scholarly journals The Use of Trapezoidal Oriented Fuzzy Numbers in Portfolio Analysis

Symmetry ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1722
Author(s):  
Anna Łyczkowska-Hanćkowiak
Keyword(s):  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Portfolio Analysis ◽  
Discount Factor ◽  
Weighted Sum ◽  
Investment Portfolio ◽  
Present Value ◽  
Discount Factors ◽  
Theoretical Considerations

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.

scholarly journals Sharpe’s Ratio for Oriented Fuzzy Discount Factor

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 272 ◽  
Author(s):  
Anna Łyczkowska-Hanćkowiak
Keyword(s):  
Fuzzy Number ◽  
Rating Scale ◽  
Portfolio Analysis ◽  
Return Rate ◽  
Discount Factor ◽  
Present Value ◽  
Financial Instrument ◽  
Numerical Examples ◽  
Definition Of

The analysis presented in this paper regards the security of a present value given as an ordered fuzzy number. The present value was estimated in an imprecise manner and supplemented by the forecast of its coming changes. A discount factor of such security is an ordered fuzzy number of the orientation identical to the oriented present value that determines it. All classical methods of portfolio analysis are based on the definition of the return rate. In the case of securities with a fuzzy present value, a discount factor is a better tool for portfolio analysis than the return rate, which implies the chosen methods of management of securities should be revised and transformed to equivalent methods based on a discount factor. This would enable the use of those methods in the case of a financial instrument of the oriented fuzzy present value. This paper presents example results of the realization of such a postulate. The main aim of the paper is to generalize Sharpe’s ratio to a case of investment recommendations management formulated for a security characterized by an oriented discount factor. A five-degree rating scale was used. The whole deliberation is illustrated by broad numerical examples.

scholarly journals Behavioural Present Value Defined as Fuzzy Number – a New Approach

2015 ◽  
Vol 15 (2) ◽  
pp. 27-41 ◽  
Author(s):  
Krzysztof Piasecki ◽  
Joanna Siwek
Keyword(s):  
Financial Market ◽  
Fuzzy Number ◽  
Formal Model ◽  
Market Equilibrium ◽  
Present Value ◽  
New Approach ◽  
Behavioural Factors ◽  
The Impact ◽  
Numerical Case Study

Abstract The behavioural present value is defined as a fuzzy number assessed under the impact of chosen behavioural factors. The first formal model turned out to be burdened with some formal defects which are finally corrected in the presented article. In this way a new modified formal model of a behavioural present value is obtained. New model of the behavioural present value is used to explain the phenomenon of market equilibrium on the efficient financial market remaining in the state of financial imbalance. These considerations are illustrated by means of extensive numerical case study.

scholarly journals Oriented Fuzzy Numbers vs. Fuzzy Numbers

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 523
Author(s):  
Krzysztof Piasecki ◽  
Anna Łyczkowska-Hanćkowiak
Keyword(s):  
Real World ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Formal Model ◽  
Original Study ◽  
Portfolio Analysis ◽  
Algebraic Structures ◽  
Equivalent Models ◽  
Real World Problems

A formal model of an imprecise number can be given as, inter alia, a fuzzy number or oriented fuzzy numbers. Are they formally equivalent models? Our main goal is to seek formal differences between fuzzy numbers and oriented fuzzy numbers. For this purpose, we examine algebraic structures composed of numerical spaces equipped with addition, dot multiplication, and subtraction determined in a usual way. We show that these structures are not isomorphic. It proves that oriented fuzzy numbers and fuzzy numbers are not equivalent models of an imprecise number. This is the first original study of a problem of a dissimilarity between oriented fuzzy numbers and fuzzy numbers. Therefore, any theorems on fuzzy numbers cannot automatically be extended to the case of oriented fuzzy numbers. In the second part of the article, we study the purposefulness of a replacement of fuzzy numbers by oriented fuzzy numbers. We show that for a portfolio analysis, oriented fuzzy numbers are more useful than fuzzy numbers. Therefore, we conclude that oriented fuzzy numbers are an original and useful tool for modelling a real-world problems.

scholarly journals PROSPEK PENGOLAHAN MENGKUDU MENJADI SARI MORINDA DI KABUPATEN OKU TIMUR (Studi Kasus Kelompok Pangan Olahan Nay-Nay).

