Some types of filters in MTL-algebras

The aim of this work is to introduce the concepts of IMTL-filters and strong MTL-filters in MTL-algebras and show that these filters are related to IMTL-algebras and strong MTL-algebras, respectively. We also introduce the concepts of EIMTL and associative filters in MTL-algebras. The relationships...

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Published inFuzzy sets and systems Vol. 187; no. 1; pp. 92 - 102
Main Authors Borzooei, R.A., Khosravi Shoar, S., Ameri, R.
Format Journal Article
LanguageEnglish
Published Kidlington Elsevier B.V 16.01.2012
Elsevier
Subjects
(positive) Implicative filter
Algebra
Applied sciences
Associative
Associative rings and algebras
BL-algebra
Circuit properties
Computer science; control theory; systems
Construction
Digital circuits
EIMTL-filter
Electric, optical and optoelectronic circuits
Electronic circuits
Electronics
Exact sciences and technology
Fantastic filter
Fuzzy set theory
IMTL-filter
Information, signal and communications theory
Mathematical methods
Mathematics
Miscellaneous
MTL-algebra
Quotients
Sciences and techniques of general use
Strong filter
Telecommunications and information theory
Theoretical computing
BL-algebra
IMTL-filter
Fantastic filter
EIMTL-filter
MTL-algebra
Strong filter
(positive) Implicative filter
Fuzzy system
Information processing
Fuzzy set
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Abstract The aim of this work is to introduce the concepts of IMTL-filters and strong MTL-filters in MTL-algebras and show that these filters are related to IMTL-algebras and strong MTL-algebras, respectively. We also introduce the concepts of EIMTL and associative filters in MTL-algebras. The relationships between these filters and quotient algebras that are constructed via these filters are described. We clarify that EIMTL, IMTL and fantastic filters coincide in BL-algebras, whereas they have different properties in MTL-algebras; moreover, the relations between them are delineated. We prove that strong filters include some current filters such as implicative, positive implicative and fantastic filters.
AbstractList The aim of this work is to introduce the concepts of IMTL-filters and strong MTL-filters in MTL-algebras and show that these filters are related to IMTL-algebras and strong MTL-algebras, respectively. We also introduce the concepts of EIMTL and associative filters in MTL-algebras. The relationships between these filters and quotient algebras that are constructed via these filters are described. We clarify that EIMTL, IMTL and fantastic filters coincide in BL-algebras, whereas they have different properties in MTL-algebras; moreover, the relations between them are delineated. We prove that strong filters include some current filters such as implicative, positive implicative and fantastic filters.
Author Khosravi Shoar, S.
Ameri, R.
Borzooei, R.A.
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  surname: Borzooei
  fullname: Borzooei, R.A.
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  givenname: S.
  surname: Khosravi Shoar
  fullname: Khosravi Shoar, S.
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  organization: Department of Mathematics, Payam Noor University, Tehran, Iran
– sequence: 3
  givenname: R.
  surname: Ameri
  fullname: Ameri, R.
  email: rameri@ut.ac.ir
  organization: Department of Mathematics, Tehran University, Tehran, Iran
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Cites_doi 10.1023/A:1022935811257
10.1007/s00500-007-0178-7
10.1007/s00500-007-0182-y
10.1016/j.fss.2007.05.003
10.1007/s001530100088
10.1016/S0165-0114(01)00098-7
10.1002/malq.200310082
10.1007/s00500-005-0534-4
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Issue 1
Keywords BL-algebra
IMTL-filter
Fantastic filter
EIMTL-filter
MTL-algebra
Strong filter
(positive) Implicative filter
Fuzzy system
Information processing
Fuzzy set
Language English
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Snippet The aim of this work is to introduce the concepts of IMTL-filters and strong MTL-filters in MTL-algebras and show that these filters are related to...
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StartPage 92
SubjectTerms (positive) Implicative filter
Algebra
Applied sciences
Associative
Associative rings and algebras
BL-algebra
Circuit properties
Computer science; control theory; systems
Construction
Digital circuits
EIMTL-filter
Electric, optical and optoelectronic circuits
Electronic circuits
Electronics
Exact sciences and technology
Fantastic filter
Fuzzy set theory
IMTL-filter
Information, signal and communications theory
Mathematical methods
Mathematics
Miscellaneous
MTL-algebra
Quotients
Sciences and techniques of general use
Strong filter
Telecommunications and information theory
Theoretical computing
Title Some types of filters in MTL-algebras
URI https://dx.doi.org/10.1016/j.fss.2011.09.001
https://search.proquest.com/docview/963896272
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