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...
Saved in:
Published in | Fuzzy sets and systems Vol. 187; no. 1; pp. 92 - 102 |
---|---|
Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Kidlington
Elsevier B.V
16.01.2012
Elsevier |
Subjects | |
Online Access | Get full text |
Cover
Loading…
Summary: | 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. |
---|---|
Bibliography: | ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
ISSN: | 0165-0114 1872-6801 |
DOI: | 10.1016/j.fss.2011.09.001 |