1970 ◽  
Vol 2 (02) ◽  
pp. 41-48
Author(s):  
Wardi Saleh
Keyword(s):  
Interest Rate ◽  
Production Process ◽  
Value Added ◽  
Discount Factor ◽  
Added Value ◽  
Present Value ◽  
Production Value ◽  
The Cost

The purpose of this research were to : (1) To know the cost and income of processing mengkudu become morinda juice in Regency OKU East, (2) To know value added of processing mengkudu become sari morinda in Regency OKU East, (3) To know feasibility of processing Mengkudu become morinda juice in Kabpaten OKU East. This research was conducted in Srikaton Village, Buay Madang Timur District, East OKU Regency. This research was conducted in April - May 2015 with the method of case study conducted directly to one farmer who do the making of noni juice in Srikaton Village. This study found that the cost of processing production to morindan mengkuduku morindan in Srikaton Village Buay Madang District East OKU Regency is Rp 351.500 / production process. While the income of Rp 898,500 / production process, the amount of added value obtained from the production value minus the cost between Rp 991.500 / production process and processing mengkudu become morinda juice deserve to be developed dengang NPV criteria present value of home industry juice morinda at an interest rate of 18% Rp 4.715.86 at the highest interest rate ie 36% of Rp -260.924maka value of NPV> 0 feasible business to dilanjutka. The value of Net B / C at the value of NPV that has been discount factor on the home industry business extract of morinda obtained at 1.30 and IRR of 35%.

scholarly journals On Application Oriented Fuzzy Numbers for Imprecise Investment Recommendations

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1672 ◽  
Author(s):  
Anna Łyczkowska-Hanćkowiak
Keyword(s):  
Risk Premium ◽  
Fuzzy Numbers ◽  
Rating Scale ◽  
Inverse Operator ◽  
Theoretical Background ◽  
The Family ◽  
Theoretical Considerations ◽  
Special Case ◽  
Inverse Operation

The subtraction of fuzzy numbers (FNs) is not an inverse operator to FNs addition. The family of all oriented FNs (OFNs) may be considered as symmetrical closure of all the FNs family in that the subtraction is an inverse operation to addition. An imprecise present value is modelled by a trapezoidal oriented FN (TrOFN). Then, the expected discount factor (EDF) is a TrOFFN too. This factor may be applied as a premise for invest-making. Proposed decision strategies are dependent on a comparison of an oriented fuzzy profit index and the specific profitability threshold. This way we get an investment recommendation described as a fuzzy subset on the fixed rating scale. Risk premium measure is a special case of profit index. Further in the paper, the Sharpe’s ratio, the Jensen’s ratio, the Treynor’s ratio, the Sortino’s ratio, Roy’s criterion and the Modiglianis’ coefficient are generalised for the case when an EDF is given as a TrOFN. In this way, we get many different imprecise recommendations. For this reason, an imprecise recommendation management module is described. Obtained results show that the proposed theory can be used as a theoretical background for financial robo-advisers. All theoretical considerations are illustrated by means of a simple empirical case study.

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

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 468
Author(s):  
Krzysztof Piasecki ◽  
Anna Łyczkowska-Hanćkowiak
Keyword(s):  
Fuzzy Numbers ◽  
Asset Price ◽  
Financial Knowledge ◽  
Present Value ◽  
Market Knowledge ◽  
Value Evaluation ◽  
Starting Point ◽  
Behavioural Factors ◽  
Objective Financial Knowledge ◽  
The Impact

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.

scholarly journals Decision Making for Project Appraisal in Uncertain Environments: A Fuzzy-Possibilistic Approach of the Expanded NPV Method

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 27
Author(s):  
Konstantinos A. Chrysafis ◽  
Basil K. Papadopoulos
Keyword(s):  
Net Present Value ◽  
Fuzzy Numbers ◽  
Cost Of Capital ◽  
Weighted Average ◽  
Present Value ◽  
Major Drawback ◽  
Project Appraisal ◽  
Equity Cost ◽  
Set Up ◽  
Intelligent Methods

