The main aim of this paper is to introduce a neurosophic subsethood measure for single valued neutrosophic sets. For this purpose, we first introduce a system of axioms for subsethood measure of single valued neutrosophic sets. Then we give a simple subsethood measure based to distance measure. Finally, to show effectiveness of intended subsethood measure, an application is presented in multicriteria decision making problem and results obtained are discussed. Though having a simple measure for calculation, the subsethood measure presents a new approach to deal with neutrosophic information.

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 truthhesitancy 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.

The process of multiple criteria decision making (MCDM) is of determining the best choice among all of the probable alternatives. The problem of supplier selection on which decision maker has usually vague and imprecise knowledge is a typical example of multi criteria group decision-making problem. The conventional crisp techniques has not much effective for solving MCDM problems because of imprecise or fuzziness nature of the linguistic assessments. To find the exact values for MCDM problems is both difficult and impossible in more cases in real world. So, it is more reasonable to consider the values of alternatives according to the criteria as single valued neutrosophic sets (SVNS). This paper deal with the technique for order preference by similarity to ideal solution (TOPSIS) approach and extend the TOPSIS method to MCDM problem with single valued neutrosophic information. The value of each alternative and the weight of each criterion are characterized by single valued neutrosophic numbers. Here, the importance of criteria and alternatives is identified by aggregating individual opinions of decision makers (DMs) via single valued neutrosophic weighted averaging (IFWA) operator. The proposed method is, easy use, precise and practical for solving MCDM problem with single valued neutrosophic data. Finally, to show the applicability of the developed method, a numerical experiment for supplier choice is given as an application of single valued neutrosophic TOPSIS method at end of this paper.

Due to the technological developments around the world, the amount of information that researchers work on increases continuously. This information density contains incomplete and uncertain data that cannot be fully expressed with crisp numbers. Fuzzy sets, intuitionistic fuzzy sets, and neutrosophic sets are useful tools to manage such information, but these concepts use a symmetrical and uniform scale to express data, whereas real‐life problems contain nonsymmetrical and non‐uniform information. Intuitionistic multiplicative sets (IMSs) are effective tools for dealing with these real‐life problems. However, IMSs cannot handle real‐life problems completely because indeterminate information depends on membership and non‐membership information of IMSs, which is a restriction for decision makers and also for decision problems. To overcome this limitation, this paper generalizes the IMSs by using simplified neutrosophic set and introduces a novel approach that is called simplified neutrosophic multiplicative sets (SNMSs). Firstly, we define SNMS, show their set‐based operations, and then give a description of simplified neutrosophic multiplicative numbers (SNMNs). Based on SNMNs, we develop two simplified neutrosophic multiplicative aggregation operators on SNMNs that are called simplified neutrosophic multiplicative weighted arithmetic average operator and simplified neutrosophic multiplicative weighted geometric average operator. Furthermore, we define some simplified neutrosophic multiplicative distance measures. Finally, using a model based on water‐filling algorithm for determining criteria weights, we give a numerical example to demonstrate the effectiveness of the introduced concept with the proposed simplified neutrosophic multiplicative simplified neutrosophic multiplicative‐TODIM method.

Molodtsov [35] initiated the soft set theory, which can be used as a generic mathematical tool for dealing with uncertainty. Maji [30] defined the concept of neutrosophic soft set which is based on a combination of the neutrosophic set and soft set models. In this paper, we give the notion of neutrosophic soft set with a new style and present some algebraic properties. We define several distance measures between neutrosophic soft sets and give an axiomatic definition of neutrosophic entropy for a neutrosophic soft set. To find the most ideal alternatives from all possible alternatives, we propose a method based on similarity measure. Thus we can rank all possible alternatives. Finally, the proposed similarity measure is applied to a multicriteria decision making problem.