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Quasi- and pseudo-inverses of monotone functions, and the construction of t-norms. (English) Zbl 0953.26008
Summary: Several properties of quasi- and pseudo-inverses of a non-decreasing real function are discussed. Based on a result of Schweizer and Sklar, for a given triangular norm $$T$$ and non-decreasing function $$f$$ a construction method leading to a commutative, fully ordered semigroup on the unit interval is given. A similar construction based on the pseudo-inverse implies that the resulting operation will be bounded from above by the minimum, but then the associativity may be violated. Several sufficient conditions for constructing new t-norms from a given one and a non-decreasing function $$f$$, based on its quasi-inverse and on its pseudo-inverse, respectively, are discussed, together with illustrative examples.

##### MSC:
 2.6e+51 Fuzzy real analysis 3e+72 Theory of fuzzy sets, etc.
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##### References:
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