Some Remarks on Strong Fuzzy Metrics and Strong Fuzzy Approximating Metrics with Applications in Word Combinatorics
Noticing that ordinary metrics do not present an adequate tool for the study of analytic problems of word combinatorics, as well as in the research of some problems related to theoretical computer science, we propose to use fuzzy metrics in this type of problems. Specifically, the so-called strong f...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-02-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/5/738 |
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| author | Raivis Bēts Alexander Šostak |
| author_facet | Raivis Bēts Alexander Šostak |
| author_sort | Raivis Bēts |
| collection | DOAJ |
| description | Noticing that ordinary metrics do not present an adequate tool for the study of analytic problems of word combinatorics, as well as in the research of some problems related to theoretical computer science, we propose to use fuzzy metrics in this type of problems. Specifically, the so-called strong fuzzy metric seems to be more appropriate here. In the first part of the paper, we study some special classes of strong fuzzy metrics, topological and lattice properties of certain families of strong fuzzy metrics, and, more generally, strong k-fuzzy metrics. Noticing that one of the standard axioms of a strong fuzzy metric can be easily violated when applied in real situations, in the second part of the paper we introduce more general, approximating fuzzy metrics and illustrate their applicability with some numerical examples. |
| first_indexed | 2024-03-09T20:31:32Z |
| format | Article |
| id | doaj.art-dcfdd364c8444cb8b30ed7d972061ea8 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T20:31:32Z |
| publishDate | 2022-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-dcfdd364c8444cb8b30ed7d972061ea82023-11-23T23:22:54ZengMDPI AGMathematics2227-73902022-02-0110573810.3390/math10050738Some Remarks on Strong Fuzzy Metrics and Strong Fuzzy Approximating Metrics with Applications in Word CombinatoricsRaivis Bēts0Alexander Šostak1Institute of Mathematics and Computer Science, University of Latvia, LV-1459 Riga, LatviaInstitute of Mathematics and Computer Science, University of Latvia, LV-1459 Riga, LatviaNoticing that ordinary metrics do not present an adequate tool for the study of analytic problems of word combinatorics, as well as in the research of some problems related to theoretical computer science, we propose to use fuzzy metrics in this type of problems. Specifically, the so-called strong fuzzy metric seems to be more appropriate here. In the first part of the paper, we study some special classes of strong fuzzy metrics, topological and lattice properties of certain families of strong fuzzy metrics, and, more generally, strong k-fuzzy metrics. Noticing that one of the standard axioms of a strong fuzzy metric can be easily violated when applied in real situations, in the second part of the paper we introduce more general, approximating fuzzy metrics and illustrate their applicability with some numerical examples.https://www.mdpi.com/2227-7390/10/5/738strong fuzzy metricsstandard fuzzy metricword combinatoricsapproximating fuzzy metrick-fuzzy metric |
| spellingShingle | Raivis Bēts Alexander Šostak Some Remarks on Strong Fuzzy Metrics and Strong Fuzzy Approximating Metrics with Applications in Word Combinatorics Mathematics strong fuzzy metrics standard fuzzy metric word combinatorics approximating fuzzy metric k-fuzzy metric |
| title | Some Remarks on Strong Fuzzy Metrics and Strong Fuzzy Approximating Metrics with Applications in Word Combinatorics |
| title_full | Some Remarks on Strong Fuzzy Metrics and Strong Fuzzy Approximating Metrics with Applications in Word Combinatorics |
| title_fullStr | Some Remarks on Strong Fuzzy Metrics and Strong Fuzzy Approximating Metrics with Applications in Word Combinatorics |
| title_full_unstemmed | Some Remarks on Strong Fuzzy Metrics and Strong Fuzzy Approximating Metrics with Applications in Word Combinatorics |
| title_short | Some Remarks on Strong Fuzzy Metrics and Strong Fuzzy Approximating Metrics with Applications in Word Combinatorics |
| title_sort | some remarks on strong fuzzy metrics and strong fuzzy approximating metrics with applications in word combinatorics |
| topic | strong fuzzy metrics standard fuzzy metric word combinatorics approximating fuzzy metric k-fuzzy metric |
| url | https://www.mdpi.com/2227-7390/10/5/738 |
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