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The Extended Alpha-triple I Algorithm Based on the Generalized Implication Operator

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Abstract

In this paper, the classical implication operator is generalized, and then the definition of generalized implication operator on [0, 1] is proposed. Based on generalized implication operator, the extended alpha-triple I principle is presented by generalizing the alpha-triple I algorithm. By analyzing the essence of alpha-triple Fuzzy Modus Ponens (FMP) and alpha-triple Fuzzy Modus Tollens (FMT) principles, and based on the generalized implication operator, the generalized calculating formula of extended alpha-triple I algorithm is proposed. At the same time, the reversibility on the proposed alpha-triple I algorithm is discussed. It is proved that Compositional Rule of Inference (CRI) is a special case of extended alpha-triple I algorithm. Finally, two implication operations are proposed to validate the proposed generalized equation.

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Authors and Affiliations

  1. School of Information Engineering, University of Science and Technology Beijing, Beijing, China

    Bingru Yang, Zhangyan Xu & Wei Song

  2. Computer Department, Guangxi Normal University, Guilin, China

    Zhangyan Xu

Authors
  1. Bingru Yang
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  2. Zhangyan Xu
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  3. Wei Song
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Correspondence to Bingru Yang.

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Yang, B., Xu, Z. & Song, W. The Extended Alpha-triple I Algorithm Based on the Generalized Implication Operator. Fuzzy Optim Decis Making 5, 141–152 (2006). https://doi.org/10.1007/s10700-006-7332-z

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  • DOI: https://doi.org/10.1007/s10700-006-7332-z

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