Expected Value Operator of Random Fuzzy Variable and Random Fuzzy Expected Value Models

2003 ◽  
Vol 11 (02) ◽  
pp. 195-215 ◽  
Author(s):  
Yian-Kui Liu ◽  
Baoding Liu
Keyword(s):  
Fuzzy Variable ◽  
Expected Value ◽  
Fuzzy Simulation ◽  
Hybrid Intelligent Algorithm ◽  
Random Fuzzy Variable ◽  
Decision Systems ◽  
Expected Value Operator ◽  
Fuzzy Expected Value ◽  
Possibility Space ◽  
Definition Of

Random fuzzy variable is 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.

ANALYSIS AND ALGORITHMS OF BIFUZZY SYSTEMS

2004 ◽  
Vol 12 (03) ◽  
pp. 357-376 ◽  
Author(s):  
JIAN ZHOU ◽  
BAODING LIU
Keyword(s):  
Numerical Experiments ◽  
Fuzzy Variable ◽  
Expected Value ◽  
Real Numbers ◽  
Fuzzy Variables ◽  
Chance Distribution ◽  
Expected Value Operator ◽  
Possibility Space ◽  
Bifuzzy Variable

A fuzzy variable is a function from a possibility space to the set of real numbers, while a bifuzzy variable is a function from a possibility space to the set of fuzzy variables. In this paper, a concept of chance distribution is originally presented for bifuzzy variable, and the linearity of expected value operator of bifuzzy variable is proved. Furthermore, bifuzzy simulations are designed and illustrated by some numerical experiments.

scholarly journals A FUZZY BASED APPROACH FOR EARLY REQUIREMENT PRIORITIZATION

2015 ◽  
Vol 15 (2) ◽  
pp. 6480-6490
Author(s):  
Mohd Muqeem ◽  
Dr. Md. Rizwan Beg
Keyword(s):  
Software Development ◽  
Early Phase ◽  
Fuzzy Variable ◽  
Requirement Engineering ◽  
Expected Value ◽  
Inference System ◽  
Complex Time ◽  
Fuzzy Variables ◽  
Expected Value Operator ◽  
Requirement Prioritization

The importance of the prioritization in commercial software development has been analyzed by many researchers. The gathered requirements are required to be put into an order of some priority. In other words we can say that there is a need to prioritize the requirements. It is evident that most of the approaches and techniques proposed in recent research to prioritize the requirements have not been widely adopted. These approaches are too complex, time consuming, or inconsistent and difficult to implement In this paper we propose a fuzzy based approach for requirement prioritization in which  requirement are prioritized in early phase of requirement engineering as post elicitation step. This category of prioritization is known as early requirement prioritization. The proposed fuzzy based approach considers the nature of requirements by modeling their attributes as fuzzy variables. As such, these variables are integrated into a fuzzy based inference system in which the requirements represented as input attributes and ranked via the expected value operator of a fuzzy variable.

Computing the Risk Indicators in Fuzzy Systems

2012 ◽  
Vol 5 (4) ◽  
pp. 63-84 ◽  
Author(s):  
Irina Georgescu
Keyword(s):  
Risk Aversion ◽  
Risk Premium ◽  
Stochastic Dominance ◽  
Probabilistic Models ◽  
Fuzzy Variable ◽  
Risk Indicators ◽  
Credibility Theory ◽  
Fuzzy Variables ◽  
Risk Situation ◽  
Definition Of

The modeling of complex risk situations imposes the existence of multiple ways to represent the risk and compare the risk situations between them. In probabilistic models, risk is described by random variables and risk situations are compared by stochastic dominance. In possibilistic or credibilistic models, risk is represented by fuzzy variables. This paper concerns three indicators of dominance associated with fuzzy variables. This allows the definition of three notions of fuzzy dominance: dominance in possibility, dominance in necessity and dominance in credibility. These three types of dominance are possibilistic and credibilistic versions of stochastic dominance. Each type offers a modality of ranking risk situations modeled by fuzzy variables. In the paper some properties of the three indicators of dominance are proved and relations between the three types of fuzzy dominance are established. For triangular fuzzy numbers formulas for the computation of these indicators are obtained. The paper also contains a contribution on a theory of risk aversion in the context of credibility theory. Using the credibilistic expected utility a notion of risk premium is defined as a measure of risk aversion of an agent in front of a risk situation described by a fuzzy variable and an approximate calculation formula of this indicator is proved.

A Fuzzy Programming Model of Supplier Selection

2012 ◽  
Vol 468-471 ◽  
pp. 668-673 ◽  
Author(s):  
Hua Jiang ◽  
Zhi Gang Lu
Keyword(s):  
Supplier Selection ◽  
Programming Model ◽  
Fuzzy Programming ◽  
Chance Constrained Programming ◽  
Hybrid Intelligent Algorithm ◽  
Fuzzy Variables ◽  
Fuzzy Expected Value ◽  
Order Quantities ◽  
Constrained Programming ◽  
Fuzzy Programming Model

An integrated supplier selection problem under fuzzy environment is studied in this paper. Firstly, the linear weight method is used to calculate the scores of suppliers according to their different attributes, such as: quality, service, warranty, delivery, reputation and position, which are assumed as fuzzy variables. Secondly, a fuzzy expected value programming model and a fuzzy chance-constrained programming model are proposed to select the best combination of the suppliers and determine the order quantities. A hybrid intelligent algorithm, based on fuzzy simulation, genetic algorithm and neural network, is used to solve the two models. Finally, a numerical example is given to illustrate the effectiveness of the proposed models.

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