Type-2 operations on finite chains

Type-2 operations on finite chains

The algebra of truth values for fuzzy sets of type-2 consists of all mappings from the unit interval into itself, with operations certain convolutions of these mappings with respect to pointwise max and min. This algebra generalizes the truth-value algebras of both type-1 and of interval-valued fuzzy sets, and has been studied rather extensively both from a theoretical and applied point of view...

Smooth associative operations on finite chains

Operations on Concavoconvex Type-2 Fuzzy Sets

about to represent. Once the membership function has been established (estimated or defined), the concept is described very precisely as the membership values are exact numerical quantities. This seems to raise a certain dilemma of excessive precision in describing imprecise phenomena. In fact, this concern has already sparked a lot of debates starting from the very inception of fuzzy sets.” Co...

Operations on type-2 fuzzy sets

In this paper, we discuss set operations on type-2 fuzzy sets (including join and meet under minimum=product t-norm), algebraic operations, properties of membership grades of type-2 sets, and type-2 relations and their compositions. All this is needed to implement a type-2 fuzzy logic system (FLS). c © 2001 Elsevier Science B.V. All rights reserved.

Semilattice Operations on Finite Subsets

In the article we deal with a binary operation that is associative, commutative. We define for such an operation a functor that depends on two more arguments: a finite set of indices and a function indexing elements of the domain of the operation and yields the result of applying the operation to all indexed elements. The definition has a restriction that requires that either the set of indices...