Oriented Fuzzy Numbers vs. Fuzzy Numbers

Piasecki, Krzysztof; Łyczkowska-Hanćkowiak, Anna

doi:10.3390/math9050523

Cited by 5 publications

(13 citation statements)

References 47 publications

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“…For example, price closes changes may be predicted with the use of prediction table presented in [125]. In [126], it is shown that OFN application for a portfolio analysis is more useful than the analogous application of FN. For these reasons, an imprecise PV may be evaluated by OFN [42,62].…”

Section: Oriented Fuzzy Present Valuementioning

confidence: 99%

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On Present Value Evaluation under the Impact of Behavioural Factors Using Oriented Fuzzy Numbers

Piasecki

Łyczkowska-Hanćkowiak

2021

Symmetry

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In general, the present value (PV) concept is ambiguous. Therefore, behavioural factors may influence on the PV evaluation. The main aim of our paper is to propose some method of soft computing PV evaluated under the impact of behavioural factors. The starting point for our discussion is the notion of the Behavioural PV (BPV) defined as an imprecisely real-valued function of distinguished variables which can be evaluated using objective financial knowledge or subjective behavioural premises. In our paper, a BPV is supplemented with a forecast of the asset price closest to changes. Such BPV is called the oriented BPV (O-BPV). We propose to evaluate an O-BPV by oriented fuzzy numbers which are more useful for portfolio analysis than fuzzy numbers. This fact determines the significance of the research described in this article. O-BPV may be applied as input signal for systems supporting invest-making. We consider here six cases of O-BPV: overvalued asset with the prediction of a rise in its price, overvalued asset with the prediction of a fall in its price, undervalued asset with the prediction of a rise in its price, undervalued asset with the prediction of a fall in its price, fully valued asset with the prediction of a rise in its rice and fully valued asset with the prediction of a fall in its rice. All our considerations are illustrated by numerical examples. Presented examples show the way in which we transform superposition of objective market knowledge and subjective investment opinion into simple return rate.

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Section: Oriented Fuzzy Present Valuementioning

confidence: 99%

“…This replacement does not require any additional data. In [126], it is shown that oriented PV application for a portfolio analysis is more useful than the analogous application of fuzzy PV. This makes the use of O-BPV more preferred than the use of F-BPV.…”

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confidence: 99%

On Present Value Evaluation under the Impact of Behavioural Factors Using Oriented Fuzzy Numbers

Piasecki

Łyczkowska-Hanćkowiak

2021

Symmetry

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“…The notation I ≡ K means that "the interval I may be equivalently replaced by the interval K". The relationships between FNs, ordered FNs, and OFNs are discussed in detail in [34].…”

Section: Trapezoidal Oriented Fuzzy Numbers-basic Factsmentioning

confidence: 99%

“…Let symbol * denote any arithmetic operation defined in R and symbol * denote an extension of an arithmetic operation * to K [13]. Kosiński has defined arithmetic operators on ordered FNs in an intuitive way, but the addition of a dot product extended to the space K has a very high level of formal complexity [34]. Therefore, in many applications researchers limit their calculations to arithmetic operations determined in the space K Tr .…”

Section: Trapezoidal Oriented Fuzzy Numbers-basic Factsmentioning

confidence: 99%

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The Use of Trapezoidal Oriented Fuzzy Numbers in Portfolio Analysis

Łyczkowska-Hanćkowiak

2021

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Oriented fuzzy numbers are a convenient tool to manage an investment portfolio as they enable the inclusion of uncertain and imprecise information about the financial market in a portfolio analysis. This kind of portfolio analysis is based on the discount factor. Thanks to this fact, this analysis is simpler than a portfolio analysis based on the return rate. The present value is imprecise due to the fact that it is modelled with the use of oriented fuzzy numbers. In such a case, the expected discount factor is also an oriented fuzzy number. The main objective of this paper is to conduct a portfolio analysis consisting of the instruments with the present value estimated as a trapezoidal oriented fuzzy number. We consider the portfolio elements as being positively and negatively oriented. We test their discount factor. Due to the fact that adding oriented fuzzy numbers is not associative, a weighted sum of positively oriented discount factors and a weighted sum of negatively oriented factors is calculated and consequently a portfolio discount factor is obtained as a weighted addition of both sums. Also, the imprecision risk of the obtained investment portfolio is estimated using measures of energy and entropy. All theoretical considerations are illustrated by an empirical case study.

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Recommendations of Stockbrokers Versus Fuzzy Portfolio Approach in Construction Sector

Łyczkowska-Hanćkowiak,

Wójcicka-Wójtowicz

2023

Contributions to Statistics

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Oriented Fuzzy Numbers vs. Fuzzy Numbers

Cited by 5 publications

References 47 publications

On Present Value Evaluation under the Impact of Behavioural Factors Using Oriented Fuzzy Numbers

On Present Value Evaluation under the Impact of Behavioural Factors Using Oriented Fuzzy Numbers

The Use of Trapezoidal Oriented Fuzzy Numbers in Portfolio Analysis

Recommendations of Stockbrokers Versus Fuzzy Portfolio Approach in Construction Sector

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