Concerning a quantum-like uncertainty relation for pairs of complementary fuzzy sets
This paper begins with a short (10 page) summary of the Hilbert space representation of quantum mechanics. This summary of quantum mechanical principles is particularly clear and cogent (though it is followed by a much less impressive page and a half of ``epistemological reflections''). Following this is a similarly condensed but clear account of the foundations of Brouwerian algebra. The third section of the paper applies some topological concepts to Brouwerian algebra, and leads to ``Second thoughts on Fuzzy Set Principles'', where these concepts are applied to the development of fuzzy set theory. Towards the end of the paper the author suggests a relation between the areas discussed in his paper which is expressed by his ``Fundamental Assumption'': ``The commutation gap \(\delta\) bears the same relation to quantum mechanics as the grading function \(\mu\) to the fuzzy set theory''. The analogy offered here between commutation gaps and grading functions is at this stage no more than an analogy. However the clarity of the formal discussion here and the authors plans for follow-up papers, promise some fruitful investigations in the future.
scientific article; zbMATH DE number 4019023
scientific article