Connected Degree of Fuzzifying Matroids
Polya’s plausible reasoning methods are crucial not only in discovery of mathematics results, modeling methods, and data processing methods but also in many practical problems’ solving. This paper exemplifies how to use Polya’s plausible reasoning methods to generalize the popularized notion of 2-co...
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2022-01-01
|
| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/7811196 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832562507011588096 |
|---|---|
| author | Xiu Xin Sheng Gang Li Harish Garg Heng Liu Jingjing Zhao |
| author_facet | Xiu Xin Sheng Gang Li Harish Garg Heng Liu Jingjing Zhao |
| author_sort | Xiu Xin |
| collection | DOAJ |
| description | Polya’s plausible reasoning methods are crucial not only in discovery of mathematics results, modeling methods, and data processing methods but also in many practical problems’ solving. This paper exemplifies how to use Polya’s plausible reasoning methods to generalize the popularized notion of 2-connectedness of graphs to a more universal notion of the connected degree of fuzzifying matroids. We introduce the connectedness of fuzzifying matroids, which is generalized from 2-connectedness of graphs, connectedness of matroids, and 2-connectedness of fuzzy graphs. Moreover, the connected degree of fuzzifying matroids is presented by considering the fuzziness degree of connectedness. It is proved that a fuzzifying matroid M is connected, which is equivalent to its connectedness degree ConM is the biggest (i.e., ConM=1). This, together with other properties of the connected degree of fuzzifying matroids, demonstrates the rationality of the proposed notion. Finally, we describe the concepts of this paper through some examples. |
| format | Article |
| id | doaj-art-eaf8eda0f8d9432ab3ef34dc730f7981 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-eaf8eda0f8d9432ab3ef34dc730f79812025-02-03T01:22:28ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/7811196Connected Degree of Fuzzifying MatroidsXiu Xin0Sheng Gang Li1Harish Garg2Heng Liu3Jingjing Zhao4Department of MathematicsCollege of Mathematics and StatisticsSchool of MathematicsSchool of ScienceSchool of PsychologyPolya’s plausible reasoning methods are crucial not only in discovery of mathematics results, modeling methods, and data processing methods but also in many practical problems’ solving. This paper exemplifies how to use Polya’s plausible reasoning methods to generalize the popularized notion of 2-connectedness of graphs to a more universal notion of the connected degree of fuzzifying matroids. We introduce the connectedness of fuzzifying matroids, which is generalized from 2-connectedness of graphs, connectedness of matroids, and 2-connectedness of fuzzy graphs. Moreover, the connected degree of fuzzifying matroids is presented by considering the fuzziness degree of connectedness. It is proved that a fuzzifying matroid M is connected, which is equivalent to its connectedness degree ConM is the biggest (i.e., ConM=1). This, together with other properties of the connected degree of fuzzifying matroids, demonstrates the rationality of the proposed notion. Finally, we describe the concepts of this paper through some examples.http://dx.doi.org/10.1155/2022/7811196 |
| spellingShingle | Xiu Xin Sheng Gang Li Harish Garg Heng Liu Jingjing Zhao Connected Degree of Fuzzifying Matroids Journal of Mathematics |
| title | Connected Degree of Fuzzifying Matroids |
| title_full | Connected Degree of Fuzzifying Matroids |
| title_fullStr | Connected Degree of Fuzzifying Matroids |
| title_full_unstemmed | Connected Degree of Fuzzifying Matroids |
| title_short | Connected Degree of Fuzzifying Matroids |
| title_sort | connected degree of fuzzifying matroids |
| url | http://dx.doi.org/10.1155/2022/7811196 |
| work_keys_str_mv | AT xiuxin connecteddegreeoffuzzifyingmatroids AT shenggangli connecteddegreeoffuzzifyingmatroids AT harishgarg connecteddegreeoffuzzifyingmatroids AT hengliu connecteddegreeoffuzzifyingmatroids AT jingjingzhao connecteddegreeoffuzzifyingmatroids |