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Graph labelling is the assignment of labels to the edges, vertices, or both. The issue of limiting the spread of non-interfering frequencies allotted to radio transmitters serves as the motivation for the research on labelling graphs according to different limitations. However, compared to classical models, fuzzy labelling models provide the system with greater accuracy, adaptability, and compatibility. The definition of the neutrosophic fuzzy magic labelling graph and a detailed discussion of its properties using numerical examples for the path, cycle, and star graphs in a neutrosophic environment are presented in this study. The proposed work has also been used in decision-making situations to choose the optimal subject combinations based on student interests for the best academic performance. In order to demonstrate the validity of the suggested work, a comparative analysis with the current methodology has also been conducted. [ABSTRACT FROM AUTHOR]

Aggregation operators can be used to combine and synthesise a finite number of numerical values into a single numerical value. Many areas, including decision-making, expert systems, risk analysis, and image processing, rely heavily on aggregating functions. In real-world situations, the neutrosophic set can manage the uncertainties associated with information from any decision-making challenge, whereas the fuzzy set and intuitionistic set cannot. The term "bipolarity" refers to the propensity of the human mind to weigh pros and drawbacks when thinking through decisions. Triangular norms are aggregation operators in a variety of fields, including fuzzy set theory, probability and statistics, and decision sciences. Thus, the individual assessments in this paper's study of and approach to multi-criteria decision-making (MCDM) problems that use bipolar neutrosophic numbers as the individual evaluations. Frank operational laws of bipolar neutrosophic numbers, bipolar neutrosophic Frank weighted geometric aggregation (BNFWGA) and the bipolar neutrosophic frank ordered weighted geometric aggregation (BNFOWGA) operators have been developed with its desirable properties. Additionally, the suggested aggregation operators have been used in the selection of bridges. The outcomes demonstrate the applicability and validity of the suggested approach. Comparative analysis has been performed using the current approach. [ABSTRACT FROM AUTHOR]

Neutrosophic set plays a vital role in dealing with indeterminacy in real-world problems. Differential equations represent the relation between a function and its derivatives and its applications have importance in both pedagogical and real life. In this paper, neutrosophic differential equation is proposed and solved using bipolar trapezoidal neutrosophic number and applied the concept in predicting bacterial reproduction over separate bodies with graphical representation using MATLAB. Also, comparative analysis is done with the existing method to prove the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we present a maple programming code that helps useres and scientific researchers to input single valued neutrosophic matrices, checks whether inputted matrix is single valued neutrosohic matrix, finds the complement of a single valued neutrosophic matrix, calculates score matrix, accuracy matrix and certainty matrix, finds the union and intersection of two single valued neutrosophic matrices, finds addition and product of two single valued neutrosophic matrices, also finds transpose of single valued neutrosophic matrix. This code is very important and useful in decision making problems that depend on single valued neutrosophic data. [ABSTRACT FROM AUTHOR]

Neutrosophical probability is concerned with inequitable and defective topics and processes. This is a subset of Neutrosophic measures that includes a prediction of an event (as opposed to indeterminacy) as well as a prediction of some unpredictability. When there is no such thing as a non-stochastic occurrence, the Neutrosophic probability is the probability of determining a stochastic process. It is a generalisation of classical probability, which states that the probability of correctly predicting an occurrence is zero. Until now, neutrosophic probability distributions have been derived directly from conventional statistical distributions, with fewer contributions to the determination of the for statistical distribution. We introduced the Poission distribution as a limiting case of the Binomial distribution for the first time in this study, and we also proposed Neutrosophic Exponential Distribution and Uniform Distribution for the first time. With numerical examples, the validity and soundness of the proposed notions were also tested. [ABSTRACT FROM AUTHOR]

Neutrosophic set is the universality of the fuzzy and intuitionistic fuzzy sets. If the value of grade of membership contains uncertainty then that problems or situations can be dealt by type-2 fuzzy and intuitionistic fuzzy sets. It is not possible to work in enigmatic and uncertain situations and indeterminate situations as well. This present study introduces, graphical representation of type-2 neutrosophic set (T2NS) to deal the level of uncertainty in truth, indeterminate and false part of the information from footprint of uncertainty (FOU). This graphical representation helps as a learning strategy of type-2 neutrosophic sets. Also discussed the advantage of T2NS. [ABSTRACT FROM AUTHOR]

There are various mathematical tools available to measure the level of accuracy such as Crisp, Fuzzy, Intuitionistic fuzzy sets and Neutosophic set. Further, Plithogenic set is a generalization of these four sets. This paper aims to test whether Plithogenic aggregation operation is more effective than other sets in its accuracy, while decision making. In order to obtain a better accuracy, the Plithogenic aggregation operation such as Fuzzy set [FS], Intuitionistic fuzzy set [IFS] and Neutrosophic set [NS] used tnorm and tconorm. An illustration is examined in this paper to prove the result of better accuracy using plithogenic aggregation operators in decision making. [ABSTRACT FROM AUTHOR]

Human psychological behavior is always uncertain in nature with the truth, indeterminacy and falsity of the information and hence neutrosophic logic is able to deal with this kind of real world problems as it resembles human's attitude very closely. In this paper, age group analysis and time (day or night) analysis have been carried out using interval valued neutrosophic sets. Further, the impact of the present work is presented. [ABSTRACT FROM AUTHOR]

Membership function (MF) plays a key role for getting an output of a system and hence it influences system's performance directly. Therefore choosing a MF is an essential task in fuzzy logic and neutrosophic logic as well. Uncertainty is usually represented by MFs. In this paper, a novel Matlab code is derived for trapezoidal neutrosophic function and the validity of the proposed code is proved with illustrative graphical representation. [ABSTRACT FROM AUTHOR]

An advantage of dealing indeterminacy is possible only with Neutrosophic Sets. Graph theory plays a vital role in the field of networking. If uncertainty exist in the set of vertices and edge then that can be dealt by fuzzy graphs in any application and using Neutrosophic Graph uncertainty of the problems can be completely dealt with the concept of indeterminacy. In this paper, Dombi Interval Valued Neutrosophic Graph has been proposed and Cartesian product and composition of the proposed graphs have been derived. The validity of the derived results have been proved with the numerical example. This paper expose the use of Dombi triangular norms in the area of Neutrosophic graph theory. Advantages and limitations has been discussed for Crisp, Fuzzy, Type-2 Fuzzy, Neutrosophic Set, Interval Neutrosophic Set, Neutrosophic Graph and Interval Neutrosophic Graph. [ABSTRACT FROM AUTHOR]

This paper is mainly concerned with the existence and uniqueness of solutions for fractional integrodifferential equations with interval impulses and infinite delay. The results are obtained by using Schauder's fixed point theorem. An example illustrating our main result is given. [ABSTRACT FROM AUTHOR]