scholarly journals Belief Functions on MV-Algebras of Fuzzy Sets: An Overview

2014 ◽  
pp. 173-200 ◽  
Author(s):  
Tommaso Flaminio ◽  
Lluís Godo ◽  
Tomáš Kroupa
Keyword(s):  
Fuzzy Sets ◽  
Belief Functions ◽  
Mv Algebras

BZMVdM algebras and stonian MV-algebras (applications to fuzzy sets and rough approximations)

1999 ◽  
Vol 108 (2) ◽  
pp. 201-222 ◽  
Author(s):  
G. Cattaneo ◽  
R. Giuntini ◽  
R. Pilla
Keyword(s):  
Fuzzy Sets ◽  
Mv Algebras

scholarly journals Logics for belief functions on MV-algebras

2013 ◽  
Vol 54 (4) ◽  
pp. 491-512 ◽  
Author(s):  
Tommaso Flaminio ◽  
Lluís Godo ◽  
Enrico Marchioni
Keyword(s):  
Belief Functions ◽  
Mv Algebras

scholarly journals Loomis-sikorski theorem for σ-complete MV-algebras and ℓ-groups

2000 ◽  
Vol 68 (2) ◽  
pp. 261-277 ◽  
Author(s):  
Anatolij Dvurečenskij
Keyword(s):  
Fuzzy Sets ◽  
Homomorphic Image ◽  
Representation Theorem ◽  
Strong Unit ◽  
Direct Generalization ◽  
Mv Algebra ◽  
Mv Algebras

AbstractWe show that every σ-complete MV-algebra is an MV-σ-homomorphic image of some σ-complete MV- algebra of fuzzy sets, called a tribe, which is a system of fuzzy sets of a crisp set Ω containing 1Ω and closed under fuzzy complementation and formation of min {∑nfn, 1}. Since a tribe is a direct generalization of a σ-algebra of crisp subsets, the representation theorem is an analogue of the Loomis-Sikorski theorem for MV-algebras. In addition, this result will be extended also for Dedekind σ-complete ℓ-groups with strong unit.

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