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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Notes
- 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.
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Acknowledgement
This paper was supported by the grant 16-19170S of GAČR, Czech Republic.
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Novák, V. (2018). First Steps Towards Harnessing Partial Functions in Fuzzy Type Theory. In: Medina, J., et al. Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations. IPMU 2018. Communications in Computer and Information Science, vol 853. Springer, Cham. https://doi.org/10.1007/978-3-319-91473-2_62
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DOI: https://doi.org/10.1007/978-3-319-91473-2_62
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