The shortest path problem in interval valued trapezoidal and triangular neutrosophic environment
The shortest path problem in interval valued trapezoidal and triangular neutrosophic environment

Author: Said Broumi

Publisher: Infinite Study

Published:

Total Pages: 14

ISBN-13:

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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.

Shortest Path On Interval-Valued Triangular Neutrosophic Fuzzy Graphs With Application
Shortest Path On Interval-Valued Triangular Neutrosophic Fuzzy Graphs With Application

Author: K. Kalaiarasi

Publisher: Infinite Study

Published:

Total Pages: 14

ISBN-13:

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In this article, inaugurate interval-valued triangular neutrosophic fuzzy graph (IVTNFG) of SPP, which is drew on three-sided numbers and IVTNFG. Hear a genuine application is given an illustrative model for IVTNFG. Additionally Shortest way is determined for this model. This present Dijkstra's Algorithm briefest way was checked through Python Jupiter Notebook (adaptation) programming.

Shortest Path Solution of Trapezoidal Fuzzy Neutrosophic Graph Based on Circle‐Breaking Algorithm
Shortest Path Solution of Trapezoidal Fuzzy Neutrosophic Graph Based on Circle‐Breaking Algorithm

Author: Lehua Yang

Publisher: Infinite Study

Published:

Total Pages: 22

ISBN-13:

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The shortest path problem is a topic of increasing interest in various scientific fields. The damage to roads and bridges caused by disasters makes traffic routes that can be accurately expressed become indeterminate. A neutrosophic set is a collection of the truth membership, indeterminacy membership, and falsity membership of the constituent elements. It has a symmetric form and indeterminacy membership is their axis of symmetry.

Research on the Shortest Path Solution Method of Interval Valued Neutrosophic Graphs Based on the Ant Colony Algorithm
Research on the Shortest Path Solution Method of Interval Valued Neutrosophic Graphs Based on the Ant Colony Algorithm

Author: Lehua Yang

Publisher: Infinite Study

Published:

Total Pages: 17

ISBN-13:

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The shortest path problem (SPP) is considerably important in several fields. After typhoons, the resulting damage leads to uncertainty regarding the path weight that can be expressed accurately. A neutrosophic set is a collection of the truth membership, indeterminacy membership, and falsity membership degrees of the elements. In an uncertain environment, neutrosophic numbers can express the edge distance more effectively.

Neutrosophic Shortest Path Problem (NSPP) in a Directed Multigraph
Neutrosophic Shortest Path Problem (NSPP) in a Directed Multigraph

Author: Siddhartha Sankar Biswas

Publisher: Infinite Study

Published:

Total Pages: 12

ISBN-13:

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One of the important non-linear data structures in Computer Science is graph. Most of the real life network, be it a road transportation network, or airlines network or a communication network etc., cannot be exactly transformed into a graph model, but into a Multigraphs model. The Multigraph is a topological generalization of the graph where multiple links (or edges/arcs) mayexist between two nodes unlike in graph.

Neutrosophic Set in Medical Image Analysis
Neutrosophic Set in Medical Image Analysis

Author: Yanhui Guo

Publisher: Academic Press

Published: 2019-08-08

Total Pages: 372

ISBN-13: 0128181494

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Neutrosophic Set in Medical Image Analysis gives an understanding of the concepts of NS, along with knowledge on how to gather, interpret, analyze and handle medical images using NS methods. It presents the latest cutting-edge research that gives insight into neutrosophic set's novel techniques, strategies and challenges, showing how it can be used in biomedical diagnoses systems. The neutrosophic set (NS), which is a generalization of fuzzy set, offers the prospect of overcoming the restrictions of fuzzy-based approaches to medical image analysis. - Introduces the mathematical model and concepts of neutrosophic theory and methods - Highlights the different techniques of neutrosophic theory, focusing on applying the neutrosophic set in image analysis to support computer- aided diagnosis (CAD) systems, including approaches from soft computing and machine learning - Shows how NS techniques can be applied to medical image denoising, segmentation and classification - Provides challenges and future directions in neutrosophic set based medical image analysis

