TL;DR
The paper introduces grainy numbers, a lattice structure of bit tuples, proposing an alternative negation called supplement for fuzzy set theory.
Contribution
It defines grainy numbers as a new mathematical structure and introduces the supplement negation as an alternative to traditional complement.
Findings
Grainy numbers form a lattice with addition and multiplication as meet and join.
The supplement negation offers a new approach to fuzzy set complement.
Potential applications in fuzzy logic and set theory.
Abstract
Grainy numbers are defined as tuples of bits. They form a lattice where the meet and the join operations are an addition and a multiplication. They may be substituted for the real numbers in the definition of fuzzy sets. The aim is to propose an alternative negation for the complement that we'll call supplement.
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Taxonomy
TopicsAdvanced Algebra and Logic · Fuzzy Logic and Control Systems · Multi-Criteria Decision Making