The concept of (∈, ∈ ∨ )-fuzzy hyperideal of an ordered LA-semihypergroup is introduced by the ordered fuzzy points, and related properties are investigated. We study the relations between different (∈, ∈ ∨ )-fuzzy hyperideal of an ordered LA-semihypergroup. Furthermore, we study some results on homomorphisms of (∈, ∈ ∨ )-fuzzy hyperideals.

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In this paper, we study the hyperideals of ordered LA-semihypergroups in terms of (∈, ∈∨q k)fuzzy sets which is a new generalization of fuzzy hyperideals. We study the relation between different (∈, ∈ ∨ q k)-fuzzy hyperideals in regular ordered LA-semihypergroups. Finally the upper parts of the (∈, ∈ ∨ q k)-fuzzy LA-subsemihypergroup (resp., left hyperideal, right hyperideal, hyperideal, interior hyperideal, bi-hyperideal) is defined and some related results are provided. Keywords Ordered LA-semihypergroups • Fuzzy hyperideals • (∈, ∈ ∨ q k)-Fuzzy hyperideals Mathematics Subject Classification 20N20 1 Introduction Hyperstructure theory was given by a French mathematician Marty (1934). Since then, several authors continued their researches in this direction. Some basic definitions and theorems about Communicated by Marcos Eduardo Valle.

Graphs allow us to study the different patterns of inside the data by making a mental image. The aim of this paper is to develop a neutrosophic cubic graph structure, which is the extension of neutrosophic cubic graphs. As neutrosophic cubic graphs are defined for one set of edges between vertices, while neutrosophic cubic graphs structures are defined for more than one set of edges. Further, we defined some basic operations, such as Cartesian product, composition, union, join, cross product, strong product, and lexicographic product of two neutrosophic cubic graph structures. Several types of other interesting properties of neutrosophic cubic graph structures are discussed in this paper. Finally, a decisionmaking algorithm based on the idea of neutrosophic cubic graph structures is constructed. The proposed decision-making algorithm is applied in a decision-making problem to check the validity.

<abstract> <p>The current study proposes the idea of the N-cubic Pythagorean fuzzy set with their basic arithmetic operations to aggregate these sets. We define the score and accuracy functions for the comparison purpose. Finally, we discuss Chang's extent analysis of AHP under the environment of the N-cubic Pythagorean fuzzy set using the idea of triangular N-cubic Pythagorean fuzzy set. As an application, we discuss the reason for the downfall of international airlines using the developed approach.</p> </abstract>