@MISC{FUZZY_6.MIZ,
 TITLE = {Definition of Centroid Method as Defuzzification},
 AUTHOR = {Mitsuishi, Takashi},
  DAY = {23},
  MONTH = {July},
  YEAR = {2022},
  ADDRESS1 = {Faculty of Business and Informatics, Nagano University, Japan},
 SUMMARY = {In this study, the centroid method which is one of the fuzzy inference
  processes is formulated \cite{Mizumoto:1990}.
  The centroid method is the most popular of all defuzzied methods
  (\cite{Ross:2010}, \cite{Leekwijck:1999}, \cite{Katafuchi:2001}).
  By this method, defuzzified crisp value is obtained from domain
  of membership function as weighted average \cite{Mamdani:1974}.
  Since the integral is used in centroid method,
  the integrability and bounded properties of membership functions
  are also mentioned.
  In this paper, the properties of piecewise linear functions
  consisting of two straight lines are mainly described.}}

@book{Ross:2010,
author="Ross, Timothy J.",
title="Fuzzy Logic With Engineering Application",
publisher="John Wiley and Sons Ltd",
year="2010"}

@article{Leekwijck:1999,
  title={Defuzzification: criteria and classification},
  author={Van Leekwijck, Werner and Kerre, Etienne E},
  journal={Fuzzy sets and systems},
  volume={108},
  number={2},
  pages={159--178},
  year={1999},
  publisher={Elsevier}
}

@article{Katafuchi:2001,
  title={Investigation of Deffuzification in
  Fuzzy Inference: Proposal of a New Defuzzification Method (in Japanese)},
  author={Katafuchi, Tetsuro and Asai, Kiyoji and Fujita, Hiroshi},
  journal={Medical Imaging and Information Sciences},
  volume={18},
  number={1},
  pages={19-30},
  year={2001},
  doi={10.11318/mii1984.18.19}
}

@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"}


@inproceedings{Mizumoto:1990,
  title={Improvement of fuzzy control (IV)-Case by product-sum-gravity method},
  author={Mizumoto, Masaharu},
  booktitle={Proc. 6th Fuzzy System Symposium, 1990},
  pages={9--13},
  year={1990}
}


@INPROCEEDINGS{8712319,
  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{7274550,
  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 Lukasiewicz t-norm}, 
  year={2015},
  volume={},
  number={},
  pages={71-74},
  doi={10.1109/ICCIS.2015.7274550}}

@article{mitsuishi2009compactness,
  title={Compactness of family of fuzzy sets in {$L^2$} space with application to optimal control},
  author={Mitsuishi, Takashi and Shidama, Yasunari},
  journal={IEICE transactions on fundamentals of electronics, communications and computer sciences},
  volume={92},
  number={4},
  pages={952--957},
  year={2009},
  publisher={The Institute of Electronics, Information and Communication Engineers}
}

@ARTICLE{4497918,
  author={Seki, Hirosato and Ishii, Hiroaki and Mizumoto, Masaharu},
  journal={IEEE Transactions on Fuzzy Systems}, 
  title={On the Generalization of Single Input Rule Modules Connected Type Fuzzy Reasoning Method}, 
  year={2008},
  volume={16},
  number={5},
  pages={1180-1187},
  doi={10.1109/TFUZZ.2008.924182}}

%% SoSE
@INPROCEEDINGS{6575237,  
  author={T. {Mitsuishi} and T. {Terashima} and N. {Shimada} and T. {Homma} and Y. {Shidama}},
  booktitle={2013 8th International Conference on System of Systems Engineering}, 
  title={SIRMs fuzzy approximate reasoning using L-R fuzzy number as premise valuable}, 
  year={2013},
  volume={},
  number={},
  pages={25-27},
  doi={10.1109/SYSoSE.2013.6575237}}

