A Decision-Making Approach Based on a Multi <em>Q</em>-Hesitant Fuzzy Soft Multi-Granulation Rough Model
In this paper, we propose a new hybrid model, multi <i>Q</i>-hesitant fuzzy soft multi-granulation rough set model, by combining a multi <i>Q</i>-hesitant fuzzy soft set and multi-granulation rough set. We demonstrate some useful properties of these multi <i>Q</i>...
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| Format: | Article |
| Language: | English |
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MDPI AG
2018-12-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/10/12/711 |
| _version_ | 1811262354404409344 |
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| author | Kholood Mohammad Alsager Noura Omair Alshehri Muhammad Akram |
| author_facet | Kholood Mohammad Alsager Noura Omair Alshehri Muhammad Akram |
| author_sort | Kholood Mohammad Alsager |
| collection | DOAJ |
| description | In this paper, we propose a new hybrid model, multi <i>Q</i>-hesitant fuzzy soft multi-granulation rough set model, by combining a multi <i>Q</i>-hesitant fuzzy soft set and multi-granulation rough set. We demonstrate some useful properties of these multi <i>Q</i>-hesitant fuzzy soft multi-granulation rough sets. Furthermore, we define multi <i>Q</i>-hesitant fuzzy soft (<inline-formula> <math display="inline"> <semantics> <mrow> <msup> <mi>M</mi> <mi>k</mi> </msup> <mi>Q</mi> <mi>H</mi> <mi>F</mi> <mi>S</mi> </mrow> </semantics> </math> </inline-formula>) rough approximation operators in terms of <inline-formula> <math display="inline"> <semantics> <mrow> <msup> <mi>M</mi> <mi>k</mi> </msup> <mi>Q</mi> <mi>H</mi> <mi>F</mi> <mi>S</mi> </mrow> </semantics> </math> </inline-formula> relations and <inline-formula> <math display="inline"> <semantics> <mrow> <msup> <mi>M</mi> <mi>k</mi> </msup> <mi>Q</mi> <mi>H</mi> <mi>F</mi> <mi>S</mi> </mrow> </semantics> </math> </inline-formula> multi-granulation rough approximation operators in terms of <inline-formula> <math display="inline"> <semantics> <mrow> <msup> <mi>M</mi> <mi>k</mi> </msup> <mi>Q</mi> <mi>H</mi> <mi>F</mi> <mi>S</mi> </mrow> </semantics> </math> </inline-formula> relations. We study the main properties of lower and upper <inline-formula> <math display="inline"> <semantics> <mrow> <msup> <mi>M</mi> <mi>k</mi> </msup> <mi>Q</mi> <mi>H</mi> <mi>F</mi> <mi>S</mi> </mrow> </semantics> </math> </inline-formula> rough approximation operators and lower and upper <inline-formula> <math display="inline"> <semantics> <mrow> <msup> <mi>M</mi> <mi>k</mi> </msup> <mi>Q</mi> <mi>H</mi> <mi>F</mi> <mi>S</mi> </mrow> </semantics> </math> </inline-formula> multi-granulation rough approximation operators. Moreover, we develop a general framework for dealing with uncertainty in decision-making by using the multi <i>Q</i>-hesitant fuzzy soft multi-granulation rough sets. We analyze the photovoltaic systems fault detection to show the proposed decision methodology. |
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| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-12T19:23:51Z |
| publishDate | 2018-12-01 |
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| series | Symmetry |
