Some New Operations of (a, β, g) Interval Cut Set of Interval Valued Neutrosophic Sets

Some New Operations of (a, β, g) Interval Cut Set of Interval Valued Neutrosophic Sets
Author: Mehmet Şahin
Publisher: Infinite Study
Total Pages: 18
Release:
Genre: Mathematics
ISBN:

In this paper, we define the disjunctive sum, difference and Cartesian product of two interval valued neutrosophic sets and study their basic properties. The notions of the (a, β, g) interval cut set of interval valued neutrosophic sets and the (a, β, g) strong interval cut set of interval valued neutrosophic sets are put forward. Some related properties have been established with proof, examples and counter examples.

NEUTROSOPHIC TRIPLET STRUCTURES, Volume I

NEUTROSOPHIC TRIPLET STRUCTURES, Volume I
Author: Memet Sahin
Publisher: Infinite Study
Total Pages: 23
Release:
Genre: Mathematics
ISBN:

A bipolar neutrosophic set (BNS) is an instance of a single- valued neutrosophic set. To do this, we firstly propose distance measure between two BNSs is defined by the full consideration of positive membership function and negative membership function for the forward and backward differences. Then the similarity measure, the entropy measure and the index of distance are also presented. Then, two examples are shown to verify the feasibility of the proposed method. Finally, the decision results of different similarity measures demonstrate the practicality and effectiveness of the developed method in this paper.

Neutrosophic Algebraic Structures and Their Applications

Neutrosophic Algebraic Structures and Their Applications
Author: Florentin Smarandache
Publisher: Infinite Study
Total Pages: 269
Release: 2022-08-01
Genre: Mathematics
ISBN:

Neutrosophic theory and its applications have been expanding in all directions at an astonishing rate especially after of the introduction the journal entitled “Neutrosophic Sets and Systems”. New theories, techniques, algorithms have been rapidly developed. One of the most striking trends in the neutrosophic theory is the hybridization of neutrosophic set with other potential sets such as rough set, bipolar set, soft set, hesitant fuzzy set, etc. The different hybrid structures such as rough neutrosophic set, single valued neutrosophic rough set, bipolar neutrosophic set, single valued neutrosophic hesitant fuzzy set, etc. are proposed in the literature in a short period of time. Neutrosophic set has been an important tool in the application of various areas such as data mining, decision making, e-learning, engineering, medicine, social science, and some more.

The Effect of The Neutrosophic Logic on The Decision Tree

The Effect of The Neutrosophic Logic on The Decision Tree
Author: Ahmed Hatip
Publisher: Infinite Study
Total Pages: 84
Release:
Genre: Mathematics
ISBN:

In this book, we will present the neutrosophic decision-making mechanism which is an extension of the classical decision-making process by extending the data to include the indefinite cases that are ignored by classical logic and which, in fact, support the decision-making problem. This book consists of eight chapters. In the introductory part of the thesis, the historical development process of the neutrosophic structure theory is given. In the second part, the effect of the neutrosophic logic on the decision tree has been compiled. In the third chapter, the Prospector Neutro Function with their applications were studied. In the fourth chapter, the subject of Neutro ordered R-module and their properties is examined in detail. In the fifth chapter, the Fundamental Theorem in neutrosophic Euclidean Geometry is given. In the sixth chapter, the solutions of some Kandasamy-Smarandache problems about neutrosophic complex numbers and group of units' problem are given. In the seventh chapter, the algebraic creativity in the neutrosophic square matrices and the results are given with examples. Finally, in the eighth chapter, the results and suggestions obtained in the thesis are given.

NeutroAlgebra Theory Volume I

NeutroAlgebra Theory Volume I
Author: Florentin Smarandache
Publisher: Infinite Study
Total Pages: 219
Release: 2021-06-21
Genre: Architecture
ISBN:

A collection of papers from multiple authors. In 2019 and 2020 Smarandache [1, 2, 3, 4] generalized the classical Algebraic Structures to NeutroAlgebraic Structures (or NeutroAlgebras) {whose operations and axioms are partially true, partially indeterminate, and partially false} as extensions of Partial Algebra, and to AntiAlgebraic Structures (or AntiAlgebras) {whose operations and axioms are totally false}. The NeutroAlgebras & AntiAlgebras are a new field of research, which is inspired from our real world. In classical algebraic structures, all axioms are 100%, and all operations are 100% well-defined, but in real life, in many cases these restrictions are too harsh, since in our world we have things that only partially verify some laws or some operations. Using the process of NeutroSophication of a classical algebraic structure we produce a NeutroAlgebra, while the process of AntiSophication of a classical algebraic structure produces an AntiAlgebra.

NEUTROSOPHIC TRIPLET STRUCTURES, Volume I

NEUTROSOPHIC TRIPLET STRUCTURES, Volume I
Author: Florentin Smarandache
Publisher: Infinite Study
Total Pages: 199
Release: 2019
Genre: Mathematics
ISBN: 1599735954

Neutrosophic theory and its applications have been expanding in all directions at an astonishing rate especially after of the introduction the journal entitled “Neutrosophic Sets and Systems”. New theories, techniques, algorithms have been rapidly developed. One of the most striking trends in the neutrosophic theory is the hybridization of neutrosophic set with other potential sets such as rough set, bipolar set, soft set, hesitant fuzzy set, etc. The different hybrid structures such as rough neutrosophic set, single valued neutrosophic rough set, bipolar neutrosophic set, single valued neutrosophic hesitant fuzzy set, etc. are proposed in the literature in a short period of time. Neutrosophic set has been an important tool in the application of various areas such as data mining, decision making, e-learning, engineering, medicine, social science, and some more.

Neutrosophic Triplet Partial v-Generalized Metric Space

Neutrosophic Triplet Partial v-Generalized Metric Space
Author: Memet Şahin
Publisher: Infinite Study
Total Pages: 20
Release:
Genre: Mathematics
ISBN:

In this chapter, study the notion of neutrosophic triplet partial v-generalized metric space. Then, we give some definitions and examples for neutrosophic triplet partial v-generalized metric space and obtain some properties and prove these properties. Furthermore, we show that neutrosophic triplet partial v-generalized metric space is different from neutrosophic triplet v-generalized metric space and neutrosophic triplet partial metric space.

Neutrosophic Sets and Systems, Vol. 38, 2020

Neutrosophic Sets and Systems, Vol. 38, 2020
Author: Florentin Smarandache
Publisher: Infinite Study
Total Pages: 662
Release:
Genre: Mathematics
ISBN:

“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.