Şahin, Rıdvan; Küçük, Gökçe Dilek

Linguistic neutrosophic number (LNN) is a specific form of neutrosophic number whose elements are expressed by linguistic terms. Maclaurin symmetric mean (MSM) operator is one of the basic collection operators in the modern knowledge fusion theory. Its most important feature is to consider the interrelationships among multiple input arguments. Multiple attribute group decision-making (MAGDM) with linguistic neutrosophic information is considered. First, we present some basic concepts, then we combine the MSM operator with linguistic neutrosophic environment and develop a sequence of linguistic neutrosophic MSM operators which are the linguistic neutrosophic Maclaurin symmetric mean (LNMSM) operator, the weighted linguistic neutrosophic Maclaurin symmetric mean (WLNMSM) operator, linguistic neutrosophic dual Maclaurin symmetric mean (LNDMSM) operator, and the weighted linguistic neutrosophic dual Maclaurin symmetric mean (WLNDMSM) operator. We look into some features of them such as monotonicity, boundedness, and idempotency and then discuss some special situations of these operators. A new idea based on the WLNMSM operator is proposed to solve an MAGDM problem where evaluation information is composed of LNNs. It is worth mentioning that the weight information of the decision-makers (DMs) and the attributes are completely unknown. In conclusion, a comparison analysis is performed with the existing methods. The developed method is based on both the WLNMSM operator which considers the interrelationships among any number of input arguments and LNNs which is a combination of the neutrosophic numbers, linguistic variables. At the same time, it also has the advantages of mentioned components. So, it enables preventing the loss or distortion of the original decision information in the decision-making process.

Şahin, Rıdvan; Küçük, Gökçe Dilek

Simplified neutrosophic set is a convenient tool proposed for dealing with complex problems; it is effective in providing more data for decision-making process. In this study, we develop a simplified neutrosophic ordered weighted distance operator which combines the neutrosophic distance measures and the ordered weighted average distance in the same formulation. It is a new handy aggregation operator that considers the situations where the input data are represented in simplified neutrosophic numbers, and it also contains diverse distance aggregation operators. Parameterized families of simplified neutrosophic ordered weighted distance operator are handled. Moreover, we establish a new neutrosophic group decision-making method based on the simplified neutrosophic ordered weighted distance operator, which has 2 extended approaches for determining the weights of decision makers and decision attributes in decision-making process, respectively. Finally, an illustrative example demonstrates the application of the proposed method. The effectiveness and advantages of the proposed method are shown by the comparative analysis with existing relative methods.

Küçük, Gökçe Dilek; Şahin, Rıdvan

The simplified neutrosophic set (SNS) is a useful model to describe the indeterminacy information which widely exists in the real world. In this paper, we develop a multicriteria decision-making (MCDM) method under simplified neutrosophic environment in which the information about weights of criteria is completely unknown, and the decision criterion values take the form of simplified neutrosophic numbers (SNNs). In order to determine the weighting vector of the criteria, we establish an optimization model based on the basic ideal of the traditional gray relational analysis (GRA) method. By solving this model, we get a simple and exact formula which can be used to determine the criterion weights. Moreover, we utilize the dice similarity measure to determine the similarity measures between each alternative decision and the related ideal decisions. Then, based on the traditional GRA method and the technique for order preference by similarity to ideal solution (TOPSIS), some calculation steps are presented for solving a simplified neutrosophic multicriteria decision-making problem with completely unknown weight information. To avoid information loss, this model does not use the aggregation process of decision information. Comparisons of the suggested methodology with other methods are also made. Finally, a numerical example and an experimental analysis are proposed to illustrate the application of the proposed model.