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Fuzzy inference has played a significant role in many applications. Although the simplified fuzzy inference method is currently mostly used, the problem is that the number of fuzzy rules becomes very huge and so the setup and adjustment of fuzzy rules become difficult. On the other hand, Yubazaki et al. have proposed a "single input rule modules connected fuzzy inference method" (SIRMs method) whose final output is obtained by summarizing the product of the importance degrees and the inference results from single input fuzzy rule module. Seki et al. have shown that the simplified fuzzy inference method and the SIRMs method are equivalent when the sum of diagonal elements in rules of the simplified fuzzy inference method is equal to that of cross diagonal elements. This paper clarifies the conditions for the infimum and supremum of the fuzzy inference method using the single input type fuzzy inference method, from the view point of fuzzy inference.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E92-A No.2 pp.611-617

- Publication Date
- 2009/02/01

- Publicized

- Online ISSN
- 1745-1337

- DOI
- 10.1587/transfun.E92.A.611

- Type of Manuscript
- PAPER

- Category
- General Fundamentals and Boundaries

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Hirosato SEKI, Hiroaki ISHII, "On the Infimum and Supremum of Fuzzy Inference by Single Input Type Fuzzy Inference" in IEICE TRANSACTIONS on Fundamentals,
vol. E92-A, no. 2, pp. 611-617, February 2009, doi: 10.1587/transfun.E92.A.611.

Abstract: Fuzzy inference has played a significant role in many applications. Although the simplified fuzzy inference method is currently mostly used, the problem is that the number of fuzzy rules becomes very huge and so the setup and adjustment of fuzzy rules become difficult. On the other hand, Yubazaki et al. have proposed a "single input rule modules connected fuzzy inference method" (SIRMs method) whose final output is obtained by summarizing the product of the importance degrees and the inference results from single input fuzzy rule module. Seki et al. have shown that the simplified fuzzy inference method and the SIRMs method are equivalent when the sum of diagonal elements in rules of the simplified fuzzy inference method is equal to that of cross diagonal elements. This paper clarifies the conditions for the infimum and supremum of the fuzzy inference method using the single input type fuzzy inference method, from the view point of fuzzy inference.

URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E92.A.611/_p

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@ARTICLE{e92-a_2_611,

author={Hirosato SEKI, Hiroaki ISHII, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={On the Infimum and Supremum of Fuzzy Inference by Single Input Type Fuzzy Inference},

year={2009},

volume={E92-A},

number={2},

pages={611-617},

abstract={Fuzzy inference has played a significant role in many applications. Although the simplified fuzzy inference method is currently mostly used, the problem is that the number of fuzzy rules becomes very huge and so the setup and adjustment of fuzzy rules become difficult. On the other hand, Yubazaki et al. have proposed a "single input rule modules connected fuzzy inference method" (SIRMs method) whose final output is obtained by summarizing the product of the importance degrees and the inference results from single input fuzzy rule module. Seki et al. have shown that the simplified fuzzy inference method and the SIRMs method are equivalent when the sum of diagonal elements in rules of the simplified fuzzy inference method is equal to that of cross diagonal elements. This paper clarifies the conditions for the infimum and supremum of the fuzzy inference method using the single input type fuzzy inference method, from the view point of fuzzy inference.},

keywords={},

doi={10.1587/transfun.E92.A.611},

ISSN={1745-1337},

month={February},}

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TY - JOUR

TI - On the Infimum and Supremum of Fuzzy Inference by Single Input Type Fuzzy Inference

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 611

EP - 617

AU - Hirosato SEKI

AU - Hiroaki ISHII

PY - 2009

DO - 10.1587/transfun.E92.A.611

JO - IEICE TRANSACTIONS on Fundamentals

SN - 1745-1337

VL - E92-A

IS - 2

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - February 2009

AB - Fuzzy inference has played a significant role in many applications. Although the simplified fuzzy inference method is currently mostly used, the problem is that the number of fuzzy rules becomes very huge and so the setup and adjustment of fuzzy rules become difficult. On the other hand, Yubazaki et al. have proposed a "single input rule modules connected fuzzy inference method" (SIRMs method) whose final output is obtained by summarizing the product of the importance degrees and the inference results from single input fuzzy rule module. Seki et al. have shown that the simplified fuzzy inference method and the SIRMs method are equivalent when the sum of diagonal elements in rules of the simplified fuzzy inference method is equal to that of cross diagonal elements. This paper clarifies the conditions for the infimum and supremum of the fuzzy inference method using the single input type fuzzy inference method, from the view point of fuzzy inference.

ER -