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A Bibliometric Analysis of the Explainable Artificial Intelligence Research Field Read chapter Read first chapter

2018 | OriginalPaper | Chapter

First Steps Towards Harnessing Partial Functions in Fuzzy Type Theory

Author : Vilém Novák

Published in: Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations

Publisher: Springer International Publishing

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Abstract

In this paper we present how the theory of partial functions can be developed in the fuzzy type theory and show how the theory elaborated by Lapierre [3] and Lepage [4] can be included in it. Namely, the latter is developed as a special theory whose models contain the partial functions in the sense introduced by both authors.

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previous chapter New Negations on the Type-2 Membership Degrees
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Footnotes
1
It is required that Sq gives square root for all elements from \(M_{\epsilon }\), on which it is defined and may give arbitrary elements otherwise.
 
2
We silently assumed that the crisp inequality \(\ge \) is also defined.
 
3
In fact, we can consider here some arbitrary type \(\alpha \) provided that we will specify its properties characterizing people.
 
Literature
1.
Andrews, P.: An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof. Kluwer, Dordrecht (2002)CrossRef
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4.
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6.
Novák, V.: A comprehensive theory of trichotomous evaluative linguistic expressions. Fuzzy Sets Syst. 159(22), 2939–2969 (2008)MathSciNetCrossRef
7.
8.
9.
Novák, V.: Fuzzy type theory with partial functions. Iran. J. Fuzzy Syst. (submitted)
10.
Metadata
Title
First Steps Towards Harnessing Partial Functions in Fuzzy Type Theory
Author
Vilém Novák
Copyright Year
2018
Book
Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations

Print ISBN: 978-3-319-91472-5

Electronic ISBN: 978-3-319-91473-2

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-91473-2_62

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