Vasantha Kandasamy W.B.

Bio: Vasantha Kandasamy W.B. is an academic researcher. The author has contributed to research in topics: Prime (order theory) & Ring (mathematics). The author has an hindex of 6, co-authored 6 publications receiving 65 citations.

A Classical Group of Neutrosophic Triplet Groups Using {Z2p, ×}

Abstract: In this paper we study the neutrosophic triplet groups for a ∈ Z 2 p and prove this collection of triplets a , n e u t ( a ) , a n t i ( a ) if trivial forms a semigroup under product, and semi-neutrosophic triplets are included in that collection. Otherwise, they form a group under product, and it is of order ( p − 1 ) , with ( p + 1 , p + 1 , p + 1 ) as the multiplicative identity. The new notion of pseudo primitive element is introduced in Z 2 p analogous to primitive elements in Z p , where p is a prime. Open problems based on the pseudo primitive elements are proposed. Here, we restrict our study to Z 2 p and take only the usual product modulo 2 p .

Neutrosophic Triplets in Neutrosophic Rings

Abstract: The neutrosophic triplets in neutrosophic rings 〈 Q ∪ I 〉 and 〈 R ∪ I 〉 are investigated in this paper. However, non-trivial neutrosophic triplets are not found in 〈 Z ∪ I 〉 . In the neutrosophic ring of integers Z \ { 0 , 1 } , no element has inverse in Z. It is proved that these rings can contain only three types of neutrosophic triplets, these collections are distinct, and these collections form a torsion free abelian group as triplets under component wise product. However, these collections are not even closed under component wise addition.

Neutrosophic Quadruple Vector Spaces and Their Properties

Abstract: In this paper authors for the first time introduce the concept of Neutrosophic Quadruple (NQ) vector spaces and Neutrosophic Quadruple linear algebras and study their properties. Most of the properties of vector spaces are true in case of Neutrosophic Quadruple vector spaces. Two vital observations are, all quadruple vector spaces are of dimension four, be it defined over the field of reals R or the field of complex numbers C or the finite field of characteristic p, Z p ; p a prime. Secondly all of them are distinct and none of them satisfy the classical property of finite dimensional vector spaces. So this problem is proposed as a conjecture in the final section.

Semi-Idempotents in Neutrosophic Rings

Abstract: In complex rings or complex fields, the notion of imaginary element i with i 2 = − 1 or the complex number i is included, while, in the neutrosophic rings, the indeterminate element I where I 2 = I is included. The neutrosophic ring 〈 R ∪ I 〉 is also a ring generated by R and I under the operations of R. In this paper we obtain a characterization theorem for a semi-idempotent to be in 〈 Z p ∪ I 〉 , the neutrosophic ring of modulo integers, where p a prime. Here, we discuss only about neutrosophic semi-idempotents in these neutrosophic rings. Several interesting properties about them are also derived and some open problems are suggested.

Study of Imaginative Play in Children Using Single-Valued Refined Neutrosophic Sets

Abstract: This paper introduces Single Valued Refined Neutrosophic Set (SVRNS) which is a generalized version of the neutrosophic set. It consists of six membership functions based on imaginary and indeterminate aspect and hence, is more sensitive to real-world problems. Membership functions defined as complex (imaginary), a falsity tending towards complex and truth tending towards complex are used to handle the imaginary concept in addition to existing memberships in the Single Valued Neutrosophic Set (SVNS). Several properties of this set were also discussed. The study of imaginative pretend play of children in the age group from 1 to 10 years was taken for analysis using SVRNS, since it is a field which has an ample number of imaginary aspects involved. SVRNS will be more apt in representing these data when compared to other neutrosophic sets. Machine learning algorithms such as K-means, parallel axes coordinate, etc., were applied and visualized for a real-world application concerned with child psychology. The proposed algorithms help in analysing the mental abilities of a child on the basis of imaginative play. These algorithms aid in establishing a correlation between several determinants of imaginative play and a child’s mental abilities, and thus help in drawing logical conclusions based on it. A brief comparison of the several algorithms used is also provided.

