Lattices of convex normal functions

13 years 4 months ago

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The algebra of truth values of type-2 fuzzy sets is the set of all functions from the unit interval into itself, with operations de ned 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. Key words: Type-2 fuzzy sets, normal and convex fuzzy sets, complete lattice, De Morgan algebra, continuous lattice

John Harding, Carol L. Walker, Elbert A. Walker

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