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.

Eroğlu, Hasan; Şahin, Ridvan

In this study, a new score and distance function which provides more accurate results than the studies in the literature and considers the decision maker’s cognition has been proposed. In order to show the effects of the new score function coefficients on neutrosophic numbers, a new representation named “4D Plot” has been proposed. VIKOR (Vlse Kriterijumska Optimizacija Kompromisno Resenje which means multicriteria optimization and compromise solution in Serbian) method, which is based on the creation of a conciliatory solution within the framework of alternatives and evaluation criteria, provides highly effective results in multiple criteria decision-making problems. Neutrosophic numbers play an active role in facilitating the decision-making process in many studies. In this context, extension of the classical VIKOR method is introduced in detail in this study. The framework of the extended neutrosophic VIKOR method has been established. The proposed method has been applied to the renewable energy alternative selection problem in Turkey and compared with different methods and different scenarios. It has been shown that the proposed method gives more effective and accurate results. Furthermore, the sensitivity and accuracy of the study are enhanced by a sensitivity analysis. We have extended the classical VIKOR method for SVN numbers with a newly generalized score function and a distance measure. As a novel and newly presentation named “The 4D Plot” has been developed and applied in this paper to SVN numbers for presenting the effect of the new score function. The renewable energy alternative selection was made in Turkey with the proposed method by the opinions of the experts and the ranking of the alternatives was obtained. A sensitivity analysis has been made to show the accuracy and validity of the study. With the proposed distance measure and score function, it is shown that more accurate results can be found in multiple criteria decision-making problems. The model will provide solutions for many soft computing problems such as engineering and economy by finding more effective and accurate results in the neutrosophic number space according to the preference of decision makers. As a future work, the presented functions and framework can be adapted to different MCDM problems.