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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 has been studied rather extensively in the last few years, both from an applications point of view and a theoretical one. Most of the theory goes through when is replaced by any two...
Monads and their t-algebras have been studied as an important link between categories and universal algebra. Monads of fuzzy sets, that is, monads which are mappings from sets to complete Heyting algebras, have also been studied for some time (see, e.g.,). This paper reviews two important kinds of monads in this category, singleton monads and fuzzy theories. It is shown that fuzzy theories may have...
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