ABSORBENT ORDERED FILTERS AND THEIR FUZZIFICATIONS IN IMPLICATIVE SEMIGROUPS

Document Type: Research Paper

Authors

1 Department of Mathematics Education and (RINS), Gyeongsang National University, Chinju 660-701, Korea

2 Department of Mathematics, University of Ulsan, Ulsan 680-749, Korea

3 Department of Information Technology, Salalah College of Technology, Post Box: 608, Salalah-211, Sultanate of Oman

Abstract

The notion of absorbent ordered filters in implicative semigroups
is introduced, and its fuzzification is considered. Relations among (fuzzy) ordered
filters, (fuzzy) absorbent ordered filters, and (fuzzy) positive implicative
ordered filters are stated. The extensionproperty for (fuzzy) absorbent ordered
filters is established. Conditions for (fuzzy) ordered filters to be (fuzzy)
absorbent ordered filters are provided. The notions of normal/maximal fuzzy
absorbent ordered filters and complete absorbent ordered filters are introduced
and their properties are investigated.

Keywords


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