"and"- and "or"-operations for "double", "triple", etc. fuzzy sets

© 2014 IEEE. In the traditional fuzzy logic, the expert's degree of confidence d(A & B) in a complex statement A & B (or A V B) is uniquely determined by his/her degrees of confidence d(A) and d(B) in the statements A and B, as f & (d(A), d(B)) for an appropriate 'and'-ope...

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Main Authors: Hung T. Nguyen, Vladik Kreinovich, Olga Kosheleva
Format: Conference Proceeding
Published: 2018
Online Access:https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84912529656&origin=inward
http://cmuir.cmu.ac.th/jspui/handle/6653943832/45750
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Institution: Chiang Mai University
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spelling th-cmuir.6653943832-457502018-01-24T06:16:55Z "and"- and "or"-operations for "double", "triple", etc. fuzzy sets Hung T. Nguyen Vladik Kreinovich Olga Kosheleva © 2014 IEEE. In the traditional fuzzy logic, the expert's degree of confidence d(A & B) in a complex statement A & B (or A V B) is uniquely determined by his/her degrees of confidence d(A) and d(B) in the statements A and B, as f & (d(A), d(B)) for an appropriate 'and'-operation (t-norm). In practice, for the same degrees d(A) and d(B), we may have different degrees d(A & B) depending on the relation between A and B. The best way to take this relation into account is to explicitly elicit the corresponding degrees d(A & B) and d(A V B), i.e., to come up with a 'double' fuzzy set. If we only elicit information about pairs of statements, then we still need to estimate, e.g., the degree d(A & B & C) based on the known values d(A), d(B), d(C), d(A & B), d(A & C), and d(B & C). In this paper, we explain how to produce such 'and'-operations for 'double' fuzzy sets - and how to produce similar 'or'-operations. 2018-01-24T06:16:55Z 2018-01-24T06:16:55Z 2014-01-01 Conference Proceeding 10987584 2-s2.0-84912529656 10.1109/FUZZ-IEEE.2014.6891598 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84912529656&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/45750
institution Chiang Mai University
building Chiang Mai University Library
country Thailand
collection CMU Intellectual Repository
description © 2014 IEEE. In the traditional fuzzy logic, the expert's degree of confidence d(A & B) in a complex statement A & B (or A V B) is uniquely determined by his/her degrees of confidence d(A) and d(B) in the statements A and B, as f & (d(A), d(B)) for an appropriate 'and'-operation (t-norm). In practice, for the same degrees d(A) and d(B), we may have different degrees d(A & B) depending on the relation between A and B. The best way to take this relation into account is to explicitly elicit the corresponding degrees d(A & B) and d(A V B), i.e., to come up with a 'double' fuzzy set. If we only elicit information about pairs of statements, then we still need to estimate, e.g., the degree d(A & B & C) based on the known values d(A), d(B), d(C), d(A & B), d(A & C), and d(B & C). In this paper, we explain how to produce such 'and'-operations for 'double' fuzzy sets - and how to produce similar 'or'-operations.
format Conference Proceeding
author Hung T. Nguyen
Vladik Kreinovich
Olga Kosheleva
spellingShingle Hung T. Nguyen
Vladik Kreinovich
Olga Kosheleva
"and"- and "or"-operations for "double", "triple", etc. fuzzy sets
author_facet Hung T. Nguyen
Vladik Kreinovich
Olga Kosheleva
author_sort Hung T. Nguyen
title "and"- and "or"-operations for "double", "triple", etc. fuzzy sets
title_short "and"- and "or"-operations for "double", "triple", etc. fuzzy sets
title_full "and"- and "or"-operations for "double", "triple", etc. fuzzy sets
title_fullStr "and"- and "or"-operations for "double", "triple", etc. fuzzy sets
title_full_unstemmed "and"- and "or"-operations for "double", "triple", etc. fuzzy sets
title_sort "and"- and "or"-operations for "double", "triple", etc. fuzzy sets
publishDate 2018
url https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84912529656&origin=inward
http://cmuir.cmu.ac.th/jspui/handle/6653943832/45750
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