Some Remarks on the Solutions to the Functional Equation I(x, y) = I(x, I(x, y)) for D-Operations
Some Remarks on the Solutions to the Functional Equation I(x, y) = I(x, I(x, y)) for D-Operations
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DOI：
10.1007/978-3-642-14055-6_70
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发表时间：
2010-06
期刊：
影响因子：
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通讯作者：
S. Massanet;J. Torrens
中科院分区：
文献类型：
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作者：
S. Massanet;J. Torrens
本文研究了迭代函数方程I（x，y）=I（x，I（x，y）），其中I表示一个模糊蕴涵.该方程来自清晰逻辑中的重言式，是根据A. Xie和F. Qin（2010）Information Sciences，doi：10.1016/j.ins.2010.01.023，阐明了可以使用哪些类型的连续t-范数和t-余范数来生成满足上述方程的D-运算。
This paper is devoted to the iterative functional equationI(x,y) =I(x,I(x,y)) for allx,y∈ [0,1] whereIdenotes a fuzzy implication. This equation, that comes from a tautology in crisp logic, is revised from the results obtained in A. Xie and F. Qin (2010) Information Sciences, doi:10.1016/j.ins.2010.01.023, clarifying which kinds of continuous t-norms and t-conorms can be used in order to generate D-operations satisfying the mentioned equation.