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Öğe Correlation coefficient of single-valued neutrosophic hesitant fuzzy sets and its applications in decision making(Springer London, 2017) Şahin R.; Liu P.As a combination of the hesitant fuzzy set (HFS) and the single-valued neutrosophic set (SVNS), the single-valued neutrosophic hesitant fuzzy set (SVNHFS) is an important concept to handle uncertain and vague information existing in real life, which consists of three membership functions including hesitancy, as the truth-hesitancy membership function, the indeterminacy-hesitancy membership function and the falsity-hesitancy membership function, and encompasses the fuzzy set, intuitionistic fuzzy set (IFS), HFS, dual hesitant fuzzy set (DHFS) and SVNS. Correlation and correlation coefficient have been applied widely in many research domains and practical fields. This paper, motivated by the idea of correlation coefficients derived for HFSs, IFSs, DHFSs and SVNSs, focuses on the correlation and correlation coefficient of SVNHFSs and investigates their some basic properties in detail. By using the weighted correlation coefficient information between each alternative and the optimal alternative, a decision-making method is established to handling the single-valued neutrosophic hesitant fuzzy information. Finally, an effective example is used to demonstrate the validity and applicability of the proposed approach in decision making, and the relationship between the each existing method and the developed method is given as a comparison study. © 2016, The Natural Computing Applications Forum.Öğe Maximizing deviation method for neutrosophic multiple attribute decision making with incomplete weight information(Springer-Verlag London Ltd, 2016) Şahin R.; Liu P.This paper develops a method for solving the multiple attribute decision-making problems with the single-valued neutrosophic information or interval neutrosophic information. We first propose two discrimination functions referred to as score function and accuracy function for ranking the neutrosophic numbers. An optimization model to determine the attribute weights that are partly known is established based on the maximizing deviation method. For the special situations where the information about attribute weights is completely unknown, we propose another optimization model. A practical and useful formula which can be used to determine the attribute weights is obtained by solving a proposed nonlinear optimization problem. To aggregate the neutrosophic information corresponding to each alternative, we utilize the neutrosophic weighted averaging operators which are the single-valued neutrosophic weighted averaging operator and the interval neutrosophic weighted averaging operator. Thus, we can determine the order of alternatives and choose the most desirable one(s) based on the score function and accuracy function. Finally, some illustrative examples are presented to verify the proposed approach and to present its effectiveness and practicality. © 2015, The Natural Computing Applications Forum.Öğe Possibility-induced simplified neutrosophic aggregation operators and their application to multi-criteria group decision-making(Taylor and Francis Ltd., 2017) Şahin R.; Liu P.Simplified neutrosophic set (SNS) is an appropriate tool used to express the incompleteness, indeterminacy and uncertainty of the evaluation objects in decision-making process. In this study, we define the concept of possibility SNS including two types of information such as the neutrosophic performance provided from the evaluation objects and its possibility degree using a value ranging from zero to one. Then by extending the existing neutrosophic information, aggregation models for SNSs that cannot be used effectively to fusion the two different information described above, we propose two novel neutrosophic aggregation operators considering possibility, which are named as a possibility-induced simplified neutrosophic weighted arithmetic averaging operator and possibility-induced simplified neutrosophic weighted geometric averaging operator, and discuss their properties. Moreover, we develop a useful method based on the proposed aggregation operators for solving a multi-criteria group decision-making problem with the possibility simplified neutrosophic information, in which the weights of decision-makers and decision criteria are calculated based on entropy measure. Finally, a practical example is utilised to show the practicality and effectiveness of the proposed method. © 2016 Informa UK Limited, trading as Taylor & Francis Group.Öğe Some approaches to multi criteria decision making based on exponential operations of simplified neutrosophic numbers(IOS Press, 2017) Şahin R.; Liu P.Simplified neutrosophic set (SNS) is a powerful tool that attracts the attention of many scholars in dealing with uncertainty and vagueness. A SNS is based on a combination of simplified neutrosophic numbers (SNNs), whose its basic components are characterized by a truth-membership degree, an indeterminacy-membership degree and a falsity-membership degree of an object in evaluation data. Aggregation operators used to synthesize simplified neutrosophic information is commonly not very effective in case where the criteria weights provided by decision makers are in form of SNNs rather than exact real numbers. In this paper, we propose two new operational laws in which the bases are positive real numbers and interval numbers, respectively and the exponents are SNNs, and discuss some of their desired properties. Then we apply them to derive two weighted exponential aggregation operators, such as the simplified neutrosophic weighted exponential aggregation (SNWEA) operator and dual simplified neutrosophic weighted exponential aggregation (DSNWEA) operator. Additionally, two approaches for multi-criteria decision-making (MCDM) problems under the neutrosophic weight data are explored by applying these aggregation operators. At the end of the study, a convenient example is provided to demonstrate the availability and effectiveness of the proposed methods. © 2017 IOS Press and the authors. All rights reserved.
