An Easy-to-Understand Method to Construct Desired Distance-Like Measures
Metrics and their weaker forms are used to measure the difference between two data (or other things). There are many metrics that are available but not desired by a practitioner. This paper recommends in a plausible reasoning manner an easy-to-understand method to construct desired distance-like mea...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2021/5571546 |
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| _version_ | 1832544187268988928 |
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| author | Wen Qing Fu Sheng Gang Li Harish Garg Heng Liu Ahmed Mostafa Khalil Jingjing Zhao |
| author_facet | Wen Qing Fu Sheng Gang Li Harish Garg Heng Liu Ahmed Mostafa Khalil Jingjing Zhao |
| author_sort | Wen Qing Fu |
| collection | DOAJ |
| description | Metrics and their weaker forms are used to measure the difference between two data (or other things). There are many metrics that are available but not desired by a practitioner. This paper recommends in a plausible reasoning manner an easy-to-understand method to construct desired distance-like measures: to fuse easy-to-obtain (or easy to be coined by practitioners) pseudo-semi-metrics, pseudo-metrics, or metrics by making full use of well-known t-norms, t-conorms, aggregation operators, and similar operators (easy to be coined by practitioners). The simple reason to do this is that data for a real world problem are sometimes from multiagents. A distance-like notion, called weak interval-valued pseudo-metrics (briefly, WIVP-metrics), is defined by using known notions of pseudo-semi-metrics, pseudo-metrics, and metrics; this notion is topologically good and shows precision, flexibility, and compatibility than single pseudo-semi-metrics, pseudo-metrics, or metrics. Propositions and detailed examples are given to illustrate how to fabricate (including using what “material”) an expected or demanded WIVP-metric (even interval-valued metric) in practical problems, and WIVP-metric and its special cases are characterized by using axioms. Moreover, some WIVP-metrics pertinent to quantitative logic theory or interval-valued fuzzy graphs are constructed, and fixed point theorems and common fixed point theorems in weak interval-valued metric spaces are also presented. Topics and strategies for further study are also put forward concretely and clearly. |
| format | Article |
| id | doaj-art-34cc6077ba1545e28d9660e5ae4dd822 |
| institution | Kabale University |
| issn | 1099-0526 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-34cc6077ba1545e28d9660e5ae4dd8222025-02-03T10:53:47ZengWileyComplexity1099-05262021-01-01202110.1155/2021/55715465571546An Easy-to-Understand Method to Construct Desired Distance-Like MeasuresWen Qing Fu0Sheng Gang Li1Harish Garg2Heng Liu3Ahmed Mostafa Khalil4Jingjing Zhao5College of Mathematics and StatisticsCollege of Mathematics and StatisticsSchool of MathematicsSchool of ScienceDepartment of MathematicsSchool of PsychologyMetrics and their weaker forms are used to measure the difference between two data (or other things). There are many metrics that are available but not desired by a practitioner. This paper recommends in a plausible reasoning manner an easy-to-understand method to construct desired distance-like measures: to fuse easy-to-obtain (or easy to be coined by practitioners) pseudo-semi-metrics, pseudo-metrics, or metrics by making full use of well-known t-norms, t-conorms, aggregation operators, and similar operators (easy to be coined by practitioners). The simple reason to do this is that data for a real world problem are sometimes from multiagents. A distance-like notion, called weak interval-valued pseudo-metrics (briefly, WIVP-metrics), is defined by using known notions of pseudo-semi-metrics, pseudo-metrics, and metrics; this notion is topologically good and shows precision, flexibility, and compatibility than single pseudo-semi-metrics, pseudo-metrics, or metrics. Propositions and detailed examples are given to illustrate how to fabricate (including using what “material”) an expected or demanded WIVP-metric (even interval-valued metric) in practical problems, and WIVP-metric and its special cases are characterized by using axioms. Moreover, some WIVP-metrics pertinent to quantitative logic theory or interval-valued fuzzy graphs are constructed, and fixed point theorems and common fixed point theorems in weak interval-valued metric spaces are also presented. Topics and strategies for further study are also put forward concretely and clearly.http://dx.doi.org/10.1155/2021/5571546 |
| spellingShingle | Wen Qing Fu Sheng Gang Li Harish Garg Heng Liu Ahmed Mostafa Khalil Jingjing Zhao An Easy-to-Understand Method to Construct Desired Distance-Like Measures Complexity |
| title | An Easy-to-Understand Method to Construct Desired Distance-Like Measures |
| title_full | An Easy-to-Understand Method to Construct Desired Distance-Like Measures |
| title_fullStr | An Easy-to-Understand Method to Construct Desired Distance-Like Measures |
| title_full_unstemmed | An Easy-to-Understand Method to Construct Desired Distance-Like Measures |
| title_short | An Easy-to-Understand Method to Construct Desired Distance-Like Measures |
| title_sort | easy to understand method to construct desired distance like measures |
| url | http://dx.doi.org/10.1155/2021/5571546 |
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