Neutrosophic Sets and Systems, vol. 50/2022
Neutrosophic Sets and Systems, vol. 50/2022

Author: Florentin Smarandache

Publisher: Infinite Study

Published: 2022-06-01

Total Pages: 674

ISBN-13:

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“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc. Neutrosophy is a new branch of philosophy that studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. This theory considers every notion or idea together with its opposite or negation and with their spectrum of neutralities in between them (i.e. notions or ideas supporting neither nor ). The and ideas together are referred to as . Neutrosophy is a generalization of Hegel's dialectics (the last one is based on and only). According to this theory every idea tends to be neutralized and balanced by and ideas - as a state of equilibrium. In a classical way , , are disjoint two by two. But, since in many cases the borders between notions are vague, imprecise, Sorites, it is possible that , , (and of course) have common parts two by two, or even all three of them as well. Neutrosophic Set and Neutrosophic Logic are generalizations of the fuzzy set and respectively fuzzy logic (especially of intuitionistic fuzzy set and respectively intuitionistic fuzzy logic).

Measures of Probabilistic Neutrosophic Hesitant Fuzzy Sets and the Application in Reducing Unnecessary Evaluation Processes
Measures of Probabilistic Neutrosophic Hesitant Fuzzy Sets and the Application in Reducing Unnecessary Evaluation Processes

Author: Songtao Shao

Publisher: Infinite Study

Published:

Total Pages: 23

ISBN-13:

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Distance measure and similarity measure have been applied to various multi-criteria decision-making environments, like talent selections, fault diagnoses and so on. Some improved distance and similarity measures have been proposed by some researchers. However, hesitancy is reflected in all aspects of life, thus the hesitant information needs to be considered in measures. Then, it can effectively avoid the loss of fuzzy information. However, regarding fuzzy information, it only reflects the subjective factor. Obviously, this is a shortcoming thatwill result in an inaccurate decision conclusion. Thus, based on the definition of a probabilistic neutrosophic hesitant fuzzy set (PNHFS), as an extended theory of fuzzy set, the basic definition of distance, similarity and entropy measures of PNHFS are established. Next, the interconnection among the distance, similarity and entropy measures are studied. Simultaneously, a novel measure model is established based on the PNHFSs. In addition, the new measure model is compared by some existed measures. Finally, we display their applicability concerning the investment problems, which can be utilized to avoid redundant evaluation processes.

Shortest Path with Normalized Single Valued Trapezoidal Neutrosophic Numbers
Shortest Path with Normalized Single Valued Trapezoidal Neutrosophic Numbers

Author: D. Selvi

Publisher: Infinite Study

Published:

Total Pages: 12

ISBN-13:

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In this paper we studied the network with Single Valued Trapezoidal Neutrosophic (SVTN) numbers. We propose an algorithm by transforming single valued trapezoidal neutrosophic (SVTN) numbersinto normalized single valued trapezoidal neutrosophic (NSVTN) numbers and obtain an optimal value of the short path problem using defuzzification and scoring function. Finally, a numerical example is used to illustrate the efficiency of the proposed approach.

Neutrosophic Graph Theory and Algorithms
Neutrosophic Graph Theory and Algorithms

Author: Smarandache, Florentin

Publisher: IGI Global

Published: 2019-10-25

Total Pages: 406

ISBN-13: 1799813150

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Graph theory is a specific concept that has numerous applications throughout many industries. Despite the advancement of this technique, graph theory can still yield ambiguous and imprecise results. In order to cut down on these indeterminate factors, neutrosophic logic has emerged as an applicable solution that is gaining significant attention in solving many real-life decision-making problems that involve uncertainty, impreciseness, vagueness, incompleteness, inconsistency, and indeterminacy. However, empirical research on this specific graph set is lacking. Neutrosophic Graph Theory and Algorithms is a collection of innovative research on the methods and applications of neutrosophic sets and logic within various fields including systems analysis, economics, and transportation. While highlighting topics including linear programming, decision-making methods, and homomorphism, this book is ideally designed for programmers, researchers, data scientists, mathematicians, designers, educators, researchers, academicians, and students seeking current research on the various methods and applications of graph theory.