Axiomatic Definition of Fuzzy Present Value from the Economic Point-view

Krzysztof Piasecki

Abstract

The concept of present value (PV) may be determinedas the cash flow utility which additionally satisfies the conditions: 1the utility of any current payment is equal to nominal valueof this payment; 2the utility is always an odd function of payment nominalvalue. Obtained in this way PV definition is called generalized PV definition becauseof it is more general thanthe Peccati’s axiomatic PV definition. Due behavioralreasons the PV may be imprecisely valued. The fuzzy set theory is applied as effectivetool of this imprecision description.Proposed by Calzi’s axiomatic definition of fuzzy PV (F-PV) isstrictly connected with the Peccati’s definition which is weakly consistentwith the economics. It is shown that from economical point view the general PV definition is better than the Peccati’s one. Thus,we take into accountthe generalized definition of PV as the starting point for construction of a new axiomatic F-PV definition. All axioms of generalized PV definition are extended to the case when the imprecise present value is given as any fuzzy number. Attached at the endmathematical Appendix contains explicit definitions of all notions of mathematics for fuzzy systems which are applied in this paper
Author Krzysztof Piasecki (WZ / KIiN)
Krzysztof Piasecki,,
- Department of Investment and Real Estate
Pages1-8
Publication size in sheets0.5
Book Jedlička Pavel, Firlej Krzysztof, Marešová Petra, Soukal Ivan (eds.): Hradec Economic Days : Double-blind Peer Reviewed Proceedings of the International Scientific Conference Hradec Economic Days 2020, Hradec Economic Days, vol. 10, 2020, University of Hradec Králové, ISBN 9788074357763, 906 p.
Keywords in Polishnieprecyzyjność, wartość bieżąca, liczba rozmyta
Keywords in Englishimprecision; present value;fuzzy number
DOIDOI:10.36689/uhk/hed/2020-01-069
URL http://hdl.handle.net/20.500.12603/270
Languageen angielski
Score (nominal)5
Score sourcepublisherList
ScoreMinisterial score = 5.0, 23-04-2020, ChapterFromConference
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