N-Cubic q-Rung Orthopair Fuzzy Sets: Analysis of the Use of Mobile App in the Education Sector

This study analyzes the description to examine the results of a new study and create the technique and also demonstrate the effectiveness of this technique. In this ever-changing world, students are increasingly encouraged to use mobile phones primarily to learn for educational purposes. The learning process is continuous and the goal has now been achieved. It has been replaced by online learning. Due to mobile phones as well as the many feature-oriented applications, students can study at their own place and use the application to spend their time understanding, because everything is accessible with a single click. To carry on the study we applied mobile applications for online education system. Now, because the traditional method is taken into consideration, it is normal to carry a bag full of books and copies and immerse yourself in the tradition of learning to write. However, it has been found that not all students learn when he takes notes. Therefore, we must make sure that the student focuses only on one thing at a time. To continue the research, we apply the N-cubic structure to q-rung orthopair fuzzy sets in multi-attribute group decision-making problems. This structure solves the problems of multi-attribute group decision-making techniques more generally.


Introduction
Decision-making is an empathic process that allows the selection of alternatives from a set of possible attributes. In decision-making problems the data were ambiguous and uncertain and the representation of data is no longer in real number. For this purpose many researchers developed different theories to handle such type of data. Among these researchers, Zadeh [1] developed the theme of fuzzy set (FS) theory that could determine uncertainty and vagueness in classic sets which are based on only two values logic 0 and 1. In 1975, Zadeh [2][3][4] further expanded his ideas to interval-valued fuzzy sets (IVFS). Atanassov [5,6] later came up with the idea that using intuitionistic fuzzy sets (IFS) to assist with the significance of the membership value as well as the nonmembership value. Wang et al. [7] defined some interval-valued intuitionistic fuzzy aggregation operators with basic operations and properties. Intuitionistic fuzzy set was generalized to the Pythagorean fuzzy set (PFS) [8] which described the value of membership and nonmembership with the condition that the square sum is less or equal to 1. PFS was generalized to q-rung orthopair fuzzy set [9]. In 2018 Ali [10] defined a new type of q-rung orthopair fuzzy sets where the domain of the function defining a q-ROF set is the region made up of orbits. To deal with the decision information, Liu and Wang [11] proposed the q-rung orthopair fuzzy weighted averaging operator and the q-rung orthopair fuzzy weighted geometric operator. Wei et al. [12] presented q-rung orthopair fuzzy Maclaurin symmetric mean operators and their applications to potential evaluation of emerging technology commercialization. Many researchers [13,14] used the different versions of q-rung orthopair fuzzy sets in different field such as q-rung orthopair fuzzy soft sets, q-rung orthopair fuzzy hypersoft sets, and their operators. In 2012, Jun et al. [15] combined FS and IVFS and developed the theme of cubic set. In decision-making theory aggregation operators is an important component. e conflicting criteria are included in the multi-attribute decision-making (MADM) task, and the conflicting criteria are aggregated to solve the problem [13,16]. Most aggregation operators treat criteria on an individual basis; they do not take into account how criteria interact with each other or with common criteria. Kaur and Garg [17,18] developed cubic intuitionistic fuzzy aggregation operators, which includes two components at the same time. One component provides the degree of membership in the form of an interval value for cubic intuitionistic fuzzy numbers (CIFNs), as well as the second component, gives the degree of nonmembership in the form of fuzzy values. Abbas et al. [19] have described a modified version in CIFS that is known informally as cubic Pythagorean fuzzy sets (CPFS). Zang et al. [20] generalized CPFS into cubic q-rung orthopair fuzzy sets (CqROFSs).
is allows decisionmakers to explain their ideas better in the context of a fuzzy environment. In 2009, Jun et al. [21] defined negativevalued functions as well as the N-structure. is paper is on BCK/BCI algebra as well as subtraction algebra. Rashid et al. [22] used the concept of the N-structure and developed the theme of N-cubic sets, aggregate operators, and other concepts related to it. In 2020, Petrovic and Kankaras [23] developed a hybridized IT2FS-DEMATEL-AHP-TOPSIS multicriteria decision-making approach for the selection and evaluation of criteria for determination of air traffic control radar position. Agarwal et al. [24] discussed the development of management tools and techniques in decision-making for policy makers which are based on scientific evidence. Ali et al. [25] developed Einstein geometric aggregation operators using complex intervalvalued pythagorean fuzzy set with application in green supplier chain management. We are currently employing the N-structure concept for q-ROFSs. e Cq-ROFS is a database that describes IVqROFS and q-ROFS in a way that is related to uncertainty in the information. In order to demonstrate how this structure might be used in decisionmaking, we shall examine issues relating to the N-structure of cubic q-rung orthopair fuzzy sets in this article. Although this study can manage decision-making more efficiently than fuzzy sets, using it manually is not simple. erefore, we must create computer programming in order to overcome these constraints. By merging the N-structure with cubic q-ROF sets, this structure more specifically overcame the uncertainty issues. N-cubic q-rung orthopair fuzzy sets can effectively capture expert evaluation data and minimize fuzziness in decision-making outcomes.

