Width-Based Interval-Valued Distances and Fuzzy Entropies
In this paper, we study distance measures between interval-valued fuzzy sets and entropies of interval-valued fuzzy sets. These are well-known and widely used notions in the fuzzy sets theory. The novelty of our approach is twofold: on one hand, it considers the width of intervals in order to connec...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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IEEE
2019-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/8615991/ |
| _version_ | 1818617852303769600 |
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| author | Zdenko Takac Humberto Bustince Jesus Maria Pintor Cedric Marco-Detchart Ines Couso |
| author_facet | Zdenko Takac Humberto Bustince Jesus Maria Pintor Cedric Marco-Detchart Ines Couso |
| author_sort | Zdenko Takac |
| collection | DOAJ |
| description | In this paper, we study distance measures between interval-valued fuzzy sets and entropies of interval-valued fuzzy sets. These are well-known and widely used notions in the fuzzy sets theory. The novelty of our approach is twofold: on one hand, it considers the width of intervals in order to connect the uncertainty of the output with the uncertainty of the inputs. On the other hand, it makes use of total orders between intervals, instead of partial ones, so that the usefulness of the notions related with some kind of monotonicity is fully recovered in the interval-valued setting. The construction of distance measures and entropies is done by aggregating interval-valued restricted dissimilarity functions and interval-valued normal E<sub>N</sub> -functions. For this reason, we first study these functions, both in line with the two above stated considerations. Finally, we present an illustrative example in image thresholding using an expression of the proposed interval-valued entropy to show the validity of our approach. |
| first_indexed | 2024-12-16T17:12:17Z |
| format | Article |
| id | doaj.art-8e452d435eb14fda9c7fb326a17be081 |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-12-16T17:12:17Z |
| publishDate | 2019-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-8e452d435eb14fda9c7fb326a17be0812022-12-21T22:23:23ZengIEEEIEEE Access2169-35362019-01-017140441405710.1109/ACCESS.2019.28938008615991Width-Based Interval-Valued Distances and Fuzzy EntropiesZdenko Takac0Humberto Bustince1https://orcid.org/0000-0002-1279-6195Jesus Maria Pintor2Cedric Marco-Detchart3Ines Couso4Slovak University of Technology Institute of Information Engineering, Automation and Mathematics Bratislava, Bratislava, SlovakiaDepartment of Statistics, Computer Science and Mathematics, Universidad Publica de Navarra, Pamplona, SpainDepartment of Engineering, Universidad Publica de Navarra, Pamplona, SpainDepartment of Statistics, Computer Science and Mathematics, Universidad Publica de Navarra, Pamplona, SpainDepartment of Estadistica e I.O D.M., Universidad de Oviedo, Oviedo, SpainIn this paper, we study distance measures between interval-valued fuzzy sets and entropies of interval-valued fuzzy sets. These are well-known and widely used notions in the fuzzy sets theory. The novelty of our approach is twofold: on one hand, it considers the width of intervals in order to connect the uncertainty of the output with the uncertainty of the inputs. On the other hand, it makes use of total orders between intervals, instead of partial ones, so that the usefulness of the notions related with some kind of monotonicity is fully recovered in the interval-valued setting. The construction of distance measures and entropies is done by aggregating interval-valued restricted dissimilarity functions and interval-valued normal E<sub>N</sub> -functions. For this reason, we first study these functions, both in line with the two above stated considerations. Finally, we present an illustrative example in image thresholding using an expression of the proposed interval-valued entropy to show the validity of our approach.https://ieeexplore.ieee.org/document/8615991/Admissible orderinterval-valued distanceinterval-valued entropyinterval-valued restricted dissimilarity function |
| spellingShingle | Zdenko Takac Humberto Bustince Jesus Maria Pintor Cedric Marco-Detchart Ines Couso Width-Based Interval-Valued Distances and Fuzzy Entropies IEEE Access Admissible order interval-valued distance interval-valued entropy interval-valued restricted dissimilarity function |
| title | Width-Based Interval-Valued Distances and Fuzzy Entropies |
| title_full | Width-Based Interval-Valued Distances and Fuzzy Entropies |
| title_fullStr | Width-Based Interval-Valued Distances and Fuzzy Entropies |
| title_full_unstemmed | Width-Based Interval-Valued Distances and Fuzzy Entropies |
| title_short | Width-Based Interval-Valued Distances and Fuzzy Entropies |
| title_sort | width based interval valued distances and fuzzy entropies |
| topic | Admissible order interval-valued distance interval-valued entropy interval-valued restricted dissimilarity function |
| url | https://ieeexplore.ieee.org/document/8615991/ |
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