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Author: Rozina Ali
Publisher: Infinite Study
Published: 2023-01-01
Total Pages: 5
ISBN-13:
DOWNLOAD EBOOKThe objective of this paper is to define and study for the first time the concept of symbolic 3-plithogenic vector spaces based on symbolic 3-plithogenic sets and classical vector spaces.Also, many related substructures will be defined and handled such as AH-functions, AH-spaces, and symbolic 3-plithogenic basis.
Author: Mohamed Bisher Zeina
Publisher: Infinite Study
Published: 2023-01-01
Total Pages: 13
ISBN-13:
DOWNLOAD EBOOKIn this paper we present for the first time the concept of symbolic plithogenic random variables and study its properties including expected value and variance. We build the plithogenic formal form of two important distributions that are exponential and uniform distributions. We find its probability density function and cumulative distribution function in its plithogenic form. We also derived its expected values and variance and the formulas of its random numbers generating. We finally present the fundamental form of plithogenic probability density and cumulative distribution functions. All the theorems were proved depending on algebraic approach using isomorphisms. This paper can be considered the base of symbolic plithogenic probability theory.
Author: Hamiyet Merkepçi
Publisher: Infinite Study
Published: 2023-01-01
Total Pages: 14
ISBN-13:
DOWNLOAD EBOOKSymbolic n-plithogenic sets are considered to be modern concepts that carry within their framework both an algebraic and logical structure. The concept of symbolic n-plithogenic algebraic rings is considered to be a novel generalization of classical algebraic rings with many symmetric properties. These structures can be written as linear combinations of many symmetric elements taken from other classical algebraic structures, where the square symbolic k-plithogenic real matrices are square matrices with real symbolic k-plithogenic entries. In this research, we will find easy-to-use algorithms for calculating the determinant of a symbolic 3-plithogenic/4-plithogenic matrix, and for finding its inverse based on its classical components, and even for diagonalizing matrices of these types. On the other hand, we will present a new algorithm for calculating the eigenvalues and eigenvectors associated with matrices of these types. Also, the exponent of symbolic 3-plithogenic and 4-plithogenic real matrices will be presented, with many examples to clarify the novelty of this work.
Author: P. Prabakaran
Publisher: Infinite Study
Published: 2023-01-01
Total Pages: 10
ISBN-13:
DOWNLOAD EBOOKA ring is said to be clean if every element of the ring can be written as a sum of an idempotent element and a unit element of the ring and a ring is said to be nil-clean if every element of the ring can be written as a sum of an idempotent element and a nilpotent element of the ring. In this paper, we generalize these arguments to symbolic 2-plithogenic structure. We introduce the structure of clean and nil-clean symbolic 2-plithogenic rings and some of its elementary properties are presented. Also, we have found the equivalence between classical clean(nil-clean) ring R and the corresponding symbolic 2-plithogenic ring 2-SPR.
Author: Florentin Smarandache
Publisher: Infinite Study
Published: 2017-10-01
Total Pages: 143
ISBN-13:
DOWNLOAD EBOOKWe introduce for the first time the concept of plithogeny in philosophy and, as a derivative, the concepts of plithogenic set / logic / probability / statistics in mathematics and engineering – and the degrees of contradiction (dissimilarity) between the attributes’ values that contribute to a more accurate construction of plithogenic aggregation operators and to the plithogenic relationship of inclusion (partial ordering).
Author: Tatsuo Kimura
Publisher:
Published: 2002
Total Pages: 314
ISBN-13: 9781470446406
DOWNLOAD EBOOKThis is the first introductory book on the theory of prehomogeneous vector spaces, introduced in the 1970s by Mikio Sato. The author was an early and important developer of the theory and continues to be active in the field. This book explains the basic concepts of prehomogeneous vector spaces, the fundamental theorem, the zeta functions associated with prehomogeneous vector spaces and a classification theory of irreducible prehomogeneous vector spaces. This book is written for students, and is appropriate for second-year graduate level and above. However, because it is self-contained, coverin.
Author: Florentin Smarandache
Publisher: Infinite Study
Published: 2010-08-23
Total Pages: 10
ISBN-13:
DOWNLOAD EBOOKIn this paper one generalizes the intuitionistic fuzzy set (IFS), paraconsistent set, and intuitionistic set to the neutrosophic set (NS). Many examples are presented. Distinctions between NS and IFS are underlined.
Author: Florentin Smarandache
Publisher: Infinite Study
Published: 2014
Total Pages: 125
ISBN-13: 1599732742
DOWNLOAD EBOOKNeutrosophic Statistics means statistical analysis of population or sample that has indeterminate (imprecise, ambiguous, vague, incomplete, unknown) data. For example, the population or sample size might not be exactly determinate because of some individuals that partially belong to the population or sample, and partially they do not belong, or individuals whose appurtenance is completely unknown. Also, there are population or sample individuals whose data could be indeterminate. In this book, we develop the 1995 notion of neutrosophic statistics. We present various practical examples. It is possible to define the neutrosophic statistics in many ways, because there are various types of indeterminacies, depending on the problem to solve.
Author: Mayukh Sharma
Publisher: Infinite Study
Published:
Total Pages: 14
ISBN-13:
DOWNLOAD EBOOKDeep learning has been widely used in numerous real-world engineering applications and for classification problems. Real-world data is present with neutrality and indeterminacy, which neutrosophic theory captures clearly. Though both are currently developing research areas, there has been little study on their interlinking. We have proposed a novel framework to implement neutrosophy in deep learning models. Instead of just predicting a single class as output, we have quantified the sentiments using three membership functions to understand them better. Our proposed model consists of two blocks, feature extraction, and feature classification.
Author: Nivetha Martin
Publisher: Infinite Study
Published:
Total Pages: 13
ISBN-13:
DOWNLOAD EBOOKPlithogenic sets introduced by Smarandache (2018) have disclosed new research vistas and this paper introduces the novel concept of plithogenic cognitive maps (PCM) and its applications in decision making. The new approach of defining instantaneous state neutrosophic vector with the confinement of indeterminacy to (0,1] is proposed to quantify the degree of indeterminacy.
