Neutrosophic Triplets in Neutrosophic Rings

W.B., Vasantha Kandasamy; Kandasamy, Ilanthenral; Smarandache, Florentín

doi:10.3390/math7060563

Cited by 24 publications

(38 citation statements)

References 20 publications

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“…In [7], the authors claimed that ZI  has no non-trivial neutrosophic triplets. In this section, we find the neutrosophic triplets in rings ZI  , QI  and RI  .…”

Section: Resultsmentioning

confidence: 99%

“…In some papers, some authors clarified and corrected these misunderstandings and mistakes ( [4,8,9]). This paper will clarify some misunderstandings, especially pointing out some erroneous conclusions in [7] and will try to give improved results.…”

Section: Introductionmentioning

confidence: 91%

“…In this paper, some mistakes about the neutrosophic triplets of neutrosophic rings in [7] are pointed out and corrected. For this purpose, the neutrosophic triplets in neutrosophic rings ZI  , QI  and RI  are reinvestigated.…”

Section: Theorem 35mentioning

confidence: 99%

“…As a result of the calculations, it was seen that ZI  has non-trivial neutrosophic triplets. Also neutrosophic triplets of the rings QI  and RI  in [7] was calculated incomplete. In this paper, we gave all neutrosophic triplets in those rings.…”

Section: Theorem 35mentioning

confidence: 99%

See 3 more Smart Citations

Neutrosophic triplets in some neutrosophic rings

Çeven

Ozan

2020

Cumhuriyet Science Journal

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In this paper, some mistakes about the neutrosophic triplets of some neutrosophic rings in the literature are pointed out and corrected. For this purpose, the neutrosophic triplets in neutrosophic rings ZI  , QI  and RI  where Z, Q and R denote the ring of integers, field of rationals and field of reals respectively are reinvestigated. It was claimed that ZI  has only trivial neutrosophic triplet in a paper which was recently published in Mathematics. But, as a result of the calculations, it was seen that ZI  has non-trivial neutrosophic triplets. Also neutrosophic triplets of the rings QI  and RI  in the same literature was calculated incomplete.

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“…In [7], the authors claimed that ZI  has no non-trivial neutrosophic triplets. In this section, we find the neutrosophic triplets in rings ZI  , QI  and RI  .…”

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 91%

Section: Theorem 35mentioning

confidence: 99%

Section: Theorem 35mentioning

confidence: 99%

See 2 more Smart Citations

Neutrosophic triplets in some neutrosophic rings

Çeven

Ozan

2020

Cumhuriyet Science Journal

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“…Generally, one can categorize matrix inversion methods into two different groups: (a) the recursive (or iterative) methods; and (b) the direct methods [7,24,25,26].…”

Section: Introductionmentioning

confidence: 99%

A Novel Recurrent Neural Network-Based Ultra-Fast, Robust, and Scalable Solver for Inverting a “Time-Varying Matrix”

Tavakkoli

Chedjou

Kyamakya

2019

Sensors

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The concept presented in this paper is based on previous dynamical methods to realize a time-varying matrix inversion. It is essentially a set of coupled ordinary differential equations (ODEs) which does indeed constitute a recurrent neural network (RNN) model. The coupled ODEs constitute a universal modeling framework for realizing a matrix inversion provided the matrix is invertible. The proposed model does converge to the inverted matrix if the matrix is invertible, otherwise it converges to an approximated inverse. Although various methods exist to solve a matrix inversion in various areas of science and engineering, most of them do assume that either the time-varying matrix inversion is free of noise or they involve a denoising module before starting the matrix inversion computation. However, in the practice, the noise presence issue is a very serious problem. Also, the denoising process is computationally expensive and can lead to a violation of the real-time property of the system. Hence, the search for a new ‘matrix inversion’ solving method inherently integrating noise-cancelling is highly demanded. In this paper, a new combined/extended method for time-varying matrix inversion is proposed and investigated. The proposed method is extending both the gradient neural network (GNN) and the Zhang neural network (ZNN) concepts. Our new model has proven that it has exponential stability according to Lyapunov theory. Furthermore, when compared to the other previous related methods (namely GNN, ZNN, Chen neural network, and integration-enhanced Zhang neural network or IEZNN) it has a much better theoretical convergence speed. To finish, all named models (the new one versus the old ones) are compared through practical examples and both their respective convergence and error rates are measured. It is shown/observed that the novel/proposed method has a better practical convergence rate when compared to the other models. Regarding the amount of noise, it is proven that there is a very good approximation of the matrix inverse even in the presence of noise.

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Constructing smarter and more sustainable urban ecosystems: a dynamic analysis of challenges and initiatives

Rodrigues

Ferreira

2023

Ann Oper Res

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Cities’ weaknesses have been revealed by their struggle to respond to current challenges (e.g., pandemic crises and population and urbanization exponential growth). Urban planners are thus increasingly concerned about implementing initiatives in their metropolises that favor a better present and future quality of life. In this context, cities need to become enablers of economic and social development and increased prosperity through the integration of technologies into projects promoting smarter and more sustainable urban ecosystems. These ecosystems are, however, highly complex due to their specificities and multifaceted nature, which makes analyzing them a difficult endeavor. Based on a constructivist and complementarity logic, this study sought to develop a multicriteria analysis model to support relevant decision-making processes in this study context. A panel of experts was recruited to create the analysis system using a combination of cognitive mapping and the decision-making trial and evaluation laboratory technique in an neutrosophic context. This approach overcomes various flaws identified in previous related research. The entire procedure focused on enhancing the experts’ learning through participation not only to structure the problem under analysis but also to identify and prioritize the factors and/or determinants of smartness and urban sustainability. The model provides a holistic, solid, and clear vision of the decision problem that fosters appropriate choices when creating and evaluating smart, sustainable urban ecosystems.

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Neutrosophic Triplets in Neutrosophic Rings

Cited by 24 publications

References 20 publications

Neutrosophic triplets in some neutrosophic rings

Neutrosophic triplets in some neutrosophic rings

A Novel Recurrent Neural Network-Based Ultra-Fast, Robust, and Scalable Solver for Inverting a “Time-Varying Matrix”

Constructing smarter and more sustainable urban ecosystems: a dynamic analysis of challenges and initiatives

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