Triangular Norms on Partially Ordered Sets

doi:10.1002/malq.70014

Triangular Norms on Partially Ordered Sets

2026-05-01

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DOI：10.1002/malq.70014

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In this study, we extend the additively generated triangular norms from the framework of the unit interval to that of partially ordered sets. We present several conditions under which this formula yields a t-norm, where are partially ordered sets, and are monotone functions and is a t-norm/t-conorm on . The partially ordered semigroups induced by are order-preserving/order-reversing homomorphic to semigroup deformations of the semigroup induced by .

Keywords:

additive generator

homomorphism

partially ordered semigroup

t-norm

Triangular Norms on Partially Ordered Sets

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