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Granular Logic with Closeness Relation \(``\sim_{\lambda}"\) and Its Reasoning

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Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing (RSFDGrC 2005)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3641))

Abstract

Significance of granular logic, including the operational rules, studying background, is presented in this paper. This closeness relation \(``\sim_{\lambda}"\) is quoted in granular logic,and the closeness relation \(``\sim_{\lambda}"\) quoted in granular logic is defined via logical truth values. Hence, we induce several new relative properties and inference rules in the granular logic with the closeness relation. The granular logical reasoning systems with the closeness relation \(``\sim_{\lambda}"\) are also established. And this paper proves a few real examples by deductive reasoning in the systems. Significance of granular logic with closeness relation ~ λ is also described in the paper.

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Liu, Q., Wang, Q. (2005). Granular Logic with Closeness Relation \(``\sim_{\lambda}"\) and Its Reasoning. In: Ślęzak, D., Wang, G., Szczuka, M., Düntsch, I., Yao, Y. (eds) Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing. RSFDGrC 2005. Lecture Notes in Computer Science(), vol 3641. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11548669_73

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  • DOI: https://doi.org/10.1007/11548669_73

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28653-0

  • Online ISBN: 978-3-540-31825-5

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