Multi-valued Connectives for Fuzzy Sets

TL;DR

This paper introduces a method to construct multi-valued t-norms and t-conorms using pairs of single-valued norms, resulting in interval-valued structures that combine features of different norms for fuzzy set applications.

Contribution

It proposes a novel procedure for creating multi-valued t-norms and t-conorms from existing single-valued norms, enabling more flexible fuzzy logic operations.

Findings

Produces interval-valued t-norms and t-conorms from single-valued pairs

Creates superlattice structures as multivalued analogs of lattices

Combines desirable properties of different t-norms and t-conorms

Abstract

We present a procedure for the construction of multi-valued t-norms and t-conorms. Our procedure makes use of a pair of single-valued t-norms and the respective dual t-conorms and produces interval-valued t-norms and t-conorms. In this manner we combine desirable characteristics of different t-norms and t-conorms; if we use the t-norm min and t-conorm max, then the resulting structure is a superlattice, i.e. the multivalued analog of a lattice.