Some types of filters in MTL-algebras

• Published in: Fuzzy sets and systems Vol. 187; no. 1; pp. 92 - 102
• Main Authors: Borzooei, R.A., Khosravi Shoar, S., Ameri, R.
• Format: Journal Article
• Language: English
• 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
• ISSN: 0165-0114; 1872-6801
• DOI: 10.1016/j.fss.2011.09.001

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.