@ARTICLE{FUZZY_5.MIZ,
  AUTHOR = {Mitsuishi, Takashi},
  TITLE = {Some Properties of Membership Functions Composed 
    of Triangle Functions and Piecewise Linear Functions},
  NOTE = {This work has been partially supported by 
   the domestic research grant of University of Marketing 
  and Distribution Sciences 2019-2020.},
  DAY = {30},
  MONTH = {June},
  YEAR = {2021},
  ADDRESS1 = {University of Marketing and Distribution Sceinces, Kobe, Japan},
  SUMMARY = {In this study, various sets of membership functions (fuzzy sets) 
  are formalized. At first, the set of membership functions 
  \cite{FUZZY_1.ABS,FUZZY_2.ABS} is defined. Next, sine curve, cosine curve 
   and Gaussian function that ranges are limited to interval $[0,1]$ are formalized.
   On the other hand, not only curve membership functions mentioned above but also
   membership functions composed of straight lines like triangular and trapezoidal 
   functions are formalized.
   Moreover, different from the definition in \cite{FUZNUM_1.ABS} formalizations of 
   triangular and trapezoidal function composed of two straight lines, 
    minimum function and maximum functions are proposed.}}
  SECTION1 = {Preliminaries},
  SECTION2 = {The Set of Membership Functions},}

@article{Mamdani:1974,
author="MAMDANI, E. H.",
title="Application of fuzzy algorithms for control of simple dynamic plant",
journal="Proc. IEE",
year="1974",
volume="121",
number="12",
pages="1585-1588",
URL="https://ci.nii.ac.jp/naid/20000916707/",
}

@InProceedings{Mitsuishi:2012,
author="Mitsuishi, Takashi
and Terashima, Takanori
and Shimada, Nami
and Homma, Toshimichi
and Sawada, Kiyoshi
and Shidama, Yasunari",
editor="Huang, Runhe
and Ghorbani, Ali A.
and Pasi, Gabriella
and Yamaguchi, Takahira
and Yen, Neil Y.
and Jin, Beijing",
title="Continuity of Defuzzification on {L$^2$} Space for Optimization of Fuzzy Control",
booktitle="Active Media Technology",
year="2012",
publisher="Springer Berlin Heidelberg",
address="Berlin, Heidelberg",
pages="73--81",
abstract="The purpose of this study is to consider the fuzzy optimal control based on the functional analysis. We used a mathematical approach to compute optimal solutions. The feedback of fuzzy control is evaluated through approximate reasoning using the center of sums defuzzification method or the height method on IF-THEN fuzzy rules. The framework consists of two propositions: To guarantee the convergence of optimal solution, a set of fuzzy membership functions (admissible fuzzy controller) which are selected out of continuous function space is compact metrizable. And assuming approximate reasoning to be a functional on the set of membership functions, its continuity is proved. Then, we show the existence of a fuzzy controller which minimizes (maximizes) the integral performance function of the nonlinear feedback fuzzy system.",
isbn="978-3-642-35236-2"
}

@INPROCEEDINGS{Mitsuishi:2018,  
  author={T. {Mitsuishi}},  
  booktitle={2018 International Electrical Engineering Congress (iEECON)},   
  title={Uncertain Defuzzified Value of Periodic Membership Function},   
  year={2018},  volume={},  number={},  pages={1-4},  
  doi={10.1109/IEECON.2018.8712319}
}


@INPROCEEDINGS{Mitsuishi:2015,
  author={T. {Mitsuishi} and N. {Shimada} and T. {Homma} and M. {Ueda} and M. {Kochizawa} and Y. {Shidama}},
  booktitle={2015 IEEE 7th International Conference on Cybernetics and Intelligent Systems (CIS) and IEEE Conference on Robotics, Automation and Mechatronics (RAM)}, 
  title={Continuity of approximate reasoning using fuzzy number under {\L}ukasiewicz t-norm}, 
  year={2015},
  volume={},
  number={},
  pages={71-74},
% doi={10.1109/ICCIS.2015.7274550}
}
