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The purpose of this paper is to give a straightforward mathematical treatment of algebras of fuzzy truth values for type-2 fuzzy sets.
This paper presents a framework for fuzzy set theory in which fuzzy values are intervals.
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… (More)
In this paper, we examine and compare De Morgan-, Kleene-, and Booleandisjunctive and conjunctive normal forms and consider their role in fuzzy settings. In particular, we describe normal forms and… (More)
The setup of a mathematical propositional logic is given in algebraic terms, describing exactly when two choices of truth value algebras give the same logic. The propositional logic obtained when the… (More)
Fuzzy logic and neural networks provide new methods for designing control systems. Fuzzy logic controllers do not require a complete analytical model of a dynamic system and can provide… (More)
The lattice Lu of upper semicontinuous convex normal functions with convolution ordering arises in studies of type-2 fuzzy sets. In 2002, M. Kawaguchi and M. Miyakoshi  showed that this lattice is… (More)
This paper is concerned with the definition of t-norms on the algebra of truth values of type-2 fuzzy sets. Our proposed definition extends the definition of ordinary t-norms on the unit interval and… (More)
We focus on a particular type of multi-criteria aggregation imperative called prioritized aggregation. This imperative is characteristic of situations where lack of satisfaction for criteria denoted… (More)
The algebra of truth values for fuzzy sets of type-2, due to Zadeh, contains as subalgebras those of type-1 and of interval-valued fuzzy sets. It also contains many other interesting subalgebras,… (More)