A random set and prototype theory interpretation of intuitionistic fuzzy sets

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Abstract

An interpretation of intuitionistic fuzzy sets is proposed based on random set theory and prototype theory. The extension of fuzzy labels are modelled by lower and upper random set neighbourhoods, identifying those element of the universe within an uncertain distance threshold of a set of prototypical elements. These neighbourhoods are then generalised to compound fuzzy descriptions generated as logical combinations of basic fuzzy labels. The single point coverage functions of these lower and upper random sets are then shown to generate lower and upper membership functions satisfying the min-max combination rules of interval fuzzy set theory, the latter being isomophic to intuitionistic fuzzy set theory.
Translated title of the contributionA Random Set and Prototype Theory Interpretation of Intuitionistic Fuzzy Sets
Original languageEnglish
Title of host publicationInformation Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Methods
EditorsEyke Hüllermeier, Rudolf Kruse, Frank Hoffmann
PublisherSpringer
Pages618 - 628
Number of pages10
ISBN (Electronic) 9783642140556
ISBN (Print)9783642140549
Publication statusPublished - Jul 2010

Publication series

NameCommunications in Computer and Information Science
Volume80

Bibliographical note

13th International Conference, IPMU (Information Processing and Management of Uncertainty) 2010, Dortmund, Germany, June 28–July 2, 2010. Proceedings, Part I

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