The First Moments and Semi-Moments of Fuzzy Variables Based on an Optimism-Pessimism Measure with Application for Portfolio Selection

2020 ◽  
Vol 16 (02) ◽  
pp. 271-290
Author(s):  
Justin Dzuche ◽  
Christian Deffo Tassak ◽  
Jules Sadefo Kamdem ◽  
Louis Aimé Fono
Keyword(s):  
Linear Combination ◽  
Portfolio Selection ◽  
Fuzzy Variable ◽  
Expected Value ◽  
Mathematical Science ◽  
Optimal Portfolios ◽  
Fuzzy Variables ◽  
Convex Linear Combination

Possibility, necessity and credibility measures are used in the literature in order to deal with imprecision. Recently, Yang and Iwamura [L. Yang and K. Iwamura, Applied Mathematical Science 2(46) (2008) 2271–2288] introduced a new measure as convex linear combination of possibility and necessity measures and they determined some of its axioms. In this paper, we introduce characteristics (parameters) of a fuzzy variable based on that measure, namely, expected value, variance, semi-variance, skewness, kurtosis and semi-kurtosis. We determine some properties of these characteristics and we compute them for trapezoidal and triangular fuzzy variables. We display their application for the determination of optimal portfolios when assets returns are described by triangular or trapezoidal fuzzy variables.

scholarly journals A FUZZY BASED APPROACH FOR EARLY REQUIREMENT PRIORITIZATION

2015 ◽  
Vol 15 (2) ◽  
pp. 6480-6490
Author(s):  
Mohd Muqeem ◽  
Dr. Md. Rizwan Beg
Keyword(s):  
Software Development ◽  
Early Phase ◽  
Fuzzy Variable ◽  
Requirement Engineering ◽  
Expected Value ◽  
Inference System ◽  
Complex Time ◽  
Fuzzy Variables ◽  
Expected Value Operator ◽  
Requirement Prioritization

The importance of the prioritization in commercial software development has been analyzed by many researchers. The gathered requirements are required to be put into an order of some priority. In other words we can say that there is a need to prioritize the requirements. It is evident that most of the approaches and techniques proposed in recent research to prioritize the requirements have not been widely adopted. These approaches are too complex, time consuming, or inconsistent and difficult to implement In this paper we propose a fuzzy based approach for requirement prioritization in which  requirement are prioritized in early phase of requirement engineering as post elicitation step. This category of prioritization is known as early requirement prioritization. The proposed fuzzy based approach considers the nature of requirements by modeling their attributes as fuzzy variables. As such, these variables are integrated into a fuzzy based inference system in which the requirements represented as input attributes and ranked via the expected value operator of a fuzzy variable.

scholarly journals Portfolio Selection Based on Distance between Fuzzy Variables

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Weiyi Qian ◽  
Mingqiang Yin
Keyword(s):  
Mathematical Models ◽  
Portfolio Selection ◽  
Expected Value ◽  
Simple Method ◽  
Numerical Examples ◽  
Fuzzy Variables ◽  
Fuzzy Environment ◽  
Investment Return ◽  
New Models ◽  
Different Types

This paper researches portfolio selection problem in fuzzy environment. We introduce a new simple method in which the distance between fuzzy variables is used to measure the divergence of fuzzy investment return from a prior one. Firstly, two new mathematical models are proposed by expressing divergence as distance, investment return as expected value, and risk as variance and semivariance, respectively. Secondly, the crisp forms of the new models are also provided for different types of fuzzy variables. Finally, several numerical examples are given to illustrate the effectiveness of the proposed approach.

ANALYSIS AND ALGORITHMS OF BIFUZZY SYSTEMS

2004 ◽  
Vol 12 (03) ◽  
pp. 357-376 ◽  
Author(s):  
JIAN ZHOU ◽  
BAODING LIU
Keyword(s):  
Numerical Experiments ◽  
Fuzzy Variable ◽  
Expected Value ◽  
Real Numbers ◽  
Fuzzy Variables ◽  
Chance Distribution ◽  
Expected Value Operator ◽  
Possibility Space ◽  
Bifuzzy Variable

A fuzzy variable is a function from a possibility space to the set of real numbers, while a bifuzzy variable is a function from a possibility space to the set of fuzzy variables. In this paper, a concept of chance distribution is originally presented for bifuzzy variable, and the linearity of expected value operator of bifuzzy variable is proved. Furthermore, bifuzzy simulations are designed and illustrