The operations of t‐norm (TN) and t‐conorm (TCN), developed by Dombi, are generally known as Dombi operations, which have an advantage of flexibility within the working behavior of parameter. In this paper, we use Dombi operations to construct a few Q‐rung orthopair fuzzy Dombi aggregation operators: Q‐rung orthopair fuzzy Dombi weighted average operator, Q‐rung orthopair fuzzy Dombi order weighted average operator, Q‐rung orthopair fuzzy Dombi hybrid weighted average operator, Q‐rung orthopair fuzzy Dombi weighted geometric operator, Q‐rung orthopair fuzzy Dombi order weighted geometric operator, and Q‐rung orthopair fuzzy Dombi hybrid weighted geometric operator. The different features of these proposed operators are reviewed. At that point, we have used these operators to build up a model to solve the multiple‐attribute decision making issues under Q‐rung orthopair fuzzy environment. Ultimately, a realistic instance is stated to substantiate the created model and to exhibit its applicability and viability.

More general form of "quasi-coincident with" relation (q) is introduced, and related properties are investigated. The notions of (∈, ∈ ∨ q δ 0 )-fuzzy subgroups, q δ 0 -level sets and ∈ ∨ q δ 0 -level sets are introduced, and related results are investigated. Relations between an (∈, ∈)-fuzzy subgroup and an (∈, ∈ ∨ q δ 0 )-fuzzy subgroup are discussed, and characterizations of (∈, ∈ ∨ q δ 0 )-fuzzy subgroups are displayed by using level sets and ∈ ∨ q δ 0 -level sets. The concepts of ∈ ∨ q δ 0 -admissible fuzzy sets, admissible (∈, ∈ ∨ q δ 0 )-fuzzy subgroups and δ-characteristic fuzzy sets are introduced. Using these notions, characterizations of admissible (∈, ∈ ∨ q δ 0 )-fuzzy subgroups and admissible subgroups are considered.2010 Mathematics Subject Classification. 20N25, 03E72. Keywords. (∈, ∈ ∨ q δ 0 )-fuzzy subgroup, q δ 0 -level set, ∈ ∨ q δ 0 -admissible fuzzy set.

No abstract

Social networks are represented using graph theory. In this case, individuals in a social network are assumed as nodes. Sometimes institutions or groups are also assumed as nodes. Institutions and such groups are assumed as cluster nodes that contain individuals or simple nodes. Hypergraphs have hyperedges that include more than one node. In this study, cluster hypergraphs are introduced to generalize the concept of hypergraphs, where cluster nodes are allowed. Sometimes competitions in the real world are done as groups. Cluster hypergraphs are used to represent such kinds of competitions. Competition cluster hypergraphs of semidirected graphs (a special type of mixed graphs called semidirected graphs, where the directed and undirected edges both are allowed) are introduced, and related properties are discussed. To define competition cluster hypergraphs, a few properties of semidirected graphs are established. Some associated terms on semidirected graphs are studied. At last, a numerical application is illustrated.

A Fermatean fuzzy set is a more powerful tool to deal with uncertainties in the given information as compared to intuitionistic fuzzy set and Pythagorean fuzzy set and has energetic applications in decision-making. Aggregation operators are very helpful for assessing the given alternatives in the decision-making process, and their purpose is to integrate all the given individual evaluation values into a unified form. In this research article, some new aggregation operators are proposed under the Fermatean fuzzy set environment. Some deficiencies of the existing operators are discussed, and then, new operational law, by considering the interaction between the membership degree and nonmembership degree, is discussed to reduce the drawbacks of existing theories. Based on Hamacher’s norm operations, new averaging operators, namely, Fermatean fuzzy Hamacher interactive weighted averaging, Fermatean fuzzy Hamacher interactive ordered weighted averaging, and Fermatean fuzzy Hamacher interactive hybrid weighted averaging operators, are introduced. Some interesting properties related to these operators are also presented. To get the optimal alternative, a multiattribute group decision-making method has been given under proposed operators. Furthermore, we have explicated the comparison analysis between the proposed and existing theories for the exactness and validity of the proposed work.

Theoretical concepts of graphs are highly utilized by computer science applications. Especially in research areas of computer science such as data mining, image segmentation, clustering, image capturing and networking. The cubic graphs are more flexible and compatible than fuzzy graphs due to the fact that they have many applications in networks. In this paper, we define the direct product, strong product, and degree of a vertex in cubic graphs and investigate some of their properties. Likewise, we introduce the notion of complete cubic graphs and present some properties of self complementary cubic graphs. Finally, We present fuzzy cubic organizational model as an example of cubic digraph in decision support system.

Operations of cubic soft sets including “AND” operation and “OR” operation based on P-orders and R-orders are introduced and some related properties are investigated. An example is presented to show that the R-union of two internal cubic soft sets might not be internal. A sufficient condition is provided, which ensure that the R-union of two internal cubic soft sets is also internal. Moreover, some properties of cubic soft subalgebras of BCK/BCI-algebras based on a given parameter are discussed.

No abstract