Neutrosophic Algebraic Structures And Their Applications
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Neutrosophic Algebraic Structures and Their Applications
Author | : Florentin Smarandache,Memet Şahin,Derya Bakbak,Vakkas Uluçay,Abdullah Kargın |
Publsiher | : Infinite Study |
Total Pages | : 269 |
Release | : 2022-08-01 |
Genre | : Mathematics |
ISBN | : 9182736450XXX |
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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 Algebraic Structures and Their Applications
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Author | : Florentin Smarandache |
Publsiher | : Unknown |
Total Pages | : 0 |
Release | : 2022 |
Genre | : Electronic Book |
ISBN | : OCLC:1404016901 |
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The algebraic structure on the neutrosophic triplet set
Author | : S. Suryoto,Harjito,T. Udjiani |
Publsiher | : Infinite Study |
Total Pages | : 7 |
Release | : 2024 |
Genre | : Mathematics |
ISBN | : 9182736450XXX |
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The notion of the neutrosophic triplet was introduced by Smarandache and Ali. This notion is based on the fundamental law of neutrosophy that for an idea X, we have neutral of X denoted as neut(X) and anti of X denoted as anti(X). This paper studied a neutrosophic triplet set which is a collection of all triple of three elements that satisfy certain properties with some binary operation. Also given some interesting properties related to them. Further, in this paper investigated that from the neutrosophic triplet group can construct a classical group under multiplicative operation for ℤ𝑛 , for some specific n. These neutrosophic triplet groups are built using only modulo integer 2p, with p is an odd prime or Cayley table.
Basic Neutrosophic Algebraic Structures and Their Application to Fuzzy and Neutrosophic Models
Author | : W. B. Vasantha Kandasamy,Florentin Smarandache |
Publsiher | : Infinite Study |
Total Pages | : 149 |
Release | : 2004-01-01 |
Genre | : Mathematics |
ISBN | : 9781931233873 |
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For the involvement of uncertainty of varying degrees, when the total of the membership degree exceeds one or less than one, then the newer mathematical paradigm shift, Fuzzy Theory proves appropriate.For the past two or three decades, Fuzzy Theory has become the potent tool to study and analyze uncertainty involved in all problems. But, many real world problems also abound with the concept of indeterminacy.In this book, the new, powerful tool of neutrosophy that deals with indeterminacy is utilized. Innovative neutrosophic models are described.The theory of neutrosophic graphs is introduced and applied to fuzzy and neutrosophic models.Neutrosophic Logic and Neutrosophic Set (generalizations of Intuitionistic Fuzzy Logic and Intuitionistic Fuzzy Set respectively) became strong tools for applications.
Basic Neutrosophic Algebraic Structures and Their Application to Fuzzy and Neutrosophic Models
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Author | : W. B. Vasantha Kandasamy |
Publsiher | : Hexis |
Total Pages | : 150 |
Release | : 2014-05-14 |
Genre | : MATHEMATICS |
ISBN | : 1461929733 |
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Algebraic Structures of Neutrosophic Triplets Neutrosophic Duplets or Neutrosophic Multisets
Author | : Florentin Smarandache,Xiaohong Zhang,Mumtaz Ali |
Publsiher | : MDPI |
Total Pages | : 478 |
Release | : 2019-04-04 |
Genre | : Mathematics |
ISBN | : 9783038973843 |
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Neutrosophy (1995) is a new branch of philosophy that studies triads of the form (,
Exploring the Algebraic Structures of Q Complex Neutrosophic Soft Fields
Author | : Mamika Ujianita Romdhini,Ashraf Al-Quran,Faisal Al-Sharqi,Mohammad K. Tahat,Abdalwali Lutfi |
Publsiher | : Infinite Study |
Total Pages | : 14 |
Release | : 2023-01-01 |
Genre | : Mathematics |
ISBN | : 9182736450XXX |
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A field is a fundamental algebraic structure that finds extensive applications in algebra and various mathematical domains. On the other hand, a Q-complex neutrosophic soft set (Q-CNSS) is a unique hybrid model that combines the characteristics of soft sets and neutrosophic sets within a complex number framework. It utilizes the effectiveness of Q-set as a powerful tool in the domain of this particular model. In this article, we leverage this model to define fields under uncertainty. We present the Q-complex neutrosophic soft field (Q-CNSF) and examine the unique algebraic properties associated with this model. Additionally, we explore the relationships between Q-CNSF and Q-neutrosophic soft field (Q-NSF). Furthermore, we define the Cartesian product of QCNSFs and delve into the relevant properties. Through this comprehensive exploration, our aim is to enhance the understanding of Q-CNSFs and their properties, ultimately contributing to the field of algebraic analysis and its practical applications in handling uncertainty and vagueness.
Neutrosophic Multigroups and Applications
Author | : Vakkas Uluçay,Memet Sahin |
Publsiher | : Infinite Study |
Total Pages | : 17 |
Release | : 2024 |
Genre | : Mathematics |
ISBN | : 9182736450XXX |
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In recent years, fuzzy multisets and neutrosophic sets have become a subject of great interest for researchers and have been widely applied to algebraic structures include groups, rings, fields and lattices. Neutrosophic multiset is a generalization of multisets and neutrosophic sets. In this paper, we proposed a algebraic structure on neutrosophic multisets is called neutrosophic multigroups which allow the truth-membership, indeterminacy-membership and falsity-membership sequence have a set of real values between zero and one.