Lattices of convex normal functions

Authors:
John Harding;Carol Walker;Elbert Walker
Affiliations:
Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM 88003, USA;Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM 88003, USA;Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM 88003, USA
Venue:
Fuzzy Sets and Systems
Year:
2008

Citing 1
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Abstract

The algebra of truth values of type-2 fuzzy sets is the set of all functions from the unit interval into itself, with operations defined in terms of certain convolutions of these functions with respect to pointwise max and min. This algebra has been studied rather extensively, both from a theoretical and from a practical point of view. It has a number of interesting subalgebras, and this paper is about the subalgebra of all convex normal functions, and closely related ones. These particular algebras are De Morgan algebras, and our concern is principally with their completeness as lattices. A special feature of our treatment is a representation of these algebras as monotone functions with pointwise order, making the operations more intuitive.