Book•
Theory and practice of uncertain programming
29 Apr 2003-
TL;DR: This book provides a self-contained, comprehensive and up-to-date presentation of uncertain programming theory, including numerous modeling ideas, hybrid intelligent algorithms, and applications in system reliability design, project scheduling problem, vehicle routing problem, facility location problem, and machine scheduling problem.
Abstract: Real-life decisions are usually made in the state of uncertainty such as randomness and fuzziness. How do we model optimization problems in uncertain environments? How do we solve these models? In order to answer these questions, this book provides a self-contained, comprehensive and up-to-date presentation of uncertain programming theory, including numerous modeling ideas, hybrid intelligent algorithms, and applications in system reliability design, project scheduling problem, vehicle routing problem, facility location problem, and machine scheduling problem. Researchers, practitioners and students in operations research, management science, information science, system science, and engineering will find this work a stimulating and useful reference.
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14 Aug 2007
TL;DR: Mathematicians, researchers, engineers, designers, and students in the field of mathematics, information science, operations research, industrial engineering, computer science, artificial intelligence, and management science will find this work a stimulating and useful reference.
Abstract: Uncertainty theory is a branch of mathematics based on normality, monotonicity, self-duality, and countable subadditivity axioms. The goal of uncertainty theory is to study the behavior of uncertain phenomena such as fuzziness and randomness. The main topics include probability theory, credibility theory, and chance theory. For this new edition the entire text has been totally rewritten. More importantly, the chapters on chance theory and uncertainty theory are completely new. This book provides a self-contained, comprehensive and up-to-date presentation of uncertainty theory. The purpose is to equip the readers with an axiomatic approach to deal with uncertainty. Mathematicians, researchers, engineers, designers, and students in the field of mathematics, information science, operations research, industrial engineering, computer science, artificial intelligence, and management science will find this work a stimulating and useful reference.
1,450 citations
Cites background from "Theory and practice of uncertain pr..."
...How to Represent a Schedule? Liu [75] suggested that a schedule should be represented by two decision vectors x and y, where x = (x1, x2, · · · , xn): integer decision vector representing n jobs with 1 ≤ xi ≤ n and xi 6= xj for all i 6= j, i, j = 1, 2, · · · , n....
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...Operational Plan Liu [75] suggested that an operational plan should be represented by three decision vectors x, y and t, where x = (x1, x2, · · · , xn): integer decision vector representing n customers with 1 ≤ xi ≤ n and xi 6= xj for all i 6= j, i, j = 1, 2, · · · , n....
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01 Jan 2009
TL;DR: In this article, a new uncertain calculus is proposed and applied to uncertain difierential equation, flnance, control, flltering and dynamical systems based on the uncertainty theory.
Abstract: In addition to the four axioms of uncertainty theory, this paper presents the flfth axiom called product measure axiom. This paper also gives an operational law of independent uncertain variables and a concept of entropy of continuous uncertain variables. Based on the uncertainty theory, a new uncertain calculus is proposed and applied to uncertain difierential equation, flnance, control, flltering and dynamical systems. Finally, an uncertain inference will be presented. c
987 citations
01 Jan 2008
TL;DR: In order to construct fuzzy counterparts of Brownian motion and stochastic calculus, some basic concepts of fuzzy process are proposed, including fuzzy calculus and fuzzy difierential equation, which are extended to hybrid process and uncertain process.
Abstract: This paper flrst reviews difierent types of uncertainty. In order to construct fuzzy counterparts of Brownian motion and stochastic calculus, this paper proposes some basic concepts of fuzzy process, including fuzzy calculus and fuzzy difierential equation. Those new concepts are also extended to hybrid process and uncertain process. A basic stock model is presented, thus opening up a way to fuzzy flnancial mathematics.
606 citations
Cites methods from "Theory and practice of uncertain pr..."
...In addition, a random fuzzy variable was proposed by Liu [7] as a fuzzy element taking “random variable” values....
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TL;DR: A comprehensive review of Uncertainty-Based Multidisciplinary Design Optimization (UMDO) theory and the state of the art in UMDO methods for aerospace vehicles is presented.
426 citations
Cites methods from "Theory and practice of uncertain pr..."
...36 uncertain systems [284]....
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...To address non-probabilistic uncertainties in optimization, fuzzy programming is also quickly developed [280-282], as well as the programming method for hybrid random and fuzzy uncertainties [283, 284]....
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TL;DR: An algorithm is devised that enables the placement of the cloudlets at user dense regions of the WMAN, and assigns mobile users to the placed cloudlets while balancing their workload, which indicates that the performance of the proposed algorithm is very promising.
Abstract: Mobile applications are becoming increasingly computation-intensive, while the computing capability of portable mobile devices is limited. A powerful way to reduce the completion time of an application in a mobile device is to offload its tasks to nearby cloudlets, which consist of clusters of computers. Although there is a significant body of research in mobile cloudlet offloading technology, there has been very little attention paid to how cloudlets should be placed in a given network to optimize mobile application performance. In this paper we study cloudlet placement and mobile user allocation to the cloudlets in a wireless metropolitan area network (WMAN). We devise an algorithm for the problem, which enables the placement of the cloudlets at user dense regions of the WMAN, and assigns mobile users to the placed cloudlets while balancing their workload. We also conduct experiments through simulation. The simulation results indicate that the performance of the proposed algorithm is very promising.
412 citations
References
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01 Aug 1996
TL;DR: A separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint.
Abstract: A fuzzy set is a class of objects with a continuum of grades of membership. Such a set is characterized by a membership (characteristic) function which assigns to each object a grade of membership ranging between zero and one. The notions of inclusion, union, intersection, complement, relation, convexity, etc., are extended to such sets, and various properties of these notions in the context of fuzzy sets are established. In particular, a separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint.
52,705 citations
TL;DR: It is rigorously established that standard multilayer feedforward networks with as few as one hidden layer using arbitrary squashing functions are capable of approximating any Borel measurable function from one finite dimensional space to another to any desired degree of accuracy, provided sufficiently many hidden units are available.
18,794 citations
Book•
[...]
21 Oct 1957
TL;DR: The more the authors study the information processing aspects of the mind, the more perplexed and impressed they become, and it will be a very long time before they understand these processes sufficiently to reproduce them.
Abstract: From the Publisher:
An introduction to the mathematical theory of multistage decision processes, this text takes a functional equation approach to the discovery of optimum policies. Written by a leading developer of such policies, it presents a series of methods, uniqueness and existence theorems, and examples for solving the relevant equations. The text examines existence and uniqueness theorems, the optimal inventory equation, bottleneck problems in multistage production processes, a new formalism in the calculus of variation, strategies behind multistage games, and Markovian decision processes. Each chapter concludes with a problem set that Eric V. Denardo of Yale University, in his informative new introduction, calls a rich lode of applications and research topics. 1957 edition. 37 figures.
14,187 citations
TL;DR: Much of what constitutes the core of scientific knowledge may be regarded as a reservoir of concepts and techniques which can be drawn upon to construct mathematical models of various types of systems and thereby yield quantitative information concerning their behavior.
12,530 citations