Abstract
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.
Highlights
Multiple attribute decision-making (MADM) or multiple criteria decision-making (MCDM) has been widely used for the purpose of ranking or selecting alternatives with respect to multiple and usually conflicting attributes
Different from the method in [13], this paper provides a new approach to determine the attribute weights based on the deviation of single valued neutrosophic sets (SVNSs) in the decision-making problem with neutrosophic information
We firstly review some basic concepts and notations related to the neutrosophic set and SVNSs, and propose a generalized single-valued neutrosophic deviation measure between two alternatives, which will be used in the rest of this paper
Summary
Multiple attribute decision-making (MADM) or multiple criteria decision-making (MCDM) has been widely used for the purpose of ranking or selecting alternatives with respect to multiple and usually conflicting attributes (criteria). In order to deal with these problems, a lot of MADM methods have been presented and applied to many fields, including management science, decision sciences, economics, society, engineering, and so on. Classical MADM methods require the decision-maker (DM) to crisply evaluate the performance of alternatives under all attributes. The information about the alternatives is often imprecise, inconsistent and subjective and the DM can only give approximate, incomplete information for some reasons. The imprecise and subjective data are usually presented and the alternatives are assessed in a fuzzy environment [1,2]
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