In this paper we study and develop the Neutrosophic Triplet Topology (NTT) that was recently introduced by Sahin et al. Like classical topology, the NTT tells how the elements of a set relate spatially to each other in a more comprehensive way using the idea of Neutrosophic Triplet Sets.
This ninth volume of Collected Papers includes 87 papers comprising 982 pages on Neutrosophic Theory and its applications in Algebra, written between 2014-2022 by the author alone or in collaboration with the following 81 co-authors (alphabetically ordered) from 19 countries: E.O. Adeleke, A.A.A. Agboola, Ahmed B. Al-Nafee, Ahmed Mostafa Khalil, Akbar Rezaei, S.A. Akinleye, Ali Hassan, Mumtaz Ali, Rajab Ali Borzooei , Assia Bakali, Cenap Özel, Victor Christianto, Chunxin Bo, Rakhal Das, Bijan Davvaz, R. Dhavaseelan, B. Elavarasan, Fahad Alsharari, T. Gharibah, Hina Gulzar, Hashem Bordbar, Le Hoang Son, Emmanuel Ilojide, Tèmítópé Gbóláhàn Jaíyéolá, M. Karthika, Ilanthenral Kandasamy, W.B. Vasantha Kandasamy, Huma Khan, Madad Khan, Mohsin Khan, Hee Sik Kim, Seon Jeong Kim, Valeri Kromov, R. M. Latif, Madeleine Al-Tahan, Mehmat Ali Ozturk, Minghao Hu, S. Mirvakili, Mohammad Abobala, Mohammad Hamidi, Mohammed Abdel-Sattar, Mohammed A. Al Shumrani, Mohamed Talea, Muhammad Akram, Muhammad Aslam, Muhammad Aslam Malik, Muhammad Gulistan, Muhammad Shabir, G. Muhiuddin, Memudu Olaposi Olatinwo, Osman Anis, Choonkil Park, M. Parimala, Ping Li, K. Porselvi, D. Preethi, S. Rajareega, N. Rajesh, Udhayakumar Ramalingam, Riad K. Al-Hamido, Yaser Saber, Arsham Borumand Saeid, Saeid Jafari, Said Broumi, A.A. Salama, Ganeshsree Selvachandran, Songtao Shao, Seok-Zun Song, Tahsin Oner, M. Mohseni Takallo, Binod Chandra Tripathy, Tugce Katican, J. Vimala, Xiaohong Zhang, Xiaoyan Mao, Xiaoying Wu, Xingliang Liang, Xin Zhou, Yingcang Ma, Young Bae Jun, Juanjuan Zhang.
Papers on neutrosophic statistics, neutrosophic probability, plithogenic set, paradoxism, neutrosophic set, NeutroAlgebra, etc. and their applications.
In this paper, we develop the notion of the basis for a smooth neutrosophic topology in a more natural way. As a sequel, we define the notion of symmetric neutrosophic quasi-coincident neighborhood systems and prove some interesting results that fit with the classical ones, to establish the consistency of theory developed. Finally, we define and discuss the concept of product topology, in this context, using the definition of basis.
This book presents the advancements and applications of neutrosophics, which are generalizations of fuzzy logic, fuzzy set, and imprecise probability. The neutrosophic logic, neutrosophic set, neutrosophic probability, and neutrosophic statistics are increasingly used in engineering applications (especially for software and information fusion), medicine, military, cybernetics, physics.In the last chapter a soft semantic Web Services agent framework is proposed to facilitate the registration and discovery of high quality semantic Web Services agent. The intelligent inference engine module of soft semantic Web Services agent is implemented using interval neutrosophic logic.
