Working Paper Article Version 1 This version is not peer-reviewed

A Topological Perspective for Interval Type-2 Fuzzy Hedges

Version 1 : Received: 16 August 2019 / Approved: 17 August 2019 / Online: 17 August 2019 (04:14:51 CEST)

How to cite: Oliveira, H. A Topological Perspective for Interval Type-2 Fuzzy Hedges. Preprints 2019, 2019080181 Oliveira, H. A Topological Perspective for Interval Type-2 Fuzzy Hedges. Preprints 2019, 2019080181

Abstract

Type-2 fuzzy sets were introduced by L. Zadeh aiming at modelling some settings in which fuzzy sets (usually called type-1 fuzzy sets) are not sufficient to reflect certain uncertainty degrees - loosely speaking, they are fuzzy sets whose membership degrees are ordinary fuzzy sets. On the other hand, fiber bundles are topological entities of extreme importance in Mathematics itself and many other scientific areas, like Physics (General Relativity, Field Theory etc.), finance modelling, and statistical inference. The present work introduces a conceptual link between the two ideas and conjectures about the potential mutual benefits that can be obtained from this viewpoint.As an objective and usable product of the presented ideas, it is described a framework for defining type-2 fuzzy hedges, proper to operate on interval type-2 fuzzy sets.

Subject Areas

type-2 fuzzy sets; fiber bundles; differential topology

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