Recently, many researchers have studied some types of sets which are extension of fuzzy sets widely. Some of them are interval‐valued fuzzy set, intuitionistic fuzzy sets, type‐2 fuzzy sets, type‐n fuzzy sets, hesitant fuzzy sets (HFSs), dual fuzzy sets, and neutrosophic sets. In solving decision‐making problems, these sets have more advantages than classical sets. In this paper, we introduce a new concept called dual type‐2 hesitant fuzzy sets (DT2HFSs) by combining concepts of the dual HFS and the type‐2 fuzzy set. Then we give correlation coefficient formulas and weighted correlation coefficient formulas between two DT2HFSs and obtain some results related to the proposed correlation coefficient formulas. On the basis of the proposed correlation coefficient formulas, we develop the clustering method under DT2HF environment. Finally, we present an application of the proposed method for a problem to illustrate the process and validate the proposed method.

The single-valued neutrosophic set plays a crucial role to handle indeterminant and inconsistent information during decision making process. In recent research, a development in neutrosophic theory is emerged, called single-valued neutrosophic matrices, are used to address uncertainties. The beauty of single-valued neutrosophic matrices is that the utilizing of several fruitful operations in decision making. In this paper, some novel operations on neutrosophic matrices of are introduced, that is, type-1 product \((\tilde \odot )\), type-2 product \((\tilde \otimes )\) and minus \((\tilde \ominus )\) between two single-valued neutrosophic matrices. Also, we introduced complement, transpose, upper and lower α −level matrices of single-valued neutrosophic matrices and discussed related properties. Furthermore, we propose a multi-criteria group decision making method based on these new operations, and give an application of the proposed method in a real life problem. Finally, we compare proposed method in this paper with proposed methods previously.

Complex fuzzy (CF) sets (CFSs) have a significant role in modelling the problems involving two-dimensional information. Recently, the extensions of CFSs have gained the attention of researchers studying decision-making methods. The complex T-spherical fuzzy set (CTSFS) is an extension of the CFSs introduced in the last times. In this paper, we introduce the Dombi operations on CTSFSs. Based on Dombi operators, we define some aggregation operators, including complex T-spherical Dombi fuzzy weighted arithmetic averaging (CTSDFWAA) operator, complex T-spherical Dombi fuzzy weighted geometric averaging (CTSDFWGA) operator, complex T-spherical Dombi fuzzy ordered weighted arithmetic averaging (CTSDFOWAA) operator, complex T-spherical Dombi fuzzy ordered weighted geometric averaging (CTSDFOWGA) operator, and we obtain some of their properties. In addition, we develop a multi-criteria decision-making (MCDM) method under the CTSF environment and present an algorithm for the proposed method. To show the process of the proposed method, we present an example related to diagnosing the COVID-19. Besides this, we present a sensitivity analysis to reveal the advantages and restrictions of our method.

In this paper, the existing definition of the group-based generalized intuitionistic fuzzy soft set is clarified and redefined by merging intuitionistic fuzzy soft set over the set of alternatives and a group of intuitionistic fuzzy sets on parameters. In this prospect, two new subsets of the group-based generalized intuitionistic fuzzy soft set are proposed and several operations are contemplated. The two new aggregation operators called generalized group-based weighted averaging and generalized group-based weighted geometric operator are introduced. The related properties of proposed operators are discussed. The recent research is emerging on multi-attribute decision making methods based on soft sets, intuitionistic fuzzy soft sets, and generalized intuitionistic fuzzy soft sets. An algorithm is structured and two case studies of multi-attribute decision makings are considered using proposed operators. Further, we provide the comparison and advantages of the proposed method, which give superiorities over recent major existing methods.

Neutrosophic set theory based on neutrosophy, which is a branch of philosophy, is an important tool for dealing with uncertainty and inconsistency data. Concept of single-valued neutrosophic set is defined as a generalization of the concept of single-valued neutrosophic set, which is useful to model some engineering applications. In this study, the concept of single-valued neutrosophic refined soft set is defined as an extension of single-valued neutrosophic refined set. Also, set theoretical operations between two single-valued neutrosophic refined soft sets are defined and some basic properties of these operations are investigated. Furthermore, two methods to calculate correlation coefficient between two single-valued neutrosophic refined soft sets are proposed, and a clustering analysis application of one of proposed methods is given.