New S-norm and T-norm Operators for Active Learning Method

Active Learning Method (ALM) is a soft computing method used for modeling and control based on fuzzy logic. All operators defined for fuzzy sets must serve as either fuzzy S-norm or fuzzy T-norm. Despite being a powerful modeling method, ALM does not possess operators which serve as S-norms and T-norms which deprive it of a profound analytical expression/form. This paper introduces two new operators based on morphology which satisfy the following conditions: First, they serve as fuzzy S-norm and T-norm. Second, they satisfy Demorgans law, so they complement each other perfectly. These operators are investigated via three viewpoints: Mathematics, Geometry and fuzzy logic.

[1]  Ieee Xplore,et al.  IEEE Transactions on Pattern Analysis and Machine Intelligence Information for Authors , 2022, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[2]  N. Otsu.  A threshold selection method from gray level histograms , 1979 .

[3]  H. O. Foulkes.  Abstract Algebra , 1967, Nature.

[4]  S. Tanimoto,et al.  Time Complexity For Serial And Parallel Propagation In Images. , 1984, Optics & Photonics.

[5]  Xinhua Zhuang,et al.  Image Analysis Using Mathematical Morphology , 1987, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[6]  Nakaji Honda,et al.  Acquisition of Knowledge for Gymnastic Bar Action by Active Learning Method , 2003, J. Adv. Comput. Intell. Intell. Informatics.

[7]  Junji Nishino,et al.  Hierarchical Fuzzy Intelligent Controller for Gymnastic Bar Actions , 1999, J. Adv. Comput. Intell. Intell. Informatics.

[8]  Linda G. Shapiro,et al.  Ordered structural shape matching with primitive extraction by mathematical morphology , 1987, Pattern Recognit..

[9]  Michio Sugeno,et al.  Fuzzy identification of systems and its applications to modeling and control , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[10]  Azriel Rosenfeld,et al.  Computer Vision , 1988, Adv. Comput..

[11]  Robert E. Tarjan,et al.  Efficiency of a Good But Not Linear Set Union Algorithm , 1972, JACM.

[12]  Nakaji Honda,et al.  Fuzzy Interpretation of Human Intelligence , 1999, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[13]  Azriel Rosenfeld,et al.  Sequential Operations in Digital Picture Processing , 1966, JACM.

[14]  Dana H. Ballard,et al.  Computer Vision , 1982 .

[15]  Jean Serra,et al.  Image Analysis and Mathematical Morphology , 1983 .

[16]  Linda G. Shapiro,et al.  A new connected components algorithm for virtual memory computers , 1983, Comput. Vis. Graph. Image Process..

[17]  Richard S. Sutton,et al.  Neuronlike adaptive elements that can solve difficult learning control problems , 1983, IEEE Transactions on Systems, Man, and Cybernetics.

[18]  Nakaji Honda,et al.  A Hardware System of Active Learning Method , 2003 .