On a class of generated triangular norms and their isomorphisms
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Cited by (9)
Characterizations of monotone right continuous functions which generate associative functions
2024, Fuzzy Sets and SystemsAdditive generators of 2-uninorms
2023, Fuzzy Sets and SystemsIsomorphic t-(sub)norms generated by the product and Galois connections
2023, Fuzzy Sets and SystemsCitation Excerpt :It is well known that each continuous Archimedean t-norm can be generated by a strictly increasing continuous multiplicative generator, or equivalently, by a strictly decreasing continuous additive generator [9]. Subsequently, by generalizing this method, more t-norms are obtained in the literature [5,8,11–15]. In particular, Zhang gives a method to construct a t-norm on a bounded partially ordered set P by a given t-norm on a bounded partially ordered set Q and a Galois connection between P and Q [15].
The constructions of non-continuous additive generators of t-conorms based on discrete additive generators of discrete t-conorms
2020, Fuzzy Sets and SystemsCitation Excerpt :With respect to Remark 2 (ii) we immediately obtain the following consequence of Theorem 6. It follows from the result proved by Viceník [9, Theorem 1] that the construction method described in the proof of Theorem 6 enables us to constructs from one discrete strictly increasing additive generator of a discrete t-conorm infinitely many additively generated border-continuous t-conorms which are pairwise non-isomorphic. We have dealt with strictly increasing additive generators so far.
Lipschitz continuity of triangular subnorms
2014, Fuzzy Sets and SystemsOn some algebraic and topological properties of generated border-continuous triangular norms
2013, Fuzzy Sets and Systems