicate the feasibility of the improved MCDM method. By comparative analysis with existing MCDM methods, the improved SMs and the sine entropy weight model not only provide a simpler and more effective method for MCDM problems with unknown criteria weights in the SNS setting, but can also overcome the insufficiency of the existing SMs and MCDM method. Full article

The purpose of this paper is to investigate the weights determination in the multiple attribute decision-making (MADM) with the single valued neutrosophic information. We first introduce a generalized single-valued neutrosophic deviation measure for a group of single valued neutrosophic sets (SVNSs), and then present a novel and simple nonlinear optimization model to determine the attribute weights by maximizing the total deviation of all attribute values, whether the attribute weights are partly known or completely unknown. Compared with the existing method based on the deviation measure, the presented approach does not normalize the optimal solution and is easier to integrate the subjective and objective information about attribute weights in the neutrosophic MADM problems. Moreover, the proposed nonlinear optimization model is solved to obtain an exact and straightforward formula for determining the attribute weights if the attribute weights are completely unknown. After the weights are obtained, the neutrosophic information of each alternative is aggregated by using the single valued neutrosophic weighted average (SVNWA) operator. In what follows, all alternatives are ranked and the most preferred one(s) is easily selected according to the score function and accuracy function. Finally, an example in literature is examined to verify the effectiveness and application of the developed approach. The example is also used to demonstrate the rationality for overcoming some drawbacks of the existing approach according to the maximizing deviation method. Full article

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. Full article