Materials and Methods
In this section we recall some basic materials and methods.
Definition 1 (see [6]). Let G ≠ ∅ be universal set, then q-ROFS H be defined as where ℧ H (r � ) and Ω H (r � ) are a mapping from G to [0, 1], also satisfy the condition as and where q ≥ 1 for all g∈G and represent the membership degree and the nonmembership degree to set H.
Definition 2 (see [6]). Let G ≠ ∅ be universal set, then (IVq-ROFS) H be defined as where ℧ H (g) and Ω H (g) are a mapping from G to [0, 1], and also satisfy the condition as and where q ≥ 1 for all g∈G and represent the membership degree and the nonmembership degree to set H.
Definition 3 (see [10]). Let X be the collection of some elements. A cubic-q-rung orthopair fuzzy set is represented as is an Intervalvalued-q-rung orthopair fuzzy set and ϑ(x) is a q-rung orthopair fuzzy set.
and ϑ(x) � (℧, Ω) and it is known as the cubic-q-rung orthopair fuzzy set number.
with the condition for all x ∈ X, otherwise we called it an external NCq-ROF set.
Using the aforementioned theorem, we obtain And, □ Case 1. e assertion that the recommended NCq-ROFHM operator transforms into the NCq-ROF basic HM operator if j � k�(1/2).

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NCq is means that it is also referred to as the N-cubic Q-rung orthopair fuzzy generalized interconnected square mean.
It is sometimes referred to as the N-cubic q-rung s fuzzy generalized mean. Computational Intelligence and Neuroscience Case 5. If j ⟶ 0, k ⟶ 0, then the existing NCq-ROFHM change into Note that we can get a variety of orthopair fuzzy sets by varying the value of the parameter q. As an illustration, the N-cubic Pythagorean fuzzy set is renovated by NCq-ROFHM if j � 1 and k � 1. In MADM situations, different characteristics typically have significant advantages. us, it appears that the NCq-ROFHM operator is indifferent with this characteristic. e weighted version of the NCq-ROFHM operator is defined as follows to address this issue: Definition 11. In this case, N λ � (A N λ , B N λ )(λ � 1, 2, . . . , n) be the NCq-ROFN family, the weight vector of NCq-ROFNs is indicated by j ≥ 0, k ≥ 0, j + k ≥ 0, and w � (w 1 , w 2 , . . . , w n ) for all w λ ∈ [0, 1] and n λ�1 w � 1. en NCq-ROFWHM: 1, 2, . . . , n) be the collection of NCq-ROFNs, j ≥ 0, k ≥ 0 and j + k ≥ 0, and w � (w 1 , w 2 , . . . , w n ) represents the weight vector of NCq-ROFNs, w λ ∈ [0, 1] and n λ�1 w � 1. en, NCq-ROFNs are also included in the resulting equation (38) as e relationship between the structure of the two attributes can be established through the HM operator. Each attribute is linked with other attributes of the HM operator. However, when it comes to decision-making issues, this condition is often not being met. To prevent the separation of characteristics we can use different partitions to solve decisionmaking problems because we remember the structure of attribute relationships. ere is no link between attributes.
Computational Intelligence and Neuroscience When they are divided by two partitions, the same attributes present in partitions have a connection to each other. With the typical HM operator, the partitions do not solve these kinds of issues so we now provide the N-cubic q-rung orthopair fuzzy power Hamy mean operator with the ability to let us know the issue. e condition given above can be mathematically explained as: where |F i | denotes the cardinality of partitions F i and g i�1 |F i | � n. By using above information, NCQ-ROFPHM operator is defined as

then equation (41) is used to generate a consequent equation that is likewise an NCq-ROFN, as shown by
Where (43) Be collection of NCq-ROFNs with g different subset F λ (λ � 1, 2, . . . , n). Consequently, the NCq-ROFPHM operators have the following characteristics.

