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Level sets and the extension principle for interval valued fuzzy sets and its application to uncertainty measures

Author:

Ronald R. YagerAuthors Info & Claims

Information Sciences—Informatics and Computer Science, Intelligent Systems, Applications: An International Journal, Volume 178, Issue 18

Pages 3565 - 3576

https://doi.org/10.1016/j.ins.2008.05.022

Published: 20 September 2008 Publication History

Abstract

We describe the representation of a fuzzy subset in terms of its crisp level sets. We then generalize these level sets to the case of interval valued fuzzy sets and provide for a representation of an interval valued fuzzy set in terms of crisp level sets. We note that in this representation while the level sets are crisp the memberships are still intervals. Once having this representation we turn to its role in the extension principle and particularly to the extension of measures of uncertainty of interval valued fuzzy sets. Two types of extension of uncertainty measures are investigated. The first, based on the level set representation, leads to extensions whose values for the measure of uncertainty are themselves fuzzy sets. The second, based on the use of integrals, results in extensions whose value for the uncertainty of an interval valued fuzzy sets is an interval.

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Cited By

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Level sets and the extension principle for interval valued fuzzy sets and its application to uncertainty measures

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cover image Information Sciences: an International Journal

Information Sciences: an International Journal Volume 178, Issue 18

September, 2008

155 pages

ISSN:0020-0255

Issue’s Table of Contents

Copyright © Elsevier Inc. © 2008.

Publisher

Elsevier Science Inc.

United States

Publication History

Published: 20 September 2008

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Cited By

Rajati M(2019)Compatibility-Based Evidential Reasoning2019 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)10.1109/FUZZ-IEEE.2019.8858941(1-6)Online publication date: 23-Jun-2019
https://dl.acm.org/doi/10.1109/FUZZ-IEEE.2019.8858941
Li XYi H(2017)Intuitionistic fuzzy matroidsJournal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology10.3233/JIFS-1750433:6(3653-3663)Online publication date: 1-Jan-2017
https://dl.acm.org/doi/10.3233/JIFS-17504
Hamrawi HCoupland SJohn R(2017)Type-2 Fuzzy Alpha-CutsIEEE Transactions on Fuzzy Systems10.1109/TFUZZ.2016.257491425:3(682-692)Online publication date: 2-Jun-2017
https://dl.acm.org/doi/10.1109/TFUZZ.2016.2574914
Anzilli LFacchinetti GPirotti T(2017)Credit risk profiling using a new evaluation of interval-valued fuzzy sets based on alpha-cuts2017 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)10.1109/FUZZ-IEEE.2017.8015613(1-6)Online publication date: 9-Jul-2017
https://dl.acm.org/doi/10.1109/FUZZ-IEEE.2017.8015613
Hu BWong HYiu K(2017)Equivalent Structures of Interval Sets and Fuzzy Interval SetsInternational Journal of Intelligent Systems10.1002/int.2194033:1(68-92)Online publication date: 14-Nov-2017
https://dl.acm.org/doi/10.1002/int.21940
Hu B(2014)Three-way decisions space and three-way decisionsInformation Sciences: an International Journal10.1016/j.ins.2014.05.015281(21-52)Online publication date: 1-Oct-2014
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Hu BKwong C(2014)On type-2 fuzzy sets and their t-norm operationsInformation Sciences: an International Journal10.1016/j.ins.2013.07.023255(58-81)Online publication date: 1-Jan-2014
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Vahdani BTavakkoli-Moghaddam RMousavi SGhodratnama A(2013)Soft computing based on new interval-valued fuzzy modified multi-criteria decision-making methodApplied Soft Computing10.1016/j.asoc.2012.08.02013:1(165-172)Online publication date: 1-Jan-2013
https://dl.acm.org/doi/10.1016/j.asoc.2012.08.020
Kupka J(2011)On fuzzifications of discrete dynamical systemsInformation Sciences: an International Journal10.1016/j.ins.2011.02.024181:13(2858-2872)Online publication date: 1-Jul-2011
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Li D(2011)Extension principles for interval-valued intuitionistic fuzzy sets and algebraic operationsFuzzy Optimization and Decision Making10.1007/s10700-010-9095-910:1(45-58)Online publication date: 1-Mar-2011
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