The structure of q-rung orthopair fuzzy sets (q-ROFSs) is a generalization of fuzzy sets (FSs), intuitionistic FSs (IFSs), and Pythagorean FSs (PFSs). The notion of q-ROFSs has the proficiency of coping with uncertainty without any restrictions. In addition, the structure of q-ROFSs can effectively cope with the situations involving dual opinions without any restrictions, instead of dealing with only single opinion or dual opinions under certain restrictions. In clustering problems, the correlation coefficients are worthwhile because they provide the degree of similarity or correlation between two elements or sets. The theme of this study is to formulate the correlation coefficients for q-ROFSs that are basically the generalization of correlation coefficients of IFSs and PFSs. Moreover, an application of these correlation coefficients to a clustering problem is proposed. Also, an analysis of the outcomes is carried out. Furthermore, a comparison is carried out among the correlation coefficients for q-ROFSs and the existing ones. Finally, the downsides of the existing works and benefits of the correlation coefficients for q-ROFSs are discussed.

The concept of fuzzy graph (FG) and its generalized forms has been developed to cope with several real-life problems having some sort of imprecision like networking problems, decision making, shortest path problems, and so on. This paper is based on some developments in generalization of FG theory to deal with situation where imprecision is characterized by four types of membership grades. A novel concept of T-spherical fuzzy graph (TSFG) is proposed as a common generalization of FG, intuitionistic fuzzy graph (IFG), and picture fuzzy graph (PFG) based on the recently introduced concept of T-spherical fuzzy set (TSFS). The significance and novelty of proposed concept is elaborated with the help of some examples, graphical analysis, and results. Some graph theoretic terms are defined and their properties are studied. Specially, the famous Dijkstra algorithm is proposed in the environment of TSFGs and is applied to solve a shortest path problem. The comparative analysis of the proposed concept and existing theory is made. In addition, the advantages of the proposed work are discussed over the existing tools.

Technology is quickly evolving and becoming part of our lives. Life has become better and easier due to the technologies. Although it has lots of benefits, it also brings serious risks and threats, known as cyberattacks, which are neutralized by cybersecurities. Since spherical fuzzy sets (SFSs) and interval-valued SFS (IVSFS) are an excellent tool in coping with uncertainty and fuzziness, the current study discusses the idea of spherical cubic FSs (SCFSs). These sets are characterized by three mappings known as membership degree, neutral degree, and nonmembership degree. Each of these degrees is spherical cubic fuzzy numbers (SCFNs) such that the summation of their squares does not exceed one. The score function and accuracy function are presented for the comparison of SCFNs. Moreover, the spherical cubic fuzzy weighted geometric (SCFWG) operators and SCF ordered weighted geometric (SCFOWG) operators are established for determining the distance between two SCFNs. Furthermore, some operational rules of the proposed operators are analyzed and multiattribute decision-making (MADM) approach based on these operators is presented. These methods are applied to make the best decision on the basis of risks factors as a numerical illustration. Additionally, the comparison of the proposed method with the existing methods is carried out; since the proposed methods and operators are the generalizations of existing methods, they provide more general, exact, and accurate results. Finally, for the legitimacy, practicality, and usefulness of the decision-making processes, a detailed illustration is given.

Neutrosophic set (NS) is an extensively used framework whenever the imprecision and uncertainty of an event is described based on three possible aspects. The association, neutral, and nonassociation degrees are the three unique aspects of an NS. More importantly, these degrees are independent which is a great plus point. On the contrary, neutrosophic graphs (NGs) and single-valued NGs (SVNGs) are applicable to deal with events that contain bulks of information. However, the concept of degrees in NGs is a handful tool for solving the problems of decision-making (DM), pattern recognition, social network, and communication network. This manuscript develops various forms of edge irregular SVNG (EISVNG), highly edge irregular SVNG (HEISVNG), strongly (EISVNG), strongly (ETISVNG), and edge irregularity on a cycle and a path in SVNGs. All these novel notions are supported by definitions, theorems, mathematical proofs, and illustrative examples. Moreover, two types of DM problems are modelled using the proposed framework. Furthermore, the computational processes are used to confirm the validity of the proposed graphs. Furthermore, the results approve that the decision-making problems can be addressed by the edge irregular neutrosophic graphical structures. In addition, the comparison between proposed and the existing methodologies is carried out.