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An elongation of the novel intuitionistic fuzzy set is a picture fuzzy set theory. The demonstration of this has been used to deal with the abstinence criteria in a decision-making problem. The uncertainty in nature occurs sometimes in real-world problems and amidst them, the prominent one is the shortest path problem (SPP) solving. In the last few years, one of the best algorithms on the network for finding SPP is Bellman–Ford. Due to uncertainty in the decision-making process, it becomes difficult for decision-makers for communicating their point of view and judgment with certainty. We conceive of SPP in this contribution via Bellman's algorithm (BA) for a network with trapezoidal picture fuzzy numbers (TPFNs). We introduce a new algorithm to stand the shortest picture fuzzy path between each pair of nodes. A TPFN is considered for the length of all edges. A numerical example for the validation of the presented algorithm has also been proposed. There has also been relative research with existing techniques showing the benefits of the new algorithm. [ABSTRACT FROM AUTHOR]

Traffic congestion is a major problem in the last few decades. Though the Government is taking various measures like installing more traffic signals, constructing fly-overs, one-ways, etc., the problem could not be addressed effectively on the heavily congested areas. The increasing number of vehicles, the dynamic population of traffic, the narrowness of roads and the absence of alternative roads or other routes are the major obstacles to reduce traffic congestion. Researchers of various streams have been working on predicting traffic volume to solve this problem. In this paper, a new method named Intuitionistic Fuzzy Grey-Markov Model(IFGMM) is introduced, which is an extension of Grey-Markov to Intuitionistic fuzzy set. The model is distinctive when compared with other models as it has a high level of accuracy performance. The forecasting result of this model is almost in proximity with the actual result of the traffic volume. In addition, the relative errors shown in this method are lesser than that of other models, due to its prediction accuracy is higher. Since the data collected in this method are taken from a heavily congested road from a metropolitan city, the proposed approach will be suitable for any congested area of the world. [ABSTRACT FROM AUTHOR]

Type-2 fuzzy sets (T2FSs) can deal with higher modeling and uncertainties which exist in the real-world application, specifically in the control systems. Particularly the climate changes are always uncertain and thus, the type-2 fuzzy controller is an effective system to handle those situations. Polyhouse is a methodology used to cultivate the plants. It breaks the seasonal hurdle of the formulation and it is also suitable for the conflictive climate conditions. Controlling and directing internal parameters of the polyhouse play an essential role in the growth of the plant. Among those, humidity is an important element when one deals with the growth of the plant in polyhouse. It affects the weather, as well as the global change of the climate and hence, the inner climate of the polyhouse will be disturbed. In this paper, operational laws for triangular interval type-2 fuzzy numbers and derived triangular interval type-2 weighted geometric (TIT2WG) operator with their desired mathematical properties using Dombi triangular norms. Also, humidity control is analyzed using interval type-2 fuzzy controller (IT2FC) with the use of derived aggregation operator which is the aim of the paper. Further stability of the system has been analyzed by applying four different defuzzification methods and the method is recommended which gives a better response. [ABSTRACT FROM AUTHOR]

Decision-making is an essential task in Science and Engineering. Since most of the real-world problems have uncertainty in nature, making the decision is challengeable one for the decision makers. Soft set has the advantage of free from the deficiency of the parameterization tools of existing theories, namely probability, fuzzy theory and the theory of rough sets. Linguistic terms mean different things to different people, so variability in expert's acceptance degree is possible. Here usage of type-1 fuzzy leads to noisy and uncertain, and the parameters also may be noisy and hence type-2 fuzzy sets may be used to address the mentioned issues. Therefore, a triangular interval type-2 fuzzy soft set has been considered in the present work by combining triangular interval type-2 fuzzy set and soft set. In this paper, a triangular interval type-2 fuzzy soft weighted arithmetic operator (TIT2FSWA) has been proposed with its desired mathematical properties; also applied the proposed methodology in a decision-making problem for profit analysis. Further comparative analysis has been made with the existing methods to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Planar graph is a special type in crisp as well as in fuzzy graphs. In fuzzy planar graphs, the planarity value is the amount of planarity of the crossed fuzzy edges, so that the intersection of fuzzy edges are possible in fuzzy graphs as compared to the planar graphs in crisp. Generally, the fuzzy planar graphs are depicted in the plane surface. In this paper, the embedding of fuzzy graphs are discussed in the surfaces like sphere and m-torus. Moreover, definition of fuzzy planar triangulation, straight-line, and piecewise embedding are also stated for planar embedding. Some of the effective definitions and theorems are illustrated with examples. Theorems like Euler's formula for plane and sphere surfaces are proved and formulated for fuzzy planar graphs. [ABSTRACT FROM AUTHOR]

In the last decade, concealed by uncertain atmosphere, many algorithms have been studied deeply to workout the shortest path problem. In this paper, we compared the shortest path problem with various existing algorithms. Finally, we concluded the best algorithm for certain environment. [ABSTRACT FROM AUTHOR]

Real-life decision-making problem has been demonstrated to cover the indeterminacy through single valued neutrosophic set. It is the extension of interval valued neutrosophic set. Most of the problems of real life involve some sort of uncertainty in it among which, one of the famous problem is finding a shortest path of the network. In this paper, a new score function is proposed for interval valued neutrosophic numbers and SPP is solved using interval valued neutrosophic numbers. Additionally, novel algorithms are proposed to find the neutrosophic shortest path by considering interval valued neutrosophic number, trapezoidal and triangular interval valued neutrosophic numbers for the length of the path in a network with illustrative example. Further, comparative analysis has been done for the proposed algorithm with the existing method with the shortcoming and advantage of the proposed method and it shows the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

An elongation of the single-valued neutrosophic set is an interval-valued neutrosophic set. It has been demonstrated to deal indeterminacy in a decision-making problem. Real-world problems have some kind of uncertainty in nature and among them; one of the influential problems is solving the shortest path problem (SPP) in interconnections. In this contribution, we consider SPP through Bellman's algorithm for a network using interval-valued neutrosophic numbers (IVNNs). We proposed a novel algorithm to obtain the neutrosophic shortest path between each pair of nodes. Length of all the edges is accredited an IVNN. Moreover, for the validation of the proposed algorithm, a numerical example has been offered. Also, a comparative analysis has been done with the existing methods which exhibit the advantages of the new algorithm. [ABSTRACT FROM AUTHOR]

Graph theory is a developing field which has many advancements and developments in real-life applications. Although graph theory has rapid growth in modeling real-life issues, some vague details in real-life problems are hard to picture using the usual graph. Fuzzy graph theory is known for its applications in modeling the human thinking, which has the same structure as graph theory. The concept of fuzzy graphs extended to Pythagorean fuzzy sets depends on real-time situations. The purpose of interval-valued Pythagorean neutrosophic sets through which the values of the degree (membership, non-membership and neutral) can be taken from the intervals instead of the numbers so that it provides more adequate information about the uncertainty than traditional sets. This motivates us to introduce interval-valued Pythagorean neutrosophic sets in applications. The proposed investigation also leads to study the interval-valued Pythagorean neutrosophic graphs (IVPNGs) and their arithmetic operations. In addition, the concept of regular, strong, product, support strong, effective balanced IVPNGs are introduced for aggregating the IVPNGs information and analysed with suitable examples. Further, a methodology for successful curriculum design is examined to illuminate the adequacy and feasibility of the developed IVPNG. [ABSTRACT FROM AUTHOR]