Representation Theorems In A L-Fuzzy Set Theory Based Algebra For Morphology

1989 ◽  
Author(s):  
Divyendu Sinha ◽  
Charles R. Giardina
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Representation Theorems

GENERALIZED COMONOTONICALLY ADDITIVE OPERATORS: REPRESENTATIONS BY CHOQUET INTEGRALS

2002 ◽  
Vol 10 (04) ◽  
pp. 329-346
Author(s):  
HEINZ J. SKALA
Keyword(s):  
Artificial Intelligence ◽  
Decision Theory ◽  
Banach Spaces ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Integral Representations ◽  
Representation Theorems ◽  
Projection Property ◽  
Choquet Integrals

Operators which behave (sub-, super-) additive on comonotonic functions occur quite naturally in many contexts, e.g. in decision theory, artificial intelligence, and fuzzy set theory. In the present paper we define comonotonicity for Riesz spaces with the principal projection property and obtain integral representations (in terms of Bochner integrals) for comonotonically additive operators acting on Riesz with the principal projection property and taking values in certain Riesz- or Banach spaces. As easy corollaries we obtain essential generalizations of representation theorems à la schmeidler, Proc. Am. Math. Soc. 97 (1986), 255 – 261. The existence of the necessary convergence theorems makes it possible to extend our results to set-valued operators. This is the topic of a further paper.

Estimating construction waste generation in residential buildings: A fuzzy set theory approach in the Brazilian Amazon

2020 ◽  
Vol 265 ◽  
pp. 121779 ◽  
Author(s):  
Luiz Maurício Furtado Maués ◽  
Brisa do Mar Oliveira do Nascimento ◽  
Weisheng Lu ◽  
Fan Xue
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Residential Buildings ◽  
Brazilian Amazon ◽  
Theory Approach ◽  
Waste Generation ◽  
Construction Waste

Knowledge fusion method based on fuzzy set theory

2020 ◽  
Vol 38 (4) ◽  
pp. 3971-3979
Author(s):  
Yana Yuan ◽  
Huaqi Chai
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Fusion Method ◽  
Knowledge Fusion

INTRODUCTION TO FUZZY SET THEORY AND APPLICATIONS

1990 ◽  
Vol 33 (1) ◽  
pp. 0306-0313 ◽  
Author(s):  
X. Q. Gui ◽  
C. E. Goering
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory
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