Neutrosophic Entropy Measures For The Normal Distribution: Theory And Applications PDF Download
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Author: Rehan Ahmad Khan Sherwani
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 16
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Book Description
Entropy is a measure of uncertainty and often used in information theory to determine the precise testimonials about unclear situations. Different entropy measures available in the literature are based on the exact form of the observations and lacks in dealing with the interval-valued data. The interval-valued data often arises from the situations having ambiguity, imprecise, unclear, indefinite, or vague states of the experiment and is called neutrosophic data. In this research modified forms of different entropy measures for normal probability distribution have been proposed by considering the neutrosophic form data. The performance of the proposed neutrosophic entropies for normal distribution has been assessed via a simulation study. Moreover, the proposed measures are also applied to two real data sets for their wide applicability.
Author: Rehan Ahmad Khan Sherwani
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 16
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Book Description
Entropy is a measure of uncertainty and often used in information theory to determine the precise testimonials about unclear situations. Different entropy measures available in the literature are based on the exact form of the observations and lacks in dealing with the interval-valued data. The interval-valued data often arises from the situations having ambiguity, imprecise, unclear, indefinite, or vague states of the experiment and is called neutrosophic data. In this research modified forms of different entropy measures for normal probability distribution have been proposed by considering the neutrosophic form data. The performance of the proposed neutrosophic entropies for normal distribution has been assessed via a simulation study. Moreover, the proposed measures are also applied to two real data sets for their wide applicability.
Author: Rehan Ahmad Khan Sherwani
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 23
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Book Description
Uncertainty, vagueness, and ambiguity surround us in many real-life problems and, therefore, always remain under consideration for researchers to quantify them. This study proposed neutrosophic discrete probability distribution as a generalization of classical or existing probability distributions, named neutrosophic geometric distribution. Case studies presented in the paper will help understand the concept and application of the proposed distribution. Several properties are derived, like the proposed distribution’s moment, characteristic, and probability-generating functions. Furthermore, the newly proposed distribution derives properties from the reliability analysis, such as survival function, hazard rate function, reversed hazard rate function, cumulative hazard rate function, mills ratio, and odds ratio. In addition, order statistics for NGD, including wth, the largest, and the smallest order statistics, are also derived from joint, median, minimum, and maximum order statistics. This examination opens the path for managing issues that follow traditional conveyances and simultaneously contain information that is not determined precisely.
Author: Han Yang
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 10
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Book Description
Information measures play an important role in the interval neutrosophic sets (INS) theory. The main purpose of this paper is to study the similarity and entropy of INS and its application in multi-attribute decision-making. We propose a new inclusion relation between interval neutrosophic sets where the importance of the three membership functions may be different. Then, we propose the axiomatic definitions of the similarity measure and entropy of the interval neutrosophic set (INS) based on the new inclusion relation. Based on the Hamming distance, cosine function and cotangent function, some new similarity measures and entropies of INS are constructed. Finally, based on the new similarity and entropy, we propose a multi-attribute decision-making method and illustrate that these new similarities and entropies are reasonable and effective.
Author: Jun Ye
Publisher: Infinite Study
ISBN:
Category :
Languages : en
Pages : 10
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Book Description
Entropy is one of many important mathematical tools for measuring uncertain/fuzzy information. As a subclass of neutrosophic sets (NSs), simplified NSs (including single-valued and interval-valued NSs) can describe incomplete, indeterminate, and inconsistent information. Based on the concept of fuzzy exponential entropy for fuzzy sets, this work proposes exponential entropy measures of simplified NSs (named simplified neutrosophic exponential entropy (SNEE) measures), including single-valued and interval-valued neutrosophic exponential entropy measures, and investigates their properties.
Author: Wen-Hua Cui
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 12
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Book Description
In order to quantify the fuzziness in the simplified neutrosophic setting, this paper proposes a generalized distance-based entropy measure and a dimension root entropy measure of simplified neutrosophic sets (NSs) (containing interval-valued and single-valued NSs) and verifies their properties. Then, comparison with the existing relative interval-valued NS entropy measures through a numerical example is carried out to demonstrate the feasibility and rationality of the presented generalized distance-based entropy and dimension root entropy measures of simplified NSs. Lastly, a decision-making example is presented to illustrate their applicability, and then the decision results indicate that the presented entropy measures are effective and reasonable. Hence, this study enriches the simplified neutrosophic entropy theory and measure approaches.
Author: Ali AYDOĞDU
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 6
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Book Description
Our aim in this work is to obtain two new entropy measures for single valued neutrosophic sets (SVNSs) and interval neutrosophic sets (INSs). Moreover, we give the essential properties of the proposed entropies. Finally, we introduce a numerical example to show that the entropy measures are more reliable and reasonable for representing the degree of uncertainty.
Author: Surapati Pramanik
Publisher: Infinite Study
ISBN:
Category :
Languages : en
Pages : 25
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Book Description
The bipolar neutrosophic set is an important extension of the bipolar fuzzy set. The bipolar neutrosophic set is a hybridization of the bipolar fuzzy set and neutrosophic set.
Author: S. K. Patro
Publisher: Infinite Study
ISBN:
Category :
Languages : en
Pages : 7
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Book Description
In this paper , the authors explore neutrosophic statistics, that was initiated by Florentin Smarandache in 1998 and developed in 2014, by presenting various examples of several statistical distributions, from the work [1]. The paper is presented with more case studies, by means of which this neutrosophic version of statistical distribution becomes more pronounced.
Author: Rehan A. Khan Sherwani
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 6
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Book Description
This research is an extension of classical statistics distribution theory as the theory did not deal with the problems having ambiguity, impreciseness, or indeterminacy. An important life-time distribution called Beta distribution from classical statistics is proposed by considering the indeterminate environment and named the new proposed distribution as neutrosophic beta distribution.
Author: Karsten Keller
Publisher: MDPI
ISBN: 3039280325
Category : Science
Languages : en
Pages : 260
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Book Description
Entropies and entropy-like quantities play an increasing role in modern non-linear data analysis. Fields that benefit from this application range from biosignal analysis to econophysics and engineering. This issue is a collection of papers touching on different aspects of entropy measures in data analysis, as well as theoretical and computational analyses. The relevant topics include the difficulty to achieve adequate application of entropy measures and the acceptable parameter choices for those entropy measures, entropy-based coupling, and similarity analysis, along with the utilization of entropy measures as features in automatic learning and classification. Various real data applications are given.
