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Volume 1, Issue 1
  • ISSN: 2666-2949
  • E-ISSN: 2666-2957

Abstract

In computer science, one often needs to deal with undefined values. For example, they naturally increase when a mistake such as the square root of a negative number or division by zero occurs. A similar problem occurs in the logical analysis of natural language. For example, the expression “Czech president in the 18th century” has no denotation because there was no Czech president before 1918. Such a situation in mathematics is characterized by partial functions, ., functions that may be undefined for specific arguments.

In this paper, we will extend the theory of intermediate quantifiers (., expressions such as “most, almost all, many, a few,” .) to deal with partially defined fuzzy sets. First, we will extend algebraic operations that are used in fuzzy logic by the additional value “undefined.” Then we will introduce intermediate quantifiers using the former. The theory of intermediate quantifiers has been developed as a special theory of higher-order fuzzy logic.

In this paper, we introduce the quantifiers semantically and show how they can be computed. The latter is also demonstrated in three illustrative examples.

The paper contributes to the development of fuzzy quantifier theory and its extension by undefined values and suggests methods for computation of truth values.

© 2022 Bentham Science Publishers
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2022-04-01
2024-11-25

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/content/journals/flme/10.2174/2666294901666210105141618
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Partial Fuzzy Quantifiers and their Computation
Journal of Fuzzy Logic and Modeling in Engineering 1, e010621189940 (2022); https://doi.org/10.2174/2666294901666210105141618
/content/journals/flme/10.2174/2666294901666210105141618
/content/journals/flme/10.2174/2666294901666210105141618
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  • Article Type:     Research Article
Keyword(s): Bochvar connectives; fuzzy generalized quantifiers; Higher-order fuzzy logic; intermediate quantifiers; partial fuzzy sets; partial fuzzy type theory; Sobocinski connectives

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