Given the real functions v: 0,1/spl rarr/0,1 and /spl sigma/,/spl pi/: 0,1/sup 2//spl rarr/0,1. First we define a functional operator SIMP where SIMP(/spl sigma/,/spl nu/):0,1/sup 2//spl rarr/0,1 and SIMP(/spl sigma/,/spl nu/) is interpreted as the "S-implication" generated by /spl nu/ and /spl sigma/. Secondly, we define functional operators NEG(/spl pi/):0,1/spl rarr/0,1 and SNOR(/spl pi/):0,1/sup 2//spl rarr/0,1 where NEG(/spl pi/) is interpreted as the "negation" generated by /spl pi/ and SNOR(/spl pi/) is interpreted as the "S-norm" (T-conorm) generated by /spl pi/. We investigate under which assumptions these operators are injective (bijective) and which properties of the "argument functions" are translated into the "value functions". Numerous well-known results on negations, S-norms, and implications can be derived within the framework of this general approach. Further results concern the mutual definability or R-implications and T-norms.
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机译：鉴于真实功能V：> 0,1 0,1 <和/ SPL Sigma /，/ SPL PI /：> 0,1 0,1 <。首先，我们定义了一个功能运算符SIMP，其中SIMP（/ SPL SIGMA /，/ SPL NU /）：> 0,1 0,1 <和simp（/ spl sigma /，/ spl nu /）被解释为由/ SPL NU /和/ SPL SIGMA /生成的“S型暗示”/。其次，我们定义了功能运算符neg（/ spl pi /）：> 0,1 0,1 0,1 <其中neg（/ spl pi /）被解释为由/ spl pi /和snO / snO（/ spl pi /）生成的“否定”被解释为由此产生的“s-norm”（t-conorm） / spl pi /。我们调查这些操作员是注射的假设（自身样品）以及“参数函数”的属性转换为“值函数”。在这种普遍方法的框架内，否定众所周知的否定结果可以获得否定，S-NURMS和含义。进一步的结果涉及互动性或r-且r-且T型规范。
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