Expected value of fuzzy variable and fuzzy expected value models

2002 ◽  
Vol 10 (4) ◽  
pp. 445-450 ◽  
Author(s):  
Baoding Liu ◽  
Yian-Kui Liu
Keyword(s):  
Fuzzy Variable ◽  
Expected Value ◽  
Fuzzy Expected Value

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.

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.

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.

Weighted Fuzzy Averages in Fuzzy Environment: Part I. Insufficient Expert Data and Fuzzy Averages

2003 ◽  
Vol 11 (02) ◽  
pp. 139-157 ◽  
Author(s):  
G. Sirbiladze ◽  
A. Sikharulidze
Keyword(s):  
Expected Value ◽  
Fuzzy Measure ◽  
Construction Process ◽  
Weighted Averages ◽  
The Third ◽  
Fuzzy Environment ◽  
Fuzzy Expected Value ◽  
Interval Extension ◽  
Finite Set ◽  
Sampling Probability

Three new versions of the most typical value (MTV)1,2 of the population (generalized weighted averages) are introduced. The first version, WFEVg, is a generalization of the weighted fuzzy expected value (WFEV)3 for any fuzzy measure g on a finite set and it coincides with the WFEV when a sampling probability distribution is used. The second and the third version are respectively the weighted fuzzy expected intervals WFEI and WFEIg which are generalizations of the WFEV, namely, MTV s of the population for a sampling distribution and for any fuzzy measure g on a finite set, respectively, when the fuzzy expected interval (FEI)4 exists but the fuzzy expected value (FEV)4 does not. The construction process is based on the Friedman-Schneider-Kandel (FSK)3 principle and results in the new MTV s called the WFEI and the WFEIg when the combinatorial interval extension of a function5 is used.

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