Identification of fuzzy sets with a class of canonically induced random sets

1980 ◽  
Author(s):  
Irwin R. Goodman
Keyword(s):  
Fuzzy Sets ◽  
Random Sets

Approximation techniques for the transformation of fuzzy sets into random sets

2008 ◽  
Vol 159 (3) ◽  
pp. 270-288 ◽  
Author(s):  
Mihai Cristian Florea ◽  
Anne-Laure Jousselme ◽  
Dominic Grenier ◽  
Éloi Bossé
Keyword(s):  
Fuzzy Sets ◽  
Random Sets ◽  
Approximation Techniques

NOVEL APPROACHES FOR THE TRANSFORMATION OF FUZZY MEMBERSHIP FUNCTION INTO BASIC PROBABILITY ASSIGNMENT BASED ON UNCERTAINTY OPTIMIZATION

2013 ◽  
Vol 21 (02) ◽  
pp. 289-322 ◽  
Author(s):  
DEQIANG HAN ◽  
CHONGZHAO HAN ◽  
YONG DENG
Keyword(s):  
Fuzzy Sets ◽  
Set Theory ◽  
Rough Set Theory ◽  
The Body ◽  
Random Sets ◽  
Fuzzy Membership Function ◽  
Uncertain Information ◽  
Unified Framework ◽  
Theoretical Frameworks ◽  
Uncertainty Reasoning

With the development of uncertainty reasoning and information fusion, there have emerged several theories including fuzzy set theory, Dempster-Shafer evidence theory, probability theory and rough set theory, etc., for representing and dealing with the uncertain information. When the fusion of the uncertain information originated from different sources is needed, how to construct a general framework for different theories of uncertainty or how to establish the connection between different theoretical frameworks has become a crucial problem. Particularly, to combine two kinds of information represented respectively by the BPA and the FMF, this paper proposes two transformations of an FMF into a BPA by solving a constrained maximization or minimization optimization problem. The objective function is the uncertainty degree of the body of evidence (BOE) and the corresponding constraints are established based on the given FMF. In fact the transformation of an FMF into a BPA is the transformation of fuzzy sets into random sets, which is currently accepted as a unified framework for several theories of uncertainty. Our proposed approaches have no predefinition of focal elements and they can be used as the general transformations of fuzzy sets into random sets. Some examples and analyses are provided to illustrate and justify the rationality and effectiveness of the proposed approaches.

scholarly journals Comparing Fuzzy Sets and Random Sets to Model the Uncertainty of Fuzzy Shorelines

2017 ◽  
Vol 9 (9) ◽  
pp. 885 ◽  
Author(s):  
Ratna Sari Dewi ◽  
Wietske Bijker ◽  
Alfred Stein
Keyword(s):  
Fuzzy Sets ◽  
Random Sets
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