The Experts below are selected from a list of 201 Experts worldwide ranked by ideXlab platform
Weihua Xu - One of the best experts on this subject based on the ideXlab platform.
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probabilistic rough set model based on dominance relation
Rough Sets and Knowledge Technology, 2014Co-Authors: Wentao Li, Weihua XuAbstract:Unlike Pawlak rough set, probabilistic rough set models allow a tolerance inaccuracy in lower and upper approximations. Dominance relation cannot establish Probability Measure Space for the universe. In this paper, the basic set assignment function, namely partition function is introduced into our work, which can transform the non-Probability Measure generated by dominance relation into a Probability Measure Space. The probabilistic rough set model is established based on dominance relation, and explained clearly through an example.
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RSKT - Probabilistic Rough Set Model Based on Dominance Relation
Rough Sets and Knowledge Technology, 2014Co-Authors: Wentao Li, Weihua XuAbstract:Unlike Pawlak rough set, probabilistic rough set models allow a tolerance inaccuracy in lower and upper approximations. Dominance relation cannot establish Probability Measure Space for the universe. In this paper, the basic set assignment function, namely partition function is introduced into our work, which can transform the non-Probability Measure generated by dominance relation into a Probability Measure Space. The probabilistic rough set model is established based on dominance relation, and explained clearly through an example.
Wentao Li - One of the best experts on this subject based on the ideXlab platform.
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probabilistic rough set model based on dominance relation
Rough Sets and Knowledge Technology, 2014Co-Authors: Wentao Li, Weihua XuAbstract:Unlike Pawlak rough set, probabilistic rough set models allow a tolerance inaccuracy in lower and upper approximations. Dominance relation cannot establish Probability Measure Space for the universe. In this paper, the basic set assignment function, namely partition function is introduced into our work, which can transform the non-Probability Measure generated by dominance relation into a Probability Measure Space. The probabilistic rough set model is established based on dominance relation, and explained clearly through an example.
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RSKT - Probabilistic Rough Set Model Based on Dominance Relation
Rough Sets and Knowledge Technology, 2014Co-Authors: Wentao Li, Weihua XuAbstract:Unlike Pawlak rough set, probabilistic rough set models allow a tolerance inaccuracy in lower and upper approximations. Dominance relation cannot establish Probability Measure Space for the universe. In this paper, the basic set assignment function, namely partition function is introduced into our work, which can transform the non-Probability Measure generated by dominance relation into a Probability Measure Space. The probabilistic rough set model is established based on dominance relation, and explained clearly through an example.
Deyi Li - One of the best experts on this subject based on the ideXlab platform.
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RSKT - Comparative study of type-2 fuzzy sets and cloud model
Lecture Notes in Computer Science, 2010Co-Authors: Deyi Li, Tao Wu, Guisheng ChenAbstract:The mathematical representation of a concept with uncertainty is one of foundations of Artificial Intelligence. Type-2 fuzzy sets study fuzziness of the membership grade to a concept. Cloud model, based on Probability Measure Space, automatically produces random membership grades of a concept through a cloud generator. The two methods both concentrate on the essentials of uncertainty and have been applied in many fields for more than ten years. However, their mathematical foundations are quite different. The detailed comparative study will discover the relationship between each other, and provide a fundamental contribution to Artificial Intelligence with uncertainty.
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RSKT - Comparative study on mathematical foundations of type-2 fuzzy set, rough set and cloud model
Lecture Notes in Computer Science, 2010Co-Authors: Deyi LiAbstract:Mathematical representation of a concept with uncertainty is one of foundations of Artificial Intelligence. The type-2 fuzzy set introduced by Mendel studies fuzziness of the membership grade of a concept. Rough set proposed by Pawlak defines an uncertain concept through two crisp sets. Cloud model, based on Probability Measure Space, automatically produces random membership grades of a concept through a cloud generator. The three methods all concentrate on the essentials of uncertainty and have been applied in many fields for more than ten years. However, their mathematical foundations are quite different. The detailed comparative study on the three methods will discover the relationship in the betweens, and provide a fundamental contribution to Artificial Intelligence with uncertainty.
Gershon Wolansky - One of the best experts on this subject based on the ideXlab platform.
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On Semi-discrete Monge Kantorovich and generalized partitions
arXiv: Optimization and Control, 2012Co-Authors: Gershon WolanskyAbstract:Let $X$ a Probability Measure Space and $\psi_1....\psi_N$ measurable, real valued functions on $X$. Consider all possible partitions of $X$ into $N$ disjoint subdomains $X_i$ on which $\int_{X_i}\psi_i$ are prescribed. We address the question of characterizing the set $(m_1,,,m_N) \in \R^N$ for which there exists a partition $X_1, ... X_N$ of $X$ satisfying $\int_{X_i}\psi_i= m_i$ and discuss some optimization problems on this set of partitions. The relation of this problem to semi-discrete version of optimal mass transportation is discussed as well.
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On semi-discrete Monge problem and generalized optimal partitions
arXiv: Optimization and Control, 2012Co-Authors: Gershon WolanskyAbstract:Let $X$ a Probability Measure Space and $\psi_1....\psi_N$ measurable, real valued functions on $X$. Consider all possible partitions of $X$ into $N$ disjoint subdomains $X_i$ on which $\int_{X_i}\psi_i$ are prescribed. We address the question of characterizing the set $(m_1,,,m_N) \in R^N$ for which there exists a partition $X_1, ...X_N$ of $X$ satisfying $\int_{X_i}\psi_i= m_i$ and discuss some optimization problems on this set of partitions. The relation of this problem to semi-discrete version of optimal mass transportation is discussed as well.
William J. Padgett - One of the best experts on this subject based on the ideXlab platform.
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Nonlinear Stochastic Integral-Equation of Hammerstein Type
2010Co-Authors: William J. PadgettAbstract:A nonlinear stochastic integral equation of the Hammerstein type in the form x(t; c) = h(t; co) + f k(t, s; co)f (s, x(s; co)) dy (s) is studied where t E S, a v-finite Measure Space with certain properties, co E Q, the supporting set of a Probability Measure Space (Q, A, P), and the integral is a Bochner integral. A random solution of the equation is defined to be a second order vector-valued stochastic process x(t; co) on S which satisfies the equation almost certainly. Using certain Spaces of functions, which are Spaces of second order vector-valued stochastic processes on S, and fixed point theory, several theorems are proved which give conditions such that a unique random solution exists.