Yian-Kui Liu

Bio: Yian-Kui Liu is an academic researcher from Tsinghua University. The author has contributed to research in topics: Fuzzy classification & Fuzzy number. The author has an hindex of 5, co-authored 5 publications receiving 2400 citations. Previous affiliations of Yian-Kui Liu include Hebei University.

Expected value of fuzzy variable and fuzzy expected value models

Abstract: This paper will present a novel concept of expected values of fuzzy variables, which is essentially a type of Choquet integral and coincides with that of random variables. In order to calculate the expected value of general fuzzy variable, a fuzzy simulation technique is also designed. Finally, we construct a spectrum of fuzzy expected value models, and integrate fuzzy simulation, neural network, and genetic algorithms to produce a hybrid intelligent algorithm for solving general fuzzy expected value models.

Expected value operator of random fuzzy variable and random fuzzy expected value models

Abstract: Random fuzzy variable is a mapping from a possibility space to a collection of random variables This paper first presents a new definition of the expected value operator of a random fuzzy variable, and proves the linearity of the operator Then, a random fuzzy simulation approach, which combines fuzzy simulation and random simulation, is designed to estimate the expected value of a random fuzzy variable Based on the new expected value operator, three types of random fuzzy expected value models are presented to model decision systems where fuzziness and randomness appear simultaneously In addition, random fuzzy simulation, neural networks and genetic algorithm are integrated to produce a hybrid intelligent algorithm for solving those random fuzzy expected valued models Finally, three numerical examples are provided to illustrate the feasibility and the effectiveness of the proposed algorithm

Fuzzy Random Variables: A Scalar Expected Value Operator

Abstract: Fuzzy random variable has been defined in several ways in literature. This paper presents a new definition of fuzzy random variable, and gives a novel definition of scalar expected value operator for fuzzy random variables. Some properties concerning the measurability of fuzzy random variable are also discussed. In addition, the concept of independent and identically distributed fuzzy random variables is introduced. Finally, a type of law of large numbers is proved.

Uncertainty Theory

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.

Theory and practice of uncertain programming

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.

Some Research Problems in 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

Fuzzy Process, 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.

A survey of credibility theory

Abstract: This paper provides a survey of credibility theory that is a new branch of mathematics for studying the behavior of fuzzy phenomena. Some basic concepts and fundamental theorems are introduced, including credibility measure, fuzzy variable, membership function, credibility distribution, expected value, variance, critical value, entropy, distance, credibility subadditivity theorem, credibility extension theorem, credibility semicontinuity law, product credibility theorem, and credibility inversion theorem. Recent developments and applications of credibility theory are summarized. A new idea on chance space and hybrid variable is also documented.