Neutrosophic Duplet Semi-Group and Cancellable Neutrosophic Triplet Groups

Abstract: The notions of the neutrosophic triplet and neutrosophic duplet were introduced by Florentin Smarandache. From the existing research results, the neutrosophic triplets and neutrosophic duplets are completely different from the classical algebra structures. In this paper, we further study neutrosophic duplet sets, neutrosophic duplet semi-groups, and cancellable neutrosophic triplet groups. First, some new properties of neutrosophic duplet semi-groups are funded, and the following important result is proven: there is no finite neutrosophic duplet semi-group.

Neutrosophic Perspectives: Triplets, Duplets, Multisets, Hybrid Operators, Modal Logic, Hedge Algebras. And Applications (second extended and improved)

Abstract: This book is part of the book-series dedicated to the advances of neutrosophic theories and their applications, started by the author in 1998. Its aim is to present the last developments in the field. This is the second extended and improved edition of Neutrosophic Perspectives (September 2017; first edition was published in June 2017). For the first time, we now introduce: — Neutrosophic Duplets and the Neutrosophic Duplet Structures; — Neutrosophic Multisets (as an extension of the classical multisets); — Neutrosophic Spherical Numbers; — Neutrosophic Overnumbers / Undernumbers / Offnumbers; — Neutrosophic Indeterminacy of Second Type; — Neutrosophic Hybrid Operators (where the heterogeneous t-norms and t-conorms may be used in designing neutrosophic aggregations); — Neutrosophic Triplet Loop; — Neutrosophic Triplet Function; — Neutrosophic Modal Logic; — and Neutrosophic Hedge Algebras. The Refined Neutrosophic Set / Logic / Probability were introduced in 2013 by F. Smarandache. Since year 2016 a new interest has been manifested by researchers for the Neutrosophic Triplets and their corresponding Neutros-ophic Triplet Algebraic Structures (introduced by F. Smarandache & M. Ali). Subtraction and Division of Neutrosophic Numbers were introduced by F. Smarandache - 2016, and Jun Ye – 2017. We also present various new applications in: neutrosophic multi-criteria decision-making, neutrosophic psychology, neutrosophic geographical function (the equatorial virtual line), neutrosophic probability in target identification, neutrosophic dynamic systems, neutrosophic quantum computers, neutrosophic theory of evolution, and neutrosophic triplet structures in our everyday life.

Generalized Neutrosophic Extended Triplet Group

Abstract: Neutrosophic extended triplet group is a new algebra structure and is different from the classical group. In this paper, the notion of generalized neutrosophic extended triplet group is proposed and some properties are discussed. In particular, the following conclusions are strictly proved: (1) an algebraic system is a generalized neutrosophic extended triplet group if and only if it is a quasi-completely regular semigroup; (2) an algebraic system is a weak commutative generalized neutrosophic extended triplet group if and only if it is a quasi-Clifford semigroup; (3) for each n ∈ Z + , n ≥ 2 , ( Z n , ⊗ ) is a commutative generalized neutrosophic extended triplet group; (4) for each n ∈ Z + , n ≥ 2 , ( Z n , ⊗ ) is a commutative neutrosophic extended triplet group if and only if n = p 1 p 2 ⋯ p m , i.e., the factorization of n has only single factor.

Indeterminate Likert scale: feedback based on neutrosophy, its distance measures and clustering algorithm

Abstract: Likert scale is the most widely used psychometric scale for obtaining feedback. The major disadvantage of Likert scale is information distortion and information loss problem that arise due to its ordinal nature and closed format. Real-world responses are mostly inconsistent, imprecise and indeterminate depending on the customers’ emotions. To capture the responses realistically, the concept of neutrosophy (study of neutralities and indeterminacy) is used. Indeterminate Likert scale based on neutrosophy is introduced in this paper. Clustering according to customer feedback is an effective way of classifying customers and targeting them accordingly. Clustering algorithm for feedback obtained using indeterminate Likert scaling is proposed in this paper. While dealing real-world scenarios, indeterminate Likert scaling is better in capturing the responses accurately.