On Novel Results about the Algebraic Properties of Symbolic 3-Plithogenic and 4-Plithogenic Real Square Matrices

On Novel Results about the Algebraic Properties of Symbolic 3-Plithogenic and 4-Plithogenic Real Square Matrices

Author: Hamiyet Merkepçi

Publisher: Infinite Study

Published: 2023-01-01

Total Pages: 14

ISBN-13:

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Symbolic 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.


Introduction to Symbolic 2-Plithogenic Probability Theory

Introduction to Symbolic 2-Plithogenic Probability Theory

Author: Mohamed Bisher Zeina

Publisher: Infinite Study

Published: 2023-01-01

Total Pages: 13

ISBN-13:

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In 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.


On Clean and Nil-clean Symbolic 2-Plithogenic Rings

On Clean and Nil-clean Symbolic 2-Plithogenic Rings

Author: P. Prabakaran

Publisher: Infinite Study

Published: 2023-01-01

Total Pages: 10

ISBN-13:

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A 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.


Plithogeny, Plithogenic Set, Logic, Probability, and Statistics

Plithogeny, Plithogenic Set, Logic, Probability, and Statistics

Author: Florentin Smarandache

Publisher: Infinite Study

Published: 2017-10-01

Total Pages: 143

ISBN-13:

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We 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).


Plithogenic Cognitive Maps in Decision Making

Plithogenic Cognitive Maps in Decision Making

Author: Nivetha Martin

Publisher: Infinite Study

Published:

Total Pages: 13

ISBN-13:

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Plithogenic 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.


Comparison of neutrosophic approach to various deep learning models for sentiment analysis

Comparison of neutrosophic approach to various deep learning models for sentiment analysis

Author: Mayukh Sharma

Publisher: Infinite Study

Published:

Total Pages: 14

ISBN-13:

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Deep 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.


Theories of Communication Networks

Theories of Communication Networks

Author: Peter R. Monge

Publisher: Oxford University Press

Published: 2003-03-27

Total Pages: 431

ISBN-13: 019803637X

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To date, most network research contains one or more of five major problems. First, it tends to be atheoretical, ignoring the various social theories that contain network implications. Second, it explores single levels of analysis rather than the multiple levels out of which most networks are comprised. Third, network analysis has employed very little the insights from contemporary complex systems analysis and computer simulations. Foruth, it typically uses descriptive rather than inferential statistics, thus robbing it of the ability to make claims about the larger universe of networks. Finally, almost all the research is static and cross-sectional rather than dynamic. Theories of Communication Networks presents solutions to all five problems. The authors develop a multitheoretical model that relates different social science theories with different network properties. This model is multilevel, providing a network decomposition that applies the various social theories to all network levels: individuals, dyads, triples, groups, and the entire network. The book then establishes a model from the perspective of complex adaptive systems and demonstrates how to use Blanche, an agent-based network computer simulation environment, to generate and test network theories and hypotheses. It presents recent developments in network statistical analysis, the p* family, which provides a basis for valid multilevel statistical inferences regarding networks. Finally, it shows how to relate communication networks to other networks, thus providing the basis in conjunction with computer simulations to study the emergence of dynamic organizational networks.