Three-Way Fuzzy Sets and Their Applications (III)
Three-way fuzzy inference is the theoretical basis of three-way fuzzy control. The proposed TCRI method is based on a Mamdani three-way fuzzy implication operator and uses one inference and simple composition operation. In order to effectively improve the TCRI method, this paper proposes a full impl...
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MDPI AG
2023-01-01
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| _version_ | 1797446125004783616 |
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| author | Qingqing Hu Xiaohong Zhang |
| author_facet | Qingqing Hu Xiaohong Zhang |
| author_sort | Qingqing Hu |
| collection | DOAJ |
| description | Three-way fuzzy inference is the theoretical basis of three-way fuzzy control. The proposed TCRI method is based on a Mamdani three-way fuzzy implication operator and uses one inference and simple composition operation. In order to effectively improve the TCRI method, this paper proposes a full implication triple I algorithm for three-way fuzzy inference and gives the triple I solution to the TFMP problem. The emphasis of our research is <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>R</mi><mn>0</mn></msub></semantics></math></inline-formula> and G<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mi>o</mi><mo>¨</mo></mover></semantics></math></inline-formula>del triple I solution, which is related to three-way residual implication, as well as Zadeh’s and Mamdani’s triple I solution, which is based on three-way fuzzy implication operator. Then the three-way fuzzy controller is constructed by the proposed Zadeh’s and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>R</mi><mn>0</mn></msub></semantics></math></inline-formula> triple I algorithm. Finally, the proposed triple I algorithm is applied to the three-way fuzzy control system, and its advantage is illustrated by the three-dimensional surface diagram of the control variable. |
| first_indexed | 2024-03-09T13:35:44Z |
| format | Article |
| id | doaj.art-13e7467b14754821b12d9cea12a98c78 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-09T13:35:44Z |
| publishDate | 2023-01-01 |
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| series | Axioms |
| spelling | doaj.art-13e7467b14754821b12d9cea12a98c782023-11-30T21:11:42ZengMDPI AGAxioms2075-16802023-01-011215710.3390/axioms12010057Three-Way Fuzzy Sets and Their Applications (III)Qingqing Hu0Xiaohong Zhang1School of Electrical and Control Engineering, Shaanxi University of Science & Technology, Xi’an 710021, ChinaSchool of Mathematics & Data Science, Shaanxi University of Science & Technology, Xi’an 710021, ChinaThree-way fuzzy inference is the theoretical basis of three-way fuzzy control. The proposed TCRI method is based on a Mamdani three-way fuzzy implication operator and uses one inference and simple composition operation. In order to effectively improve the TCRI method, this paper proposes a full implication triple I algorithm for three-way fuzzy inference and gives the triple I solution to the TFMP problem. The emphasis of our research is <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>R</mi><mn>0</mn></msub></semantics></math></inline-formula> and G<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mi>o</mi><mo>¨</mo></mover></semantics></math></inline-formula>del triple I solution, which is related to three-way residual implication, as well as Zadeh’s and Mamdani’s triple I solution, which is based on three-way fuzzy implication operator. Then the three-way fuzzy controller is constructed by the proposed Zadeh’s and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>R</mi><mn>0</mn></msub></semantics></math></inline-formula> triple I algorithm. Finally, the proposed triple I algorithm is applied to the three-way fuzzy control system, and its advantage is illustrated by the three-dimensional surface diagram of the control variable.https://www.mdpi.com/2075-1680/12/1/57three-way fuzzy setsthree-way fuzzy inferencethree-way residual implicationTriple I Algorithmthree-way fuzzy control system |
| spellingShingle | Qingqing Hu Xiaohong Zhang Three-Way Fuzzy Sets and Their Applications (III) Axioms three-way fuzzy sets three-way fuzzy inference three-way residual implication Triple I Algorithm three-way fuzzy control system |
| title | Three-Way Fuzzy Sets and Their Applications (III) |
| title_full | Three-Way Fuzzy Sets and Their Applications (III) |
| title_fullStr | Three-Way Fuzzy Sets and Their Applications (III) |
| title_full_unstemmed | Three-Way Fuzzy Sets and Their Applications (III) |
| title_short | Three-Way Fuzzy Sets and Their Applications (III) |
| title_sort | three way fuzzy sets and their applications iii |
| topic | three-way fuzzy sets three-way fuzzy inference three-way residual implication Triple I Algorithm three-way fuzzy control system |
| url | https://www.mdpi.com/2075-1680/12/1/57 |
| work_keys_str_mv | AT qingqinghu threewayfuzzysetsandtheirapplicationsiii AT xiaohongzhang threewayfuzzysetsandtheirapplicationsiii |