Generalizing the sigmoid function using continuous-valued logic

In this study, we present a continuous-valued logical approach to generalize the sigmoid function. Our starting point is kappa function, which known as unary operator in logic. First extend function (a,b) interval, and then interpret generalized limit of extended when b tend negative positive infinity, respectively. Since induced by an additive generator strict t-norm or t-conorm, dependent. Based on properties new show that it can be viewed generalization classical Also, demonstrate special case Next, provide sufficient condition for equality two functions. It well utilized logistic regression preference modeling. Here, how using function-based measure.