| spelling | doaj.art-5a16904df726472886e1ba72ba7e87b12022-12-22T03:19:31ZengMDPI AGSymmetry2073-89942018-12-01101271110.3390/sym10120711sym10120711A Decision-Making Approach Based on a Multi <em>Q</em>-Hesitant Fuzzy Soft Multi-Granulation Rough ModelKholood Mohammad Alsager0Noura Omair Alshehri1Muhammad Akram2Department of Mathematics, Faculty of Sciences, King Abdulaziz University, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, Faculty of Sciences, University of Jeddah, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, University of the Punjab, New Campus, Lahore 4590, PakistanIn this paper, we propose a new hybrid model, multi <i>Q</i>-hesitant fuzzy soft multi-granulation rough set model, by combining a multi <i>Q</i>-hesitant fuzzy soft set and multi-granulation rough set. We demonstrate some useful properties of these multi <i>Q</i>-hesitant fuzzy soft multi-granulation rough sets. Furthermore, we define multi <i>Q</i>-hesitant fuzzy soft (<inline-formula> <math display="inline"> <semantics> <mrow> <msup> <mi>M</mi> <mi>k</mi> </msup> <mi>Q</mi> <mi>H</mi> <mi>F</mi> <mi>S</mi> </mrow> </semantics> </math> </inline-formula>) rough approximation operators in terms of <inline-formula> <math display="inline"> <semantics> <mrow> <msup> <mi>M</mi> <mi>k</mi> </msup> <mi>Q</mi> <mi>H</mi> <mi>F</mi> <mi>S</mi> </mrow> </semantics> </math> </inline-formula> relations and <inline-formula> <math display="inline"> <semantics> <mrow> <msup> <mi>M</mi> <mi>k</mi> </msup> <mi>Q</mi> <mi>H</mi> <mi>F</mi> <mi>S</mi> </mrow> </semantics> </math> </inline-formula> multi-granulation rough approximation operators in terms of <inline-formula> <math display="inline"> <semantics> <mrow> <msup> <mi>M</mi> <mi>k</mi> </msup> <mi>Q</mi> <mi>H</mi> <mi>F</mi> <mi>S</mi> </mrow> </semantics> </math> </inline-formula> relations. We study the main properties of lower and upper <inline-formula> <math display="inline"> <semantics> <mrow> <msup> <mi>M</mi> <mi>k</mi> </msup> <mi>Q</mi> <mi>H</mi> <mi>F</mi> <mi>S</mi> </mrow> </semantics> </math> </inline-formula> rough approximation operators and lower and upper <inline-formula> <math display="inline"> <semantics> <mrow> <msup> <mi>M</mi> <mi>k</mi> </msup> <mi>Q</mi> <mi>H</mi> <mi>F</mi> <mi>S</mi> </mrow> </semantics> </math> </inline-formula> multi-granulation rough approximation operators. Moreover, we develop a general framework for dealing with uncertainty in decision-making by using the multi <i>Q</i>-hesitant fuzzy soft multi-granulation rough sets. We analyze the photovoltaic systems fault detection to show the proposed decision methodology.https://www.mdpi.com/2073-8994/10/12/711<i>Q</i>-hesitant fuzzy soft setmulti <i>Q</i>-hesitant fuzzy soft rough setphotovoltaic systems fault detection approachdecision-making method |
| spellingShingle | Kholood Mohammad Alsager Noura Omair Alshehri Muhammad Akram A Decision-Making Approach Based on a Multi <em>Q</em>-Hesitant Fuzzy Soft Multi-Granulation Rough Model Symmetry <i>Q</i>-hesitant fuzzy soft set multi <i>Q</i>-hesitant fuzzy soft rough set photovoltaic systems fault detection approach decision-making method |
| title | A Decision-Making Approach Based on a Multi <em>Q</em>-Hesitant Fuzzy Soft Multi-Granulation Rough Model |
| title_full | A Decision-Making Approach Based on a Multi <em>Q</em>-Hesitant Fuzzy Soft Multi-Granulation Rough Model |
| title_fullStr | A Decision-Making Approach Based on a Multi <em>Q</em>-Hesitant Fuzzy Soft Multi-Granulation Rough Model |
| title_full_unstemmed | A Decision-Making Approach Based on a Multi <em>Q</em>-Hesitant Fuzzy Soft Multi-Granulation Rough Model |
| title_short | A Decision-Making Approach Based on a Multi <em>Q</em>-Hesitant Fuzzy Soft Multi-Granulation Rough Model |
| title_sort | decision making approach based on a multi em q em hesitant fuzzy soft multi granulation rough model |
| topic | <i>Q</i>-hesitant fuzzy soft set multi <i>Q</i>-hesitant fuzzy soft rough set photovoltaic systems fault detection approach decision-making method |
| url | https://www.mdpi.com/2073-8994/10/12/711 |
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