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Multi-attribute decision making with Pythagorean fuzzy sets via conversions to intuitionistic fuzzy sets and ORESTE method

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Journal of Control and Decision 2021年第3期8卷 372-383页

作者： Zhifu Tao Jiaming Zhu Ligang Zhou Jinpei Liu Huayou Chen School of Economics Anhui UniversityHefeiAnhuiPeople’s Republic of China School of Internet Anhui UniversityHefeiAnhuiPeople’s Republic of China School of Mathematical Sciences Anhui UniversityHefeiAnhuiPeople’s Republic of China China Institute of Manufacturing Development Nanjing University of Information Science and TechnologyNanjingJiangsuPeople’s Republic of China School of Business Anhui UniversityHefeiAnhuiPeople’s Republic of China

The aim of this paper is to study the conversions between Pythagorean fuzzy sets and Atanassov’s intuitionistic fuzzy ***,an ORESTE method based on multi-attribute decision making with Pythagorean fuzzy sets is developed by utilising the developed *** this paper,according to the geometric representations of Pythagorean fuzzy sets and Atanassov’s intuitionistic fuzzy sets,two types of conversions between the two fuzzy sets are constructed,which are further used to derive information measures include entropy and cross-entropy measures of Pythagorean fuzzy ***,by combining with the ORESTE method,a direct decision procedure for multi-attribute decision making with Pythagorean fuzzy information is ***,a numerical example of the evaluation of regional energy efficiency is shown to illustrate the feasibility and validity of the developed decision procedure.

关键词： Pythagorean fuzzy sets multi-attribute decision making Atanassov’s intuitionistic fuzzy sets ORESTE entropies

A New Approach to Time-Dependent Solutions to the Non-Linear Fokker-Planck Equations Related to Arbitrary Functions of Tsallis Entropy: A Mathematical Study and Investigation

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Journal of Modern Physics 2012年第5期3卷 420-429页

作者： Alireza Heidari Seyedali Vedad Mohammadali Ghorbani Institute for Advanced Studies Tehran Iran

The following article has been retracted due to the investigation of complaints received against it. Mr. Mohammadali Ghorbani (corresponding author and also the last author) cheated the authors’ name: Alireza Heidari and Seyedali Vedad. The scientific community takes a very strong view on this matter and we treat all unethical behavior such as plagiarism seriously. This paper published in Vol.3 No.5 420-429, 2012, has been removed from this site.

关键词： Non-Linear Fokker-Planck Equations Tsallis Entropy Generalized entropies

Entropy—A Universal Concept in Sciences

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Natural Science 2014年第7期6卷 552-564页

作者： Vladimír Majerník Mathematical Institute Slovak Academy of Sciences Bratislava Slovakia

Entropy represents a universal concept in science suitable for quantifying the uncertainty of a series of random events. We define and describe this notion in an appropriate manner for physicists. We start with a brief recapitulation of the basic concept of the theory probability being useful for the determination of the concept of entropy. The history of how this concept came into its to-day exact form is sketched. We show that the Shannon entropy represents the most adequate measure of the probabilistic uncertainty of a random object. Though the notion of entropy has been introduced in classical thermodynamics as a thermodynamic state variable it relies on concepts studied in the theory of probability and mathematical statistics. We point out that whole formalisms of statistical mechanics can be rewritten in terms of Shannon entropy. The notion “entropy” is differently understood in various science disciplines: in classical physics it represents the thermodynamical state variable;in communication theory it represents the efficiency of transmission of communication;in the theory of general systems the magnitude of the configurational order;in ecology the measure for bio-diversity;in statistics the degree of disorder, etc. All these notions can be mapped on the general mathematical concept of entropy. By means of entropy, the configurational order of complex systems can be exactly quantified. Besides the Shannon entropy, there exists a class of Shannon-like entropies which converge, under certain circumstances, toward Shannon entropy. The Shannon-like entropy is sometimes easier to handle mathematically then Shannon entropy. One of the important Shannon-like entropy is well-known Tsallis entropy. The application of the Shannon and Shannon-like entropies in science is really versatile. Besides the mentioned statistical physics, they play a fundamental role in the quantum information, communication theory, in the description of disorder, etc.

关键词： Probability Uncertainty Shannon Entropy Shannon-Like entropies

Statistical Inference of Truncated Weibull-Rayleigh Distribution: Its Properties and Applications

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Open Journal of Modelling and Simulation 2021年第3期9卷 281-298页

作者： Eman H. Khalifa Dina A. Ramadan B. S. El-Desouky Department of Mathematics Faculty of Science Mansoura University Mansoura Egypt

In this paper, we derived a new distribution named as truncated Weibull Rayleigh (TW-R) distribution. Its characterization and statistical properties are obtained, such as reliability function, hazard function, reversed hazard rate function, cumulative hazard rate function, quantile function, rth moment, incomplete moments, Rényi and q entropies and order statistic. Parameter estimation is implemented using method of maximum-likelihood estimation and Fisher information matrix is derived. Finally, application of the presented new distribution to a real data representing the failure times of 63 airbcraft Windshield is given and its goodness-of-fit is demonstrated. In addition to, comparisons to other models are implemented to show the flexibility of the presented model.

关键词： Rayleigh Distribution Truncated Weibull G-Family Moments entropies Quantile Function Order Statistic Maximum Likelihood Estimator

One Parameter Family of N-Qudit Werner-Popescu States: Bipartite Separability Using Conditional Quantum Relative Tsallis Entropy

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Journal of Quantum Information Science 2018年第1期8卷 12-23页

作者： Anantha S. Nayak Sudha A. R. Usha Devi A. K. Rajagopal Department of Physics Kuvempu University Shankaraghatta Shimoga India Inspire Institute Inc. Alexandria USA Department of Physics Bangalore University Bangalore India Harish-Chandra Research Institute Allahabad India Institute of Mathematical Sciences C.I.T. Campus Chennai India

The conditional version of sandwiched Tsallis relative entropy (CSTRE) is employed to study the bipartite separability of one parameter family of N-qudit Werner-Popescu states in their 1:N-1 partition. For all N, the strongest limitation on bipartite separability is realized in the limit and is found to match exactly with the separability range obtained using an algebraic method which is both necessary and sufficient. The theoretical superiority of using CSTRE criterion to find the bipartite separability range over the one using Abe-Rajagopal (AR) q-conditional entropy is illustrated by comparing the convergence of the parameter x with respect to q, in the implicit plots of AR q-conditional entropy and CSTRE.

关键词： Entropic Separability Criterion q-Conditional entropies Non-Commuting Version of Relative Entropy