. en we get resultant equation by using equation (59) that is also a NCq-ROFNs given by
Computational Intelligence and Neuroscience ,

Multi Attribute Group Decision-Making Method as an Application
In this section we will use NCq-ROFWHM and NCq-ROFWPHM operators to examine MAGDM problems, and to show their applicability with the help of NCq-ROFNs. Let Using the expert's preference, an NCq-ROF decision matrix is created as T λ � (N λ iı ) m×n . Consider that there are 'g' divisions of the set F 1 , F 2 , F 3 , . . . . . . , F g and that there is a specified connection structure between the features while keeping in mind the natural relationship structure. ere is no link between qualities from different partitions and those from the same partition. e established operators are then used to address these decision-making (DM) difficulties. Algorithm steps are provided by Step 1: To normalize the decision matrix and obtain the benefit and cost-type data.
converting the value of the cost-type attributes first to the value of the benefit-type attributes, and then Step 2: To aggregate all the normalized data.

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Computational Intelligence and Neuroscience where Computational Intelligence and Neuroscience     Table  9: For collective NCq-ROFDM of M.
Step 3: Assume a division form among the attributes to arrive at the collective assessment values.
Step e two subsets of the five qualities are separated based on how they relate to one another fundamentally. F 1 � C 1 , C 3 , C 5 , F 1 � C 2 , C 4 . Data in the form of NCq-ROFNs must be submitted by experts for examination. e expert assessment statistics are displayed in Tables 1-4, and E i � (i � 1, 2, 3, 4).
Step 1: Given that C 3 is a cost-type attribute, we can normalize the decision-making data using equation (62). e normalized data is displayed in Tables 5-8. Step 2: To obtain the entire decision matrix, use . Additionally, we set the parameters j � 1, k � 1, and q � 3 to be true. is MAGDM seeks to identify the best choice. e complete NCq-ROF decision matrix M is shown in Table 9. Hence A 3 > A 1 > A 4 > A 2 and A 3 is best alternative. e Influence of the parameter Values on the Ranking Results. In the following section, we will investigate how the parameters q, j, and k impact the findings of the alternatives. Put j � 1, k � 1 and q � 3 in the previous computing technique for our convenience and without losing generality. From Table 10, it is clear that the ranking outcomes for the scenarios q � 4, 5, 7, 8 and A 3 > A 1 > A 4 > A 2 are identical. us the ranking outcomes are shown as in Figure 1, and finally, we can say that the other top options remain the same when the parameter's value changes.   22 Computational Intelligence and Neuroscience ese are different from the results obtained for j � 0 and k � 1 having ranking results A 4 > A 1 > A 2 > A 3 . As a result, it is possible to obtain varied ranking results by varying the values of the parameters j and k. If one parameter is fixed and the other is changed, the score and ranking results may change, as shown in Table 11. We can observe that the values of the parameters j and k affect the ranking outcomes, as shown in Figure 2.

Conclusion
In this study, we focus on the structure of N-cubic q-rung orthopair fuzzy sets. e score function under R-order and the comparison rule for two N-cubic q-rung orthopair fuzzy sets also define some aggregation operators, i.e., N-cubic q-rung orthopair fuzzy Hamy mean operator, N-cubic q-rung orthopair fuzzy weighted Hamy mean operator, N-cubic q-rung orthopair fuzzy power Hamy mean operator, and N-cubic q-rung orthopair fuzzy power weighted Hamy mean operator. N-structure can enhance decision-making performance. e recently discovered N-cubic q-ROFSs, which combine NQ-ROFSs and NIVqRFSs into a single structure, allow decision-makers greater space to work on multi-attribute group decisionmaking problems. As a result of the debate, we have discussed specific instances of the operators and created a method for solving MAGDM problems using NCq-ROFNs. In this study we analyze the use of mobile app in the education sector. Further research, problem-solving, and decision-making are possible to solve, and other operators may be able to be created through this method. In future someone can apply the N-cubic q-rung orthopair fuzzy sets in different decision-making technique.

Data Availability
No data were used to support this study.

Conflicts of Interest
e authors declare that there are no conflicts of interest regarding the publication of this article. Computational Intelligence and Neuroscience 23