Quantification of R-Fuzzy sets

The main aim of this paper is to connect R-Fuzzy sets and type-2 fuzzy sets, so as to provide a practical means to express complex uncertainty without the associated difficulty of a type-2 fuzzy set. The paper puts forward a significance measure, to provide a means for understanding the importance o...

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Main Authors: Singh Khuman, Arjab, Yang, Yingjie, John, Robert
Format: Article
Published: Elsevier 2016
Subjects:
Online Access:https://eprints.nottingham.ac.uk/31652/
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author Singh Khuman, Arjab
Yang, Yingjie
John, Robert
author_facet Singh Khuman, Arjab
Yang, Yingjie
John, Robert
author_sort Singh Khuman, Arjab
building Nottingham Research Data Repository
collection Online Access
description The main aim of this paper is to connect R-Fuzzy sets and type-2 fuzzy sets, so as to provide a practical means to express complex uncertainty without the associated difficulty of a type-2 fuzzy set. The paper puts forward a significance measure, to provide a means for understanding the importance of the membership values contained within an R-fuzzy set. The pairing of an R-fuzzy set and the significance measure allows for an intermediary approach to that of a type-2 fuzzy set. By inspecting the returned significance degree of a particular membership value, one is able to ascertain its true significance in relation, relative to other encapsulated membership values. An R-fuzzy set coupled with the proposed significance measure allows for a type-2 fuzzy equivalence, an intermediary, all the while retaining the underlying sentiment of individual and general perspectives, and with the adage of a significantly reduced computational burden. Several human based perception examples are presented, wherein the significance degree is implemented, from which a higher level of detail can be garnered. The results demonstrate that the proposed research method combines the high capacity in uncertainty representation of type-2 fuzzy sets, together with the simplicity and objectiveness of type-1 fuzzy sets. This in turn provides a practical means for problem domains where a type-2 fuzzy set is preferred but difficult to construct due to the subjective type-2 fuzzy membership.
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spelling nottingham-316522020-05-04T18:07:00Z https://eprints.nottingham.ac.uk/31652/ Quantification of R-Fuzzy sets Singh Khuman, Arjab Yang, Yingjie John, Robert The main aim of this paper is to connect R-Fuzzy sets and type-2 fuzzy sets, so as to provide a practical means to express complex uncertainty without the associated difficulty of a type-2 fuzzy set. The paper puts forward a significance measure, to provide a means for understanding the importance of the membership values contained within an R-fuzzy set. The pairing of an R-fuzzy set and the significance measure allows for an intermediary approach to that of a type-2 fuzzy set. By inspecting the returned significance degree of a particular membership value, one is able to ascertain its true significance in relation, relative to other encapsulated membership values. An R-fuzzy set coupled with the proposed significance measure allows for a type-2 fuzzy equivalence, an intermediary, all the while retaining the underlying sentiment of individual and general perspectives, and with the adage of a significantly reduced computational burden. Several human based perception examples are presented, wherein the significance degree is implemented, from which a higher level of detail can be garnered. The results demonstrate that the proposed research method combines the high capacity in uncertainty representation of type-2 fuzzy sets, together with the simplicity and objectiveness of type-1 fuzzy sets. This in turn provides a practical means for problem domains where a type-2 fuzzy set is preferred but difficult to construct due to the subjective type-2 fuzzy membership. Elsevier 2016-08-15 Article PeerReviewed Singh Khuman, Arjab, Yang, Yingjie and John, Robert (2016) Quantification of R-Fuzzy sets. Expert Systems with Applications, 55 . pp. 374-387. ISSN 0957-4174 R-Fuzzy Sets Rough Sets Fuzzy Membership Significance Type-2 Equivalence http://www.sciencedirect.com/science/article/pii/S0957417416300331 doi:10.1016/j.eswa.2016.02.010 doi:10.1016/j.eswa.2016.02.010
spellingShingle R-Fuzzy Sets
Rough Sets
Fuzzy Membership
Significance
Type-2 Equivalence
Singh Khuman, Arjab
Yang, Yingjie
John, Robert
Quantification of R-Fuzzy sets
title Quantification of R-Fuzzy sets
title_full Quantification of R-Fuzzy sets
title_fullStr Quantification of R-Fuzzy sets
title_full_unstemmed Quantification of R-Fuzzy sets
title_short Quantification of R-Fuzzy sets
title_sort quantification of r-fuzzy sets
topic R-Fuzzy Sets
Rough Sets
Fuzzy Membership
Significance
Type-2 Equivalence
url https://eprints.nottingham.ac.uk/31652/
https://eprints.nottingham.ac.uk/31652/
https://eprints.nottingham.ac.uk/31652/