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Neutrosophic Triplet Groups and their Applications to Mathematical Modelling

By Kandasamy, W. B. Vasantha

Book Id: WPLBN0100302950
Format Type: PDF (eBook)
File Size: 2.07 MB.
Reproduction Date: 10/1/2018

Title:	Neutrosophic Triplet Groups and their Applications to Mathematical Modelling
Author:	Kandasamy, W. B. Vasantha
Volume:
Language:	English
Subject:	Non Fiction, Science
Collections:	Mathematics, Authors Community
Historic Publication Date:	2018
Publisher:	Pons Editions

Member Page:	Infinite Science
Citation APA MLA Chicago Vasantha Kandasamy, W. B., & Smarandache, F. (2018). Neutrosophic Triplet Groups and their Applications to Mathematical Modelling. Retrieved from http://www.self.gutenberg.org/

Description
The innovative notion of neutrosophic triplet groups, introduced by Smarandache and Ali in 2014-2016, happens to yield the anti-element and neutral element once the element is given. It is established that the neutrosophic triplet group collection forms the classical group under product for Zn, for some specific n. However the collection is not even closed under sum. These neutrosophic triplet groups are built using only modulo integers or Cayley tables. Several interesting properties related with them are defined. It is pertinent to record that in Zn, when n is a prime number, we cannot get a neutral element which can contribute to nontrivial neutrosophic triplet groups. Further, all neutral elements in Zn are only nontrivial idempotents. We define these new operations mainly to construct mathematical models akin to Fuzzy Cognitive Maps (FCMs) model, Neutrosophic Cognitive Maps (NCMs) model and Fuzzy Relational Maps (FRMs) model. These new models are defined in chapter four of this book. These new models can find applications in discrete Artificial Neural Networks, soft computing, and social network analysis whenever the concept of indeterminate is involved.