boolean filters
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2020 ◽  
Vol 39 (3) ◽  
pp. 3949-3956
Author(s):  
Zhi Qiang Liu ◽  
Zhen Ming Ma

The present paper investigates the hesitant fuzzy filters on residuated lattices. A one-to-one correspondence between the set of all hesitant fuzzy filters and the set of all hesitant fuzzy congruences is established and a quotient residuated lattice with respect to a hesitant fuzzy filter is induced. Furthermore, several special types of hesitant fuzzy filters such as hesitant fuzzy implicative, regular and Boolean filters are introduced, and some alternative definitions of them are obtained, then some typical logical algebras are characterized by these identity forms.


2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Jianming Zhan ◽  
Qi Liu ◽  
Hee Sik Kim

Molodtsov’s soft set theory provides a general mathematical framework for dealing with uncertainty. The concepts of(M,N)-SIimplicative (Boolean) filters ofBL-algebras are introduced. Some good examples are explored. The relationships between(M,N)-SIfilters and(M,N)-SIimplicative filters are discussed. Some properties of(M,N)-SIimplicative (Boolean) filters are investigated. In particular, we show that(M,N)-SIimplicative filters and(M,N)-SIBoolean filters are equivalent.


Author(s):  
Mukkamala Sambasiva Rao ◽  
K. P. Shum

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Zhen Ming Ma

Fuzzy filters and their generalized types have been extensively studied in the literature. In this paper, a one-to-one correspondence between the set of all generalized fuzzy filters and the set of all generalized fuzzy congruences is established, a quotient residuated lattice with respect to generalized fuzzy filter is induced, and several types of generalized fuzzyn-fold filters such as generalized fuzzyn-fold positive implicative (fantastic and Boolean) filters are introduced; examples and results are provided to demonstrate the relations among these filters.


2007 ◽  
Vol 177 (24) ◽  
pp. 5725-5738 ◽  
Author(s):  
Liu Lianzhen ◽  
Li Kaitai

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