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Neutrosophic Entropy Measures For The Normal Distribution: Theory And Applications

Author: Rehan Ahmad Khan Sherwani

Publisher: Infinite Study

Published:

Total Pages: 16

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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.

Exponential Entropy for Simplified Neutrosophic Sets and Its Application in Decision Making

Author: Jun Ye

Publisher: Infinite Study

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Total Pages: 10

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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.

Entropy, Measures of Distance and Similarity of Q-Neutrosophic Soft Sets and Some Applications

Author: Majdoleen Abu Qamar

Publisher: Infinite Study

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Total Pages: 16

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The idea of the Q-neutrosophic soft set emerges from the neutrosophic soft set by upgrading the membership functions to a two-dimensional entity which indicate uncertainty, indeterminacy and falsity. Hence, it is able to deal with two-dimensional inconsistent, imprecise, and indeterminate information appearing in real life situations. In this study, the tools that measure the similarity, distance and the degree of fuzziness of Q-neutrosophic soft sets are presented. The definitions of distance, similarity and measures of entropy are introduced. Some formulas for Q-neutrosophic soft entropy were presented. The known Hamming, Euclidean and their normalized distances are generalized to make them well matched with the idea of Q-neutrosophic soft set. The distance measure is subsequently used to define the measure of similarity. Lastly, we expound three applications of the measures of Q-neutrosophic soft sets by applying entropy and the similarity measure to a medical diagnosis and decision making problems.

Entropy Measures on Neutrosophic Soft Sets and Its Application in Multi Attribute Decision Making

Author: I. Arockiarani

Publisher: Infinite Study

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Total Pages: 5

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The focus of the paper is to furnish the entropy measure for a neutrosophic set and neutrosophic soft set which is a measure of uncertainty and it permeates discourse and system. Various characterization of entropy measures are derived. Further we exemplify this concept by applying entropy in various real time decision making problems.

Entropy Measures for Plithogenic Sets and Applications in Multi-Attribute Decision Making

Author: Shio Gai Quek

Publisher: Infinite Study

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Total Pages: 17

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Plithogenic set is an extension of the crisp set, fuzzy set, intuitionistic fuzzy set, and neutrosophic sets, whose elements are characterized by one or more attributes, and each attribute can assume many values. Each attribute has a corresponding degree of appurtenance of the element to the set with respect to the given criteria. In order to obtain a better accuracy and for a more exact exclusion (partial order), a contradiction or dissimilarity degree is defined between each attribute value and the dominant attribute value. In this paper, entropy measures for plithogenic sets have been introduced.

New Entropy Measures Based on Neutrosophic Set and Their Applications to Multi-Criteria Decision Making

Author: Ali AYDOĞDU

Publisher: Infinite Study

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Total Pages: 6

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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.

Generalized Distance-Based Entropy and Dimension Root Entropy for Simplified Neutrosophic Sets

Author: Wen-Hua Cui

Publisher: Infinite Study

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Total Pages: 12

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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.

Cross Entropy Measures of Bipolar and Interval Bipolar Neutrosophic Sets and Their Application for Multi-Attribute Decision-Making

Author: Surapati Pramanik

Publisher: Infinite Study

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Total Pages: 25

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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.

Neutrosophic discrete geometric distribution

Author: Rehan Ahmad Khan Sherwani

Publisher: Infinite Study

Published: 2024-01-01

Total Pages: 23

ISBN-13:

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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.

An Entropy Measure for n-Cylindrical Fuzzy Neutrosophic Sets

Author: Sarannya Kumari R.

Publisher: Infinite Study

Published: 2024-01-01

Total Pages: 9

ISBN-13:

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n-Cylindrical fuzzy neutrosophic set (n-CyFNS) is a new variant of fuzzy neutrosophic sets. In this paper our aim is to introduce an entropy measure for n-CyFNS. Here we explained its properties along with examples. Two real life applications, one on better way of shopping and the second on teacher evaluation, based on this proposed entropy measure are also illustrated.