Abstract
In this paper, a generalized XNOR connective called fuzzy XNOR connective is introduced. First, the definition of fuzzy XNOR connective is proposed and its properties are analyzed. Then, two forms of fuzzy XNOR connectives are obtained by the composition of t-norms, t-conorms and fuzzy negations. Moreover, the relationships between fuzzy XNOR connectives and fuzzy Xor connectives introduced in Bedregal et al. (Electron Notes Theor Comput Sci 247:5–18, 2009) are discussed. At last, two new kinds of fuzzy implications are constructed by fuzzy XNOR connectives and other connectives, their main properties are also studied.
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Acknowledgments
This work is partially supported by the National Natural Science Foundation of China (Grant No. 60875034).
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Li, Y., Qin, K. & He, X. Fuzzy XNOR connectives in fuzzy logic. Soft Comput 15, 2457–2465 (2011). https://doi.org/10.1007/s00500-011-0708-1
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DOI: https://doi.org/10.1007/s00500-011-0708-1