In this paper, we define projection and bidirectional projection measures between interval rough neutrosophic sets and prove their basic properties. Then two new multi attribute decision making strategies are proposed based on interval rough neutrosophic projection and bidirectional projection measures respectively. Then the proposed methods are applied for solving multi attribute decision making problems. Finally, a numerical example is solved to show the feasibility, applicability and effectiveness of the proposed strategies.

In this paper, we define correlation coefficient measure between any two rough neutrosophic sets. We also prove some of its basic properties.. We develop a new multiple attribute group decision making method based on the proposed correlation coefficient measure. An illustrative example of medical diagnosis is solved to demonstrate the applicability and effecriveness of the proposed method.

In this paper, multi attribute decision making problem based on grey relational analysis in neutrosophic cubic set environment is investigated. In the decision making situation, the attribute weights are considered as single valued neutrosophic sets. The neutrosophic weights are converted into crisp weights. Both positve and negative GRA coefficients, and weighted GRA coefficients are determined. Hamming distances for weighted GRA coefficients and standard (ideal) GRA coefficients are determined. The relative closeness coefficients are derived in order to rank the alternatives. The (...) relative closeness coefficients are designed in ascending order. Finally, a numerical example is solved to demonstrate the applicability of the proposed approach. (shrink)

In this paper, the cosine similarity measure of neutrosophic refined (multi-) sets is proposed and its properties are studied. The concept of this cosine similarity measure of neutrosophic refined sets is the extension of improved cosine similarity measure of single valued neutrosophic. Finally, using this cosine similarity measure of neutrosophic refined set, the application of medical diagnosis is presented.

The author makes an introduction to non-standard analysis, then extends the dialectics to “neutrosophy” – which became a new branch of philosophy. This new concept helps in generalizing the intuitionistic, paraconsistent, dialetheism, fuzzy logic to “neutrosophic logic” – which is the first logic that comprises paradoxes and distinguishes between relative and absolute truth. Similarly, the fuzzy set is generalized to “neutrosophic set”. Also, the classical and imprecise probabilities are generalized to “neutrosophic probability”.

In this paper, the sine, cosine and cotangent similarity measures of interval rough neutrosophic sets is proposed. Some properties of the proposed measures are discussed. We have proposed multi attribute decision making approaches based on proposed similarity measures. To demonstrate the applicability, a numerical example is solved.

The purpose of this study is to propose new similarity measures namely rough variational coefficient similarity measure under the rough neutrosophic environment. The weighted rough variational coefficient similarity measure has been also defined. The weighted rough variational coefficient similarity measures between the rough ideal alternative and each alternative are xxxxx calculated to find the best alternative. The ranking order of all the alternatives can be determined by using the numerical values of similarity measures. Finally, an illustrative example has been provided (...) to show the effectiveness and validity of the proposed approach. Comparisons of decision results of existing rough similarity measures have been provided. (shrink)

This paper is devoted to present Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method for multi-attribute group decision making under rough neutrosophic environment. The concept of rough neutrosophic set is a powerful mathematical tool to deal with uncertainty, indeterminacy and inconsistency. In this paper, a new approach for multi-attribute group decision making problems is proposed by extending the TOPSIS method under rough neutrosophic environment. Rough neutrosophic set is characterized by the upper and lower approximation operators and the (...) pair of neutrosophic sets that are characterized by truth-membership degree, indeterminacy membership degree, and falsity membership degree. In the decision situation, ratings of alternatives with respect to each attribute are characterized by rough neutrosophic sets that reflect the decision makers’ opinion. Rough neutrosophic weighted averaging operator has been used to aggregate the individual decision maker’s opinion into group opinion for rating the importance of attributes and alternatives. Finally, a numerical example has been provided to demonstrate the applicability and effectiveness of the proposed approach. (shrink)

The notion of neutrosophic cubic set is originated from the hybridization of the concept of neutrosophic set and interval valued neutrosophic set. We define similarity measure for neutrosophic cubic sets and prove some of its basic properties. We present a new multi criteria group decision making method with linguistic variables in neutrosophic cubic set environment. Finally, we present a numerical example to demonstrate the usefulness and applicability of the proposed method.

This Paper combines interval- valued neutrouphic sets and rough sets. It studies roughness in interval- valued neutrosophic sets and some of its properties. Finally we propose a Hamming distance between lower and upper approximations of interval valued neutrosophic sets.

Cross entropy measure is one of the best way to calculate the divergence of any variable from the priori one variable. We define a new cross entropy measure under interval neutrosophic set environment.

On the basis of the combination of single-valued neutrosophic sets and hesitant fuzzy sets, this article proposes a single-valued neutrosophic hesitant fuzzy set as a further generalization of the concepts of fuzzy set, intuitionistic fuzzy set, single-valued neutrosophic set, hesitant fuzzy set, and dual hesitant fuzzy set. Then, we introduce the basic operational relations and cosine measure function of SVNHFSs. Also, we develop a single-valued neutrosophic hesitant fuzzy weighted averaging operator and a single-valued neutrosophic hesitant fuzzy weighted geometric operator and (...) investigate their properties. Furthermore, a multiple-attribute decision-making method is established on the basis of the SVNHFWA and SVNHFWG operators and the cosine measure under a single-valued neutrosophic hesitant fuzzy environment. Finally, an illustrative example of investment alternatives is given to demonstrate the application and effectiveness of the developed approach. (shrink)