New approach on differential equation via trapezoidal neutrosophic number
New approach on differential equation via trapezoidal neutrosophic number

Author: I. R. Sumathi

Publisher: Infinite Study

Published:

Total Pages: 8

ISBN-13:

DOWNLOAD EBOOK

Neutrosophic Logic is a tool based on non-standard analysis to represent mathematical model of uncertainty, vagueness, ambiguity, incompleteness, and inconsistency. In Neutrosophic set, indeterminacy is quantified explicitly whereas the truth membership, indeterminacy membership, and falsity membership are independent. This plays a vital role in many situations whenwehandle inconsistent and incomplete information. In modeling problems, differential equations have major applications in the field of science and engineering and the study of differential equationwith uncertainty is one of emerging field of research. In this paper, the differential equations in neutrosophic environment are explored, also the solution of second-order linear differential equation with trapezoidal neutrosophic numbers as boundary conditions is discussed. Furthermore, the numerical example is given to demonstrate the solution with different values of (α, β, γ )-cut of trapezoidal neutrosophic number.

Neutrosophic Sets and Systems, Vol. 38, 2020
Neutrosophic Sets and Systems, Vol. 38, 2020

Author: Florentin Smarandache

Publisher: Infinite Study

Published:

Total Pages: 662

ISBN-13:

DOWNLOAD EBOOK

“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.

Neutrosophic Sets and Systems, vol. 51/2022
Neutrosophic Sets and Systems, vol. 51/2022

Author: Florentin Smarandache

Publisher: Infinite Study

Published: 2022-09-01

Total Pages: 970

ISBN-13:

DOWNLOAD EBOOK

“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).

Neutrosophic Sets and Systems, Vol. 29, 2019
Neutrosophic Sets and Systems, Vol. 29, 2019

Author: Florentin Smarandache

Publisher: Infinite Study

Published:

Total Pages: 264

ISBN-13:

DOWNLOAD EBOOK

“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.

Neutrosophic Sets and Systems, Vol. 46, 2021
Neutrosophic Sets and Systems, Vol. 46, 2021

Author: Florentin Smarandache

Publisher: Infinite Study

Published: 2021-10-19

Total Pages: 487

ISBN-13:

DOWNLOAD EBOOK

Papers on neutrosophic programming, neutrosophic hypersoft set, neutrosophic topological spaces, NeutroAlgebra, NeutroGeometry, AntiGeometry, NeutroNearRings, neutrosophic differential equations, etc.

Neutrosophic Operational Research
Neutrosophic Operational Research

Author: Florentin Smarandache

Publisher: Springer Nature

Published: 2021-09-09

Total Pages: 628

ISBN-13: 3030571971

DOWNLOAD EBOOK

This book addresses new concepts, methods, algorithms, modeling, and applications of green supply chain, inventory control problems, assignment problems, transportation problem, linear problems and new information related to optimization for the topic from the theoretical and applied viewpoints of neutrosophic sets and logic. The book is an innovatory of new tools and procedures, such as: Neutrosophic Statistical Tests and Dependent State Samplings, Neutrosophic Probabilistic Expert Systems, Neutrosophic HyperSoft Set, Quadripartitioned Neutrosophic Cross-Entropy, Octagonal and Spherical and Cubic Neutrosophic Numbers used in machine learning. It highlights the process of neutrosofication {which means to split the universe into three parts, two opposite ones (Truth and Falsehood), and an Indeterminate or neutral one (I) in between them}. It explains Three-Ways Decision, how the universe set is split into three different distinct areas, in regard to the decision process, representing: Acceptance, Noncommitment, and Rejection, respectively. The Three-Way Decision is used in the Neutrosophic Linguistic Rough Set, which has never been done before.

Sumudu Transform for Solving Second Order Ordinary Differential Equation under Neutrosophic Initial Conditions
Sumudu Transform for Solving Second Order Ordinary Differential Equation under Neutrosophic Initial Conditions

Author: Meghna Parikh

Publisher: Infinite Study

Published: 2020-12-01

Total Pages: 18

ISBN-13:

DOWNLOAD EBOOK

The ordinary differential equation of second order is being used in many engineering disciplines and sciences to model many real-life problems. These problems are mostly uncertain, vague and incomplete and thus they require some more advanced tool for modelling. Neutrosophic logic becomes the solution of all these kind of uncertain problems as it describe the conditions of uncertainty which occurs during the process of modelling on the basis of grade of membership of truth values, indeterminacy values and falsity values, that means it consider all the uncertain parameters on the basis of these degrees. In this research paper, we have considered the ordinary differential equation of second order with neutrosophic numbers as initial conditions of spring mass system is solved using Sumudu transform method which has advantage of unit preserving property over the well established Laplace Transform method. The solution obtained at various computational points by this method is shown in the form of table. Furthermore, the results obtained at different (α, β, γ)-cut and time values are also depicted graphically and are verified analytically by de-fuzzifying the data.

Neutrosophic Sets and Systems, Book Series, Vol. 29, 2019
Neutrosophic Sets and Systems, Book Series, Vol. 29, 2019

Author: Florentin Smarandache

Publisher: Infinite Study

Published:

Total Pages: 262

ISBN-13:

DOWNLOAD EBOOK

“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.

Neutrosophic Cognitive Maps for Situation Analysis
Neutrosophic Cognitive Maps for Situation Analysis

Author: Aasim Zafar

Publisher: Infinite Study

Published:

Total Pages: 11

ISBN-13:

DOWNLOAD EBOOK

There are various factors which lead to the criminal behaviour in humans. Prominent researchers monitoring the situation of crime in Nigeria cite poverty, unemployment, family-breakdown, bribing & corruption, lack of co-operation from public and negative perception of police to be the major causes behind criminal behaviour.

Neutrosophic Completion Technique for Incomplete Higher-Order AHP Comparison Matrices
Neutrosophic Completion Technique for Incomplete Higher-Order AHP Comparison Matrices

Author: Ignacio J. Navarro

Publisher: Infinite Study

Published:

Total Pages: 19

ISBN-13:

DOWNLOAD EBOOK

The present paper proposes a neutrosophic AHP completion methodology to reduce the number of judgments required to be emitted by the decision maker. This increases the consistency of their responses, while accounting for uncertainties associated to the fuzziness of human thinking. The method is applied to a sustainable-design problem, resulting in weight estimations that allow for a reduction of up to 22% of the conventionally required comparisons, with an average accuracy below 10% between estimates and the weights resulting from a conventionally completed AHP matrix, and a root mean standard error below 15%.