Adding fuzziness to terms and powerobjects using a monadic approach

Authors:
Patrik Eklund;Jari Kortelainen;Lawrence Neff Stout
Affiliations:
Department of Computing Science, Umeå University, Sweden;Department of Information and Media Technology, Mikkeli University of Applied Sciences, Finland;Department of Mathematics and Computer Science, Illinois Wesleyan University, Illinois, USA
Venue:
Fuzzy Sets and Systems
Year:
2012

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Abstract

Fuzzy mathematics often starts by taking a piece of classical mathematics and introducing fuzziness to existing mathematical concepts, and then proceeds to a more essential adoption of a fuzzy perspective. This paper explores this progression for two important monads: the powerset monad and its generalizations to fuzzy powerobjects, and the term monad and its generalization to using fuzzy sets of operators. This brings together two lines of research previously discussed at the Linz seminars. The powerset and its fuzzy analogs are important in the development of topology in a fuzzy world and the term monad and its fuzzy analogs are vital in understanding fuzzy computer science.