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As a generalization of fuzzy sets and intuitionistic fuzzy sets, neutrosophic sets, and their combinations have been developed to represent uncertain, imprecise, incomplete, and inconsistent information existing in the real world. A neutrosophic set has the potential to be a general framework for uncertainty analysis in various spectra. On the other hand, the idea of Fermatean neutrosophic sets (FNSs) is the hybrid model of Fermatean fuzzy sets and neutrosophic sets, developed to enable the analytical management of ambiguous data from relatively typical real-world decision-making scenarios. In this work, we develop an algorithm to compare the Fermatean neutrosophic set and the neutrosophic set, Fermatean Neutrosophic Weighted Arithmetic Mean (FNWAM) and Fermatean Neutrosophic Weighted Geometric Mean (FNWGM) operators as an accuracy function in addition to the conventional aggregating operators are designed. Further, the CODAS technique for Multiple Attribute Group Decision Making (MAGDM) problems according to the defined operators is proposed. Additionally, to make a clear understanding of the presented study, a university faculty selection problem is studied to illustrate the proposed methodology. Finally, the results of the above two sets prove the authenticity of this study. [ABSTRACT FROM AUTHOR]

The Neutrosophic Set (N s e t) represents the uncertainty in data with fuzzy attributes beyond true and false values independently. The problem arises when the summation of true (T r) , false (F a) , and indeterminacy I n values crosses the membership value of one, that is, T r + I n + F a < 1 . It becomes more crucial during decision-making processes like medical diagnoses or any data sets where T r + I n + F a < 1 . To achieve this goal, the F N s e t is recently introduced. This study employs the Interval-Valued Fermatean Neutrosophic Set ( I V F N s e t ) as its chosen framework to address instances of partial ignorance within the domains of truth, falsehood, or uncertainty. This selection stands out due to its unique approach to managing such complexities within multi-decision processes when compared to alternative methodologies. Furthermore, the proposed method reduces the propensity for information loss often encountered in other techniques. IVFNS excels at preserving intricate relationships between variables even when dealing with incomplete or vague information. In the present work, we introduce the I V F N s e t , which deals with partial ignorance in true, false, or uncertain regions independently for multi-decision processes. The I V F N s e t contains the interval-valued T r m e m b e r s h i p value, I n m e m b e r s h i p value, and F a m e m b e r s h i p for knowledge representation. The algebraic properties and set theory between the interval-valued F N s e t have also been presented with an illustrative example. [ABSTRACT FROM AUTHOR]

Yager et. al. defined a q-rung orthopair fuzzy sets as a new general class of Pythagorean fuzzy set in which the sum of the qth power of the support for and support against is bonded by one. Tapan et. al. extended the concept of intuitionistic fuzzy sets as 3-rung orthopair fuzzy sets or Fermatean fuzzy sets (FFSs). Later C. Antony et. al. introduced the concept of Fermatean Neutrosophic Sets. In this work, we define Fermatean neutrosophic graphs and present some operations on Fermatean neutrosophic graphs. Further, we introduce the concepts of regular Fermatean neutrosophic graphs, strong Fermatean neutrosophic graphs, Cartesian, Composition, Lexicographic product of Fermatean neutrosophic graphs. Finally, we give the applications of Fermatean neutrosophic graphs. [ABSTRACT FROM AUTHOR]

Recently, the intelligent traffic control system and its uncertainty analysis are considered one of the hot spots for utilizing the available techniques. It became more essential when the automatic car, electric vehicle, and other smart cars have introduced the transportation. To control the traffic accident and smooth road services an intelligent traffic control system required. It will be also useful in decreasing the time, reaction time, and efficiency of traffic. However, the problem arises while characterization of true, false or uncertain regions of traffic flow and its future approximation. To deal with this issue some available mathematical technique for traffic flow using rough set, fuzzy rough set, and its extension with the neutrosophic set is discussed in this paper. Some of the papers related to graphical visualization of traffic flow is also discussed for further improvement. The rough set theory can be useful for dealing the uncertain, incomplete, and indeterminate data set. Hence, the hybridization of the neutrosophic set and rough can be considered one of the efficient tools for intelligent traffic control and its approximation via automatic red, green and yellow lights. This paper tried to provide an overview of each available technique to solve the traffic problem. It is hoped that the proposed study will be helpful for several researchers working on traffic flow, traffic accident diagnosis, and its hybridization as future research. [ABSTRACT FROM AUTHOR]

Neutrosophic set and neutrosophic logic theory are renowned theories to deal with complex, not clearly explained and uncertain real life problems, in which classical fuzzy sets/models may fail to model properly. This paper introduces an algorithm for finding minimum spanning tree (MST) of an undirected neutrosophic weighted connected graph (abbr. UNWCG) where the arc/edge lengths are represented by a single valued neutrosophic numbers. To build the MST of UNWCG, a new algorithm based on matrix approach has been introduced. The proposed algorithm is compared to other existing methods and finally a numerical example is provided. [ABSTRACT FROM AUTHOR]

The notion of interval valued neutrosophic sets is a generalization of fuzzy sets, intuitionistic fuzzy sets, interval valued fuzzy sets, interval valued intuitionstic fuzzy sets and single valued neutrosophic sets. We apply for the first time to graph theory the concept of interval valued neutrosophic sets, an instance of neutrosophic sets. We introduce certain types of interval valued neutrosophc graphs (IVNG) and investigate some of their properties with proofs and examples. [ABSTRACT FROM AUTHOR]

Fuzzy graph theory plays an important role in the study of the symmetry and asymmetry properties of fuzzy graphs. With this in mind, in this paper, we introduce new neutrosophic graphs called complex neutrosophic graphs of type 1 (abbr. CNG1). We then present a matrix representation for it and study some properties of this new concept. The concept of CNG1 is an extension of the generalized fuzzy graphs of type 1 (GFG1) and generalized single-valued neutrosophic graphs of type 1 (GSVNG1). The utility of the CNG1 introduced here are applied to a multi-attribute decision making problem related to Internet server selection. [ABSTRACT FROM AUTHOR]