In this paper, we investigate the concepts of the weighted average operator (Α_W) and weighted geometric operator (ς_W) on neutrosophic cubic sets (NCSs) to aggregate the neutrosophic cubic information. Moreover, on the basis of Α_W and ς_W and certain functions, including score, certainty, and accuracy, we develop our algorithm to multiple-criteria decision-making in NCSs, in which the assessment standards of another possibility on the characteristics yield the technique of neutrosophic cubic numbers (NCNs) to choose the greatest necessary ones. Finally, we provide a mathematical example of the technique to determine the application and usefulness of the established technique.

In this paper, we define the concept of generalized cubic subsemigroups (ideals) of a semigroup and investigate some of its related properties. In particular, we introduce the concept of $(\in _{(\widetilde{\gamma }_{1},\gamma _{2}) },\in _{(\widetil

Cubic sets are the very useful generalization of fuzzy sets where one is allowed to extend the output through a subinterval of $[0,1]$ and a number from $[0,1]$ . Generalized cubic sets generalized the cubic sets with the help of cubic point. On the other hand Soft sets were proved to be very effective tool for handling imprecision. Semigroups are the associative structures have many applications in the theory of Automata. In this paper we blend the idea of cubic sets, generalized cubic sets and semigroups with the soft sets in order to develop a generalized approach namely generalized cubic soft sets in semigroups. As the ideal theory play a fundamental role in algebraic structures through this we can make a quotient structures. So we apply the idea of neutrosophic cubic soft sets in a very particular class of semigroups namely weakly regular semigroups and characterize it through different types of ideals. By using generalized cubic soft sets we define different types of generalized cubic soft ideals in semigroups through three different ways. We discuss a relationship between the generalized cubic soft ideals and characteristic functions and cubic level sets after providing some basic operations. We discuss two different lattice structures in semigroups and show that in the case when a semigroup is regular both structures coincides with each other. We characterize right weakly regular semigroups using different types of generalized cubic soft ideals. In this characterization we use some classical results as without them we cannot prove the inter relationship between a weakly regular semigroups and generalized cubic soft ideals. This generalization leads us to a new research direction in algebraic structures and in decision making theory.

In this paper, triangular cubic hesitant fuzzy Einstein weighted averaging (TCHFEWA) operator, triangular cubic hesitant fuzzy Einstein ordered weighted averaging (TCHFEOWA) operator and triangular cubic hesitant fuzzy Einstein hybrid weighted averaging (TCHFEHWA) operator are proposed. An approach to multiple attribute group decision making with linguistic information is developed based on the TCHFEWA and the TCHFEHWA operators. Furthermore, we establish various properties of these operators and derive the relationship between the proposed operators and the existing aggregation operators. Finally, a numerical example is provided to demonstrate the application of the established approach.

The notion of a neutrosophic positive implicative $\mathcal{N}$ -ideal in $BCK$ -algebras is introduced, and several properties are investigated. Relations between a neutrosophic $\mathcal{N}$ -ideal and a neutrosophic positive implicative $\mathcal{N}$ -ideal are discussed. Characterizations of a neutrosophic positive implicative $\mathcal{N}$ -ideal are considered. Conditions for a neutrosophic $\mathcal{N}$ -ideal to be a neutrosophic positive implicative $\mathcal{N}$ -ideal are provided. An extension property of a neutrosophic positive implicative $\mathcal{N}$ -ideal based on the negative indeterminacy membership function is discussed.