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 of fuzzy variable and fuzzy expected value models

Foundations Of Statistics

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.

Theory and practice of uncertain programming

The notion of fuzziness as defined in this paper relates to situations in which the source of imprecision is not a random variable or a stochastic process, but rather a class or classes which do not possess sharply defined boundaries, e.g., the “class of bald men,” or the “class of numbers which are much greater than 10,” or the “class of adaptive systems,” etc. A basic concept which makes it possible to treat fuzziness in a quantitative manner is that of a fuzzy set, that is, a class in which there may be grades of membership intermediate between full membership and non-membership. Thus, a fuzzy set is characterized by a membership function which assigns to each object its grade of membership (a number lying between 0 and 1) in the fuzzy set. After a review of some of the relevant properties of fuzzy sets, the notions of a fuzzy system and a fuzzy class of systems are introduced and briefly analyzed. The paper closes with a section dealing with optimization under fuzzy constraints in which an approach to...

Fuzzy sets and systems

http://geocities.ws/smhurtado/2000-111-1-3-283.pdf

Possibilistic linear programming: a brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem

Fuzzy DEA: a perceptual evalution method

Portfolio selection based on fuzzy probabilities and possibility distributions

Portfolio selection based on upper and lower exponential possibility distributions

In this paper, two kinds of possibility distributions, namely, upper and lower possibility distributions are identified to reflect experts’ knowledge in portfolio selection problems. Portfolio selection models based on these two kinds of distributions are formulated by quadratic programming problems. It can be said that a portfolio return based on the lower possibility distribution has smaller possibility spread than the one on the upper possibility distribution. In addition, a possibility risk can be defined as an interval given by the spreads of the portfolio returns from the upper and the lower possibility distributions to reflect the uncertainty in real investment problems. A numerical example of a portfolio selection problem is given to illustrate our proposed approaches. ” 1999 Elsevier Science B.V. All rights reserved.

Theory and Methodology Portfolio selection based on upper and lower exponential possibility distributions

Introduction: Possibility Theory in Operations Research Possibility Models Theory of Possibilistic Systems Based on Exponential Possibility Distributions Identification of Possibility Distributions Possibilistic Regression Analysis Possibilistic Portfolio Selection Problems Discriminant Analysis Based on Possibility Distributions Rough Set Analysis.

Peijun Guo

Papers

Fuzzy DEA: a perceptual evalution method

Portfolio selection based on fuzzy probabilities and possibility distributions

Portfolio selection based on upper and lower exponential possibility distributions

Theory and Methodology Portfolio selection based on upper and lower exponential possibility distributions

Possibilistic Data Analysis for Operations Research