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 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.

Edges of Regression and Limit Normal Point of Conjugate Surfaces1

1998 ◽  
Vol 122 (4) ◽  
pp. 419-425 ◽  
Author(s):  
Ningxin Chen
Keyword(s):  
Differential Geometry ◽  
Contact Boundary ◽  
Boundary Line ◽  
Tangent Point ◽  
Common Tangent ◽  
Numerical Examples ◽  
Envelope Surface ◽  
The Common ◽  
Conjugate Surfaces ◽  
Definition Of

The presented paper utilizes the basic theory of the envelope surface in differential geometry to investigate the undercutting line, the contact boundary line and the limit normal point of conjugate surfaces in gearing. It is proved that (1) the edges of regression of the envelope surfaces are the undercutting line and the contact boundary line in theory of gearing respectively, and (2) the limit normal point is the common tangent point of the two edges of regression of the conjugate surfaces. New equations for the undercutting line, the contact boundary line and the limit normal point of the conjugate surfaces are developed based on the definition of the edges of regression. Numerical examples are taken for illustration of the above-mentioned concepts and equations. [S1050-0472(00)00104-5]

scholarly journals Analisis Kelayakan Usaha Industri Rumput Laut Bagi Industri Kecil Menengah Di Kecamatan Moro Kabupaten Karimun Provinsi Kepulauan Riau

2019 ◽  
Vol 3 (1) ◽  
pp. 82-92
Author(s):  
Fatahurrazak Fatahurrazak
Keyword(s):  
Net Present Value ◽  
Payback Period ◽  
Discount Factor ◽  
Rate Of Return ◽  
Internal Rate Of Return ◽  
Present Value ◽  
Internal Rate

Penelitian ini bertujuan untuk melihak kelayakan bisnis pada Pembangunan Kompleks Industri Maritim (Sentra Industri) Pengolahan Rumput Laut di Kecamatan Moro, Kabupaten Karimun Provinsi Kepulauan Riau dimaksudkan untuk memacu pertumbuhan industri daerah dengan keterlibatan para pihak berkepentingan termasuk pengusaha industri kecil dan menengah sehingga memberikan manfaat bagi berbagai pihak. Penyusunan pola pengembangan sentra menggunakan konsepsi sebagaimana diatur dalam perundang-undangan diharapkan menghadirkan sentra dengan prinsip lingkungan bersih, industri hijau dengan memperhatikan sanitasi dan higienitas, keseimbangan dengan ruang terbuka dan efektivitas pemanfaatan ruang dan biaya. Metodologi dalam menghasilkan keluaran tersebut di atas dilakukan dengan mempelajari data primer dan data skunder yang didapat langsung dari lokasi dan pemerintah daerah Kabupaten Karimun. dokumen sekunder berupa RPJPD – RPJMD – RTRW Kabupaten Karimun, rencana strategi terkait pengembangan industri, infrastruktur, peran institusi maupun stakeholder terkait dalam pengembangan Sentra Industri pengolahan rumput laut, dan kebijakan ekonomi daerah yang relevan. Pengumpulan data dan informasi pula dilakukan dengan observasi langsung pada lokasi, wawancara, dan kuisioner. Alat analisis yang digunakan adalah Net Present Value dengan discount factor 15%, Net B/C, Internal Rate of Return, dan Payback Period. Dan hasilnya adalah NPV > 0, layak dilaksanakan, Net B/C > 1, layak dilaksanakan, IRR > discount factor 15%, layak dilaksanakan, dan Payback Period 4,18 tahun.

Solution of Basic Inventory Model in Fuzzy and Interval Environments

2017 ◽  
pp. 65-95
Author(s):  
Sankar Prasad Mondal
Keyword(s):  
Differential Equation ◽  
Fuzzy Number ◽  
Interval Number ◽  
Inventory Model ◽  
Time Dependent ◽  
Equation Approach ◽  
Numerical Examples ◽  
Fuzzy Environment

In this present paper a basic inventory model is solved in different imprecise environments. Four different cases are discussed: 1) Crisp inventory model, that is, the quantity at present and demand is crisp number; 2) Inventory model in fuzzy environment, that is, the quantity and demand both are fuzzy number; 3) Inventory model in interval environment, that is, the quantity and demand both are interval number and lastly; 4) Inventory model in time dependent fuzzy environment, that is, quantity and demand are both time dependent fuzzy number. Different numerical examples are used to illustrate the model as well as to compute the efficiency of imprecise differential equation approach to solve the model.

