Interval-valued (α,β)-fuzzy K-algebras

Authors:
M. Akram;K. H. Dar;K. P. Shum
Affiliations:
Punjab University College of Information Technology, University of the Punjab, Old Campus, Lahore-54000, Pakistan;Department of Mathematics, G. C. University Lahore, PO Box 54000, Pakistan;Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong
Venue:
Applied Soft Computing
Year:
2011

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Abstract

The notion of interval-valued fuzzy sets was first introduced by Zadeh in 1975 as a generalization of fuzzy sets. Using the concept of interval-valued fuzzy sets, we introduce a new kind of generalized fuzzy subalgebra of a K-algebra called, an interval-valued (@a,@b)-fuzzy subalgebra. We present some interesting properties of an interval-valued (@a,@b)-fuzzy subalgebra of a K-algebra. Some characterization theorems of the interval-valued (@?,@?@?q)-fuzzy subalgebra are established. Next we investigate the properties of interval-valued fuzzy subalgebras with thresholds. Finally we present characterization theorems of implication based interval-valued fuzzy subalgebras.