As one of important parts of fuzzy logic, fuzzy inference plays a vital role in the fields of fuzzy control, artificial intelligence, affective computing, image processing and so forth. Two key problems of fuzzy inference are FMP (fuzzy modus ponens) and FMT (fuzzy modus tollens). How to get the ideal solution for FMP and FMT is a difficult problem in the area of fuzzy logic. Aiming at such problem, from the idea of symmetric implicational reasoning, triple I* method and restriction theory, we put forward and investigate the α-symmetric I* restriction method, and then generalize it to the α(x,y)-symmetric I* restriction method. To begin with, the α-symmetric I* restriction principle and the α(x,y)-symmetric I* restriction principle are established. Furthermore, the equivalent condition to let a basic restriction solution exist is given. Then the unified solutions of the α-symmetric I* restriction method and the α(x,y)-symmetric I* restriction method are achieved for R-implications and (S, N)-implications. Besides, some special cases of optimal solutions are shown. Finally, the corresponding conclusions are provided when the two methods degenerate into the α-triple I* restriction method and α(x,y)-triple I* restriction method. These research results would be an important improvement for the fields of fuzzy inference, fuzzy logic and related applications.
Published in | Mathematics and Computer Science (Volume 4, Issue 6) |
DOI | 10.11648/j.mcs.20190406.14 |
Page(s) | 130-137 |
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Copyright © The Author(s), 2019. Published by Science Publishing Group |
Fuzzy Inference, Fuzzy Implication, Triple I Method, Symmetric Implicational Method
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APA Style
Yiming Tang, Guangqing Bao. (2019). Symmetric I* Restriction Method of Fuzzy Inference. Mathematics and Computer Science, 4(6), 130-137. https://doi.org/10.11648/j.mcs.20190406.14
ACS Style
Yiming Tang; Guangqing Bao. Symmetric I* Restriction Method of Fuzzy Inference. Math. Comput. Sci. 2019, 4(6), 130-137. doi: 10.11648/j.mcs.20190406.14
AMA Style
Yiming Tang, Guangqing Bao. Symmetric I* Restriction Method of Fuzzy Inference. Math Comput Sci. 2019;4(6):130-137. doi: 10.11648/j.mcs.20190406.14
@article{10.11648/j.mcs.20190406.14, author = {Yiming Tang and Guangqing Bao}, title = {Symmetric I* Restriction Method of Fuzzy Inference}, journal = {Mathematics and Computer Science}, volume = {4}, number = {6}, pages = {130-137}, doi = {10.11648/j.mcs.20190406.14}, url = {https://doi.org/10.11648/j.mcs.20190406.14}, eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mcs.20190406.14}, abstract = {As one of important parts of fuzzy logic, fuzzy inference plays a vital role in the fields of fuzzy control, artificial intelligence, affective computing, image processing and so forth. Two key problems of fuzzy inference are FMP (fuzzy modus ponens) and FMT (fuzzy modus tollens). How to get the ideal solution for FMP and FMT is a difficult problem in the area of fuzzy logic. Aiming at such problem, from the idea of symmetric implicational reasoning, triple I* method and restriction theory, we put forward and investigate the α-symmetric I* restriction method, and then generalize it to the α(x,y)-symmetric I* restriction method. To begin with, the α-symmetric I* restriction principle and the α(x,y)-symmetric I* restriction principle are established. Furthermore, the equivalent condition to let a basic restriction solution exist is given. Then the unified solutions of the α-symmetric I* restriction method and the α(x,y)-symmetric I* restriction method are achieved for R-implications and (S, N)-implications. Besides, some special cases of optimal solutions are shown. Finally, the corresponding conclusions are provided when the two methods degenerate into the α-triple I* restriction method and α(x,y)-triple I* restriction method. These research results would be an important improvement for the fields of fuzzy inference, fuzzy logic and related applications.}, year = {2019} }
TY - JOUR T1 - Symmetric I* Restriction Method of Fuzzy Inference AU - Yiming Tang AU - Guangqing Bao Y1 - 2019/12/24 PY - 2019 N1 - https://doi.org/10.11648/j.mcs.20190406.14 DO - 10.11648/j.mcs.20190406.14 T2 - Mathematics and Computer Science JF - Mathematics and Computer Science JO - Mathematics and Computer Science SP - 130 EP - 137 PB - Science Publishing Group SN - 2575-6028 UR - https://doi.org/10.11648/j.mcs.20190406.14 AB - As one of important parts of fuzzy logic, fuzzy inference plays a vital role in the fields of fuzzy control, artificial intelligence, affective computing, image processing and so forth. Two key problems of fuzzy inference are FMP (fuzzy modus ponens) and FMT (fuzzy modus tollens). How to get the ideal solution for FMP and FMT is a difficult problem in the area of fuzzy logic. Aiming at such problem, from the idea of symmetric implicational reasoning, triple I* method and restriction theory, we put forward and investigate the α-symmetric I* restriction method, and then generalize it to the α(x,y)-symmetric I* restriction method. To begin with, the α-symmetric I* restriction principle and the α(x,y)-symmetric I* restriction principle are established. Furthermore, the equivalent condition to let a basic restriction solution exist is given. Then the unified solutions of the α-symmetric I* restriction method and the α(x,y)-symmetric I* restriction method are achieved for R-implications and (S, N)-implications. Besides, some special cases of optimal solutions are shown. Finally, the corresponding conclusions are provided when the two methods degenerate into the α-triple I* restriction method and α(x,y)-triple I* restriction method. These research results would be an important improvement for the fields of fuzzy inference, fuzzy logic and related applications. VL - 4 IS - 6 ER -