This article is based on new developments on a neutrosophic triplet group (NTG) and applications earlier introduced in 2016 by Smarandache and Ali. NTG sprang up from neutrosophic triplet set X: a collection of triplets (b, neut(b), anti(b)) for an b ∈ X that obeys certain axioms (existence of neutral(s) and opposite(s)). Some results that are true in classical groups were investigated in NTG and were shown to be either universally true in NTG or true in some peculiar types of NTG. Distinguishing features between an NTG and some other algebraic structures such as: generalized group (GG), quasigroup, loop and group were investigated. Some neutrosophic triplet subgroups (NTSGs) of a neutrosophic triplet group were studied. Applications of the neutrosophic triplet set, and our results on NTG in relation to management and sports, are highlighted and discussed.
Cognitive Intelligence with Neutrosophic Statistics in Bioinformatics investigates and presents the many applications that have arisen in the last ten years using neutrosophic statistics in bioinformatics, medicine, agriculture and cognitive science. This book will be very useful to the scientific community, appealing to audiences interested in fuzzy, vague concepts from which uncertain data are collected, including academic researchers, practicing engineers and graduate students. Neutrosophic statistics is a generalization of classical statistics. In classical statistics, the data is known, formed by crisp numbers. In comparison, data in neutrosophic statistics has some indeterminacy. This data may be ambiguous, vague, imprecise, incomplete, and even unknown. Neutrosophic statistics refers to a set of data, such that the data or a part of it are indeterminate in some degree, and to methods used to analyze the data. Introduces the field of neutrosophic statistics and how it can solve problems working with indeterminate (imprecise, ambiguous, vague, incomplete, unknown) data Presents various applications of neutrosophic statistics in the fields of bioinformatics, medicine, cognitive science and agriculture Provides practical examples and definitions of neutrosophic statistics in relation to the various types of indeterminacies
The concept of neutrosophic triplet firstly introduced by F. Smarandache and M. Ali. This notion (neutrosophic triplet) is a group of three elements that satisfy certain properties with some binary operation. These neutrosophic triplets highly depends on the proposed binary operation. In this article, we make some observations concerning Neutrosophic triplet metric space (NTMS), Neutrosophic triplet partial metric space (NTPMS), Neutrosophic triplet-b-metric space (NT-b-MS) introduced by Sahin et al. and put our observation on the definitions defined in these articles. Moreover, inspired by Ur Rahaman and Sahin et al. further we define a new topological construction named as Neutrosophic Triplet quasi-dislocated b-metric space (NT-qdb-MS) and study some properties of NT-qdb-MS. Furthermore using this construction, we establish some fixed point theorems in the context of NT-qdb-MS using graph. For the validity of our results, we also provide an example.
In a world of chaotic alignments, traditional logic with its strict boundaries of truth and falsity has not imbued itself with the capability of reflecting the reality. Despite various attempts to reorient logic, there has remained an essential need for an alternative system that could infuse into itself a representation of the real world. Out of this need arose the system of Neutrosophy (the philosophy of neutralities, introduced by FLORENTIN SMARANDACHE), and its connected logic Neutrosophic Logic, which is a further generalization of the theory of Fuzzy Logic. In this book we study the concepts of Fuzzy Cognitive Maps (FCMs) and their Neutrosophic analogue, the Neutrosophic Cognitive Maps (NCMs). Fuzzy Cognitive Maps are fuzzy structures that strongly resemble neural networks, and they have powerful and far-reaching consequences as a mathematical tool for modeling complex systems. Neutrosophic Cognitive Maps are generalizations of FCMs, and their unique feature is the ability to handle indeterminacy in relations between two concepts thereby bringing greater sensitivity into the results. Some of the varied applications of FCMs and NCMs which has been explained by us, in this book, include: modeling of supervisory systems; design of hybrid models for complex systems; mobile robots and in intimate technology such as office plants; analysis of business performance assessment; formalism debate and legal rules; creating metabolic and regulatory network models; traffic and transportation problems; medical diagnostics; simulation of strategic planning process in intelligent systems; specific language impairment; web-mining inference application; child labor problem; industrial relations: between employer and employee, maximizing production and profit; decision support in intelligent intrusion detection system; hyper-knowledge representation in strategy formation; female infanticide; depression in terminally ill patients and finally, in the theory of community mobilization and women empowerment relative to the AIDS epidemic.