A MODIFICATION OF THE INDEX OF LIOU AND WANG FOR RANKING FUZZY NUMBER

2007 ◽  
Vol 15 (04) ◽  
pp. 411-424 ◽  
Author(s):  
M. SOCORRO GARCIA ◽  
M. TERESA LAMATA
Keyword(s):  
Satisfactory Result ◽  
Coefficient Of Variation ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Mean Value ◽  
Weighted Mean ◽  
Numerical Examples ◽  
Centroid Point ◽  
Ranking Fuzzy Number ◽  
Index Of Optimism

Different methods have been proposed for ranking fuzzy numbers. These include methods based on distances, centroid point, coefficient of variation, and weighted mean value. However, there is still no method that can always give a satisfactory result to every situation; some are counterintuitive and not discriminating. This paper presents an approach for ranking fuzzy numbers with integral value that is an extension of the index of Liou and Wang. This method, that is independent of the type of membership function used, can rank more than two fuzzy numbers simultaneously. This ranking method use an index of optimism to reflect the decision maker's optimistic attitude, but rather it also contains an index of modality that represents the neutrality of the decision maker. The approach is illustrated with numerical examples.

A Modified Reliability Index Approach for Reliability-Based Design Optimization

2009 ◽  
Author(s):  
Po Ting Lin ◽  
Hae Chang Gea ◽  
Yogesh Jaluria
Keyword(s):  
Reliability Index ◽  
Reliability Based Design Optimization ◽  
Convergence Problem ◽  
Analysis Problem ◽  
Numerical Examples ◽  
Reliability Based Design ◽  
Index Approach ◽  
Convergence Problems ◽  
Definition Of ◽  
Performance Constraint

RBDO problems have been intensively studied for many decades. Since Hasofer and Lind defined a measure of the second-moment reliability index, many RBDO methods utilizing the concept of reliability index have been introduced as the Reliability Index Approach (RIA). In the RIA, a reliability analysis problem is formulated to find the reliability index for each performance constraint and the solutions are used to evaluate the failure probability. However, the traditional RIA suffers from inefficiency and convergence problems. In this paper, we revisited the definition of the reliability index and revealed the convergence problem in the traditional RIA. Furthermore, a new definition of the reliability index is proposed to correct this problem and a modified Reliability Index Approach based on this definition is developed. Numerical examples using both the traditional RIA and the modified RIA are compared and discussed.

scholarly journals Professional Development of Teachers in Colleges of Pakistan: A Comparative Case Study of Public and Private Colleges of Pakistan

2014 ◽  
Vol 3 (6) ◽  
pp. 167 ◽  
Author(s):  
Hassan Danial Aslam
Keyword(s):  
Professional Development ◽  
Quantitative Method ◽  
Research Study ◽  
Rating Scale ◽  
Comparative Case Study ◽  
Development Programs ◽  
Public And Private ◽  
Summated Rating Scale ◽  
Professional Development Programs ◽  
Definition Of

Purpose:The aim of the researchers in this effort is to identify the challenges and barrier faced by teachers in colleges of Pakistan regarding their professional development. The study also discovers realistic implication and adaptation which can be used in order to have highly professionally developed teachers in colleges.Objective of the study:The current research is conducted to find the different professional development characteristic and different factors which are beneficial in professional development of college teachers as well as the factors which are the root cause of creating deficiencies in professional development programs of teachers, especially for college teachers.Methodology:In conducting the current research study the researchers had used the qualitative method and quantitative method. In quantitative method Likert scale or in other words summated rating scale is used; as it is easiest to construct and by the definition of this scale each statement on the scale have equal importance or weight.  Sample taken to conduct this research study is 120 teachers from both the sectors as 60 public and 60 private respectively. Besides the questionnaire, interview technique is also been used to carry out the mention research.Findings: The major findings of research has reveled that professional development programs at institutional level are not carried in its required intensity moreover these programs if executed properly then could increase teachers’ satisfaction, student learning and learning output. However such programs are aimless as these programs are run without any definite purpose. Moreover it is found that there are inadequate course contents and trainers are mostly untrained. Also seminars are not conducted due to insufficient allocated funds and if seminars are conducted these results to be unproductive. Employee in educational institutions are not provided some sort of scholarship programs

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.

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