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Order norms on bounded partially ordered sets. (English) Zbl 0814.04005
Since triangular norms and conorms were introduced within the framework of probabilistic metric spaces in 1963 by Schweizer and Sklar, they have been used in fuzzy set theory for the general definition of fuzzy operators (such as union and intersection). Of course, many scholars have studied the norms and got a lot of interesting results with respect to fuzzy sets. The authors of this paper generalize more general norms from triangular norms and conorms, called order norms, on bounded partially ordered sets, give an axiomatic definition of order norms, and discuss their properties, gaining many interesting results that can play an important role in fuzzy set theory.

##### MSC:
 03E72 Theory of fuzzy sets, etc. 06A99 Ordered sets 03B52 Fuzzy logic; logic of vagueness