An <i>m</i>-Polar Fuzzy Hypergraph Model of Granular Computing
An <i>m</i>-polar fuzzy model plays a vital role in modeling of real-world problems that involve multi-attribute, multi-polar information and uncertainty. The <i>m</i>-polar fuzzy models give increasing precision and flexibility to the system as compared to the fuzzy and bipo...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2019-04-01
|
| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/11/4/483 |
| _version_ | 1798043402932060160 |
|---|---|
| author | Anam Luqman Muhammad Akram Ali N.A. Koam |
| author_facet | Anam Luqman Muhammad Akram Ali N.A. Koam |
| author_sort | Anam Luqman |
| collection | DOAJ |
| description | An <i>m</i>-polar fuzzy model plays a vital role in modeling of real-world problems that involve multi-attribute, multi-polar information and uncertainty. The <i>m</i>-polar fuzzy models give increasing precision and flexibility to the system as compared to the fuzzy and bipolar fuzzy models. An <i>m</i>-polar fuzzy set assigns the membership degree to an object belonging to <inline-formula> <math display="inline"> <semantics> <msup> <mrow> <mo>[</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>]</mo> </mrow> <mi>m</mi> </msup> </semantics> </math> </inline-formula> describing the <i>m</i> distinct attributes of that element. Granular computing deals with representing and processing information in the form of information granules. These information granules are collections of elements combined together due to their similarity and functional/physical adjacency. In this paper, we illustrate the formation of granular structures using <i>m</i>-polar fuzzy hypergraphs and level hypergraphs. Further, we define <i>m</i>-polar fuzzy hierarchical quotient space structures. The mappings between the <i>m</i>-polar fuzzy hypergraphs depict the relationships among granules occurring at different levels. The consequences reveal that the representation of the partition of a universal set is more efficient through <i>m</i>-polar fuzzy hypergraphs as compared to crisp hypergraphs. We also present some examples and a real-world problem to signify the validity of our proposed model. |
| first_indexed | 2024-04-11T22:48:35Z |
| format | Article |
| id | doaj.art-01bf97d349ed491f9bc68d5816c86137 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-11T22:48:35Z |
| publishDate | 2019-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-01bf97d349ed491f9bc68d5816c861372022-12-22T03:58:38ZengMDPI AGSymmetry2073-89942019-04-0111448310.3390/sym11040483sym11040483An <i>m</i>-Polar Fuzzy Hypergraph Model of Granular ComputingAnam Luqman0Muhammad Akram1Ali N.A. Koam2Department of Mathematics, University of the Punjab, New Campus, P.O. Box 54590, Lahore, PakistanDepartment of Mathematics, University of the Punjab, New Campus, P.O. Box 54590, Lahore, PakistanDepartment of Mathematics, College of Science, Jazan University, New Campus, P.O. Box 2097, Jazan, Saudi ArabiaAn <i>m</i>-polar fuzzy model plays a vital role in modeling of real-world problems that involve multi-attribute, multi-polar information and uncertainty. The <i>m</i>-polar fuzzy models give increasing precision and flexibility to the system as compared to the fuzzy and bipolar fuzzy models. An <i>m</i>-polar fuzzy set assigns the membership degree to an object belonging to <inline-formula> <math display="inline"> <semantics> <msup> <mrow> <mo>[</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>]</mo> </mrow> <mi>m</mi> </msup> </semantics> </math> </inline-formula> describing the <i>m</i> distinct attributes of that element. Granular computing deals with representing and processing information in the form of information granules. These information granules are collections of elements combined together due to their similarity and functional/physical adjacency. In this paper, we illustrate the formation of granular structures using <i>m</i>-polar fuzzy hypergraphs and level hypergraphs. Further, we define <i>m</i>-polar fuzzy hierarchical quotient space structures. The mappings between the <i>m</i>-polar fuzzy hypergraphs depict the relationships among granules occurring at different levels. The consequences reveal that the representation of the partition of a universal set is more efficient through <i>m</i>-polar fuzzy hypergraphs as compared to crisp hypergraphs. We also present some examples and a real-world problem to signify the validity of our proposed model.https://www.mdpi.com/2073-8994/11/4/483<i>m</i>-polar fuzzy hypergraphs<i>m</i>-polar fuzzy equivalence relationlevel hypergraphsgranular computingapplication |
| spellingShingle | Anam Luqman Muhammad Akram Ali N.A. Koam An <i>m</i>-Polar Fuzzy Hypergraph Model of Granular Computing Symmetry <i>m</i>-polar fuzzy hypergraphs <i>m</i>-polar fuzzy equivalence relation level hypergraphs granular computing application |
| title | An <i>m</i>-Polar Fuzzy Hypergraph Model of Granular Computing |
| title_full | An <i>m</i>-Polar Fuzzy Hypergraph Model of Granular Computing |
| title_fullStr | An <i>m</i>-Polar Fuzzy Hypergraph Model of Granular Computing |
| title_full_unstemmed | An <i>m</i>-Polar Fuzzy Hypergraph Model of Granular Computing |
| title_short | An <i>m</i>-Polar Fuzzy Hypergraph Model of Granular Computing |
| title_sort | i m i polar fuzzy hypergraph model of granular computing |
| topic | <i>m</i>-polar fuzzy hypergraphs <i>m</i>-polar fuzzy equivalence relation level hypergraphs granular computing application |
| url | https://www.mdpi.com/2073-8994/11/4/483 |
| work_keys_str_mv | AT anamluqman animipolarfuzzyhypergraphmodelofgranularcomputing AT muhammadakram animipolarfuzzyhypergraphmodelofgranularcomputing AT alinakoam animipolarfuzzyhypergraphmodelofgranularcomputing AT anamluqman imipolarfuzzyhypergraphmodelofgranularcomputing AT muhammadakram imipolarfuzzyhypergraphmodelofgranularcomputing AT alinakoam imipolarfuzzyhypergraphmodelofgranularcomputing |