Year: 2025
Type: preprint
Abstract: Let $θ:[0,1]\rightarrow[-\infty,+\infty]$ be a function with both $θ(x^{-})$ and $θ(x^{+})$ existing for every $x\in [0,1]$ and $\vartheta:[-\infty,+\infty]\rightarrow[-\infty,+\infty]$ be a function. In this article we completely characterize the pair $(θ,\vartheta)$ for the bivariate function $O_{θ,\vartheta}: [0,1]^{2}\rightarrow[0,1]$ given by $$O_{θ,\vartheta}(x,y)=\vartheta(θ(x)+θ(y))$$ being an overlap function. In particular, we give analytical expressions of some transformations for the pair $(θ,\vartheta)$.
Source: arXiv (Cornell University)
Authors: Liang, Li-zhi, Wang, Xue-ping
Institution: Sichuan Normal University
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Award: G144394107
OpenAlex ID: W4416958789
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