Concerning a quantum-like uncertainty relation for pairs of complementary fuzzy sets
type: Item
instance of: scholarly article
title: Concerning a quantum-like uncertainty relation for pairs of complementary fuzzy sets
zbMATH Open document ID: 0627.03007
DOI: 10.1016/0022-247X(87)90248-4
author: Mieczyslaw Albert Kaaz
published in: Journal of Mathematical Analysis and Applications
publication date: 1987-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 03B52
Mathematics Subject Classification ID: 03E72
Mathematics Subject Classification ID: 03G12
Mathematics Subject Classification ID: 06F30
Mathematics Subject Classification ID: 94D05
zbMATH DE Number: 4019023
zbMATH Keywords: uncertainty relations
zbMATH Keywords: Brouwerian algebra
zbMATH Keywords: fuzzy set
zbMATH Keywords: commutation gap
zbMATH Keywords: grading function
MaRDI profile type: Publication
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full work available at URL: 0022-247x(87)90248-4
OpenAlex ID: W2094818047
description: scientific article; zbMATH DE number 4019023