The major drawback of the classic approaches for project appraisal is the lack of the possibility to handle change requests during the project’s life cycle. This fact incorporates the concept of uncertainty in the estimation of this investment’s worth. To resolve this issue, the authors use fuzzy numbers, possibilistic moments of fuzzy numbers and the hybrid (fuzzy statistic) fuzzy estimators’ method in order to introduce a fuzzy possibilistic version of the expanded net present value method (FPeNPV). This approach consists of two factors: the fuzzy possibilistic NPV and the fuzzy option premium. For the estimation of the fuzzy NPV, some basic assumptions are taken into consideration: (1) the opportunity cost of capital, used as the present value interest factor calculated through the weighted average cost of capital (WACC), (2) the equity cost, determined through the possibilistic set-up of the capital asset pricing model CAPM, and (3) the inflation factor, also included in the estimation of the NPV. The fuzzy estimators’ method is used for the computation of the fuzzy option premium. An algorithm of nine major steps leads to the computation of the FPeNPV. This gives the administration the opportunity to adapt to potential changes in the company’s internal and external environments. In this way, the symmetry between the planning and execution phase of a project can be reinstated. The results validate the statement that fuzzy and intelligent methods remain valuable tools to express uncertainty in various scientific areas. Finally, an illustrative example aims at a thorough comprehension of this new approach of the expanded NPV method.

Directed earned value management based on ordered fuzzy numbers

2021 ◽  
pp. 1-14
Author(s):  
Seyed Taha Hossein Mortaji ◽  
Siamak Noori ◽  
Morteza Bagherpour
Keyword(s):  
Fuzzy Numbers ◽  
Lower Cost ◽  
Project Managers ◽  
Value Management ◽  
Monitoring And Control ◽  
Earned Value ◽  
Earned Value Management ◽  
Project Monitoring ◽  
And Control

Earned value management is well-known as the most efficient method of project monitoring and control providing relatively reliable information about the project performance. However, this method requires accurate estimates of the progress of project activities, which are always associated with uncertainties that, if ignored or not addressed well, lead to incorrect results. To address this issue, the application of multi-valued logic, in particular fuzzy logic, in earned value management has recently attracted a lot of attention both in practice and research. This paper introduces directed earned value management (DEVM) in which ordered fuzzy numbers are used to express the so-called uncertainties as well as to capture more information about the trend of the project progress. To evaluate the performance of the proposed method, several numerical examples and a case study are presented. The results reveal that compared to the existing methods, DEVM has a lower computational complexity. Also, it doesn’t suffer from the overestimation effect and as a result, it has a higher ability to express project-specific dynamics. In sum, the proposed method allows project managers to make informed decisions that lead to taking preventive and corrective actions promptly and at a lower cost.

Methods for evaluating the computer network security with fuzzy number intuitionistic fuzzy dual Hamy mean operators

2020 ◽  
Vol 39 (3) ◽  
pp. 4427-4441
Author(s):  
Bin Xu
Keyword(s):  
Network Security ◽  
Membership Function ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Computer Network ◽  
Information Aggregation ◽  
Security Evaluation ◽  
Uncertain Information ◽  
Intuitionistic Fuzzy ◽  
Computer Network Security

The concept of fuzzy number intuitionistic fuzzy sets (FNIFSs) is designed to effectively depict uncertain information in decision making problems which fundamental characteristic of the FNIFS is that the values of its membership function and non-membership function are depicted with triangular fuzzy numbers (TFNs). The dual Hamy mean (DHM) operator gets good performance in the process of information aggregation due to its ability to capturing the interrelationships among aggregated values. In this paper, we used the dual Hamy mean (DHM) operator and dual weighted Hamy mean (WDHM) operator with fuzzy number intuitionistic fuzzy numbers (FNIFNs) to propose the fuzzy number intuitionistic fuzzy dual Hamy mean (FNIFDHM) operator and fuzzy number intuitionistic fuzzy weighted dual Hamy mean (FNIFWDHM) operator. Then the MADM methods are proposed along with these operators. In the end, we utilize an applicable example for computer network security evaluation to prove the proposed methods.

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