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.

Degree Dominance Interval Relation-Based RSM in Intuitionistic Fuzzy Decision Systems

2011 ◽  
Vol 48-49 ◽  
pp. 357-361
Author(s):  
Bing Huang
Keyword(s):  
Knowledge Representation ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Decision Rules ◽  
Dominance Relation ◽  
Fuzzy Decision ◽  
Decision Systems ◽  
Intuitionistic Fuzzy ◽  
Interval Relation

By introducing a degree dominance relation to dominance interval intuitionistic fuzzy decision systems, we establish a degree dominance interval rough set model (RSM), which is mainly based on replacing the indiscernibility relation in classical rough set theory with the degree dominance interval relation. To simplify knowledge representation and extract some nontrivial simpler degree dominance interval intuitionistic fuzzy decision rules, we propose two attribute reductions of the degree dominance interval intuitionistic fuzzy decision systems that eliminate the redundant condition attributes that are not essential from the viewpoint of degree dominance interval intuitionistic fuzzy decision rules.

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