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1 year ago in Abstract Algebra , Fuzzy Logic By Khushboo Sharma

Why are t-norms and s-norms used in fuzzy algebra, and what are their applications for hemirings?

I'm working on formalizing uncertainty in network resource allocation, which uses a hemiring framework. I understand the basic definitions of these norms but struggle to intuitively grasp why they are the chosen tools and how they translate into practical applications.

 

T-norms S-norms Hemiring

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By Adi Answered 1 year ago

In my experience designing fuzzy control systems, t-norms and s-norms aren't arbitrary; they are the only functions that generalize logical AND and OR to a continuous scale while preserving crucial monotonicity and boundary properties. This makes them indispensable. When we move to a hemiring a structure I've used in scheduling with uncertain durations these norms allow us to define a consistent arithmetic of "partial truths." They let you add and multiply degrees of membership, turning the hemiring into a powerful toolbox for optimizing decisions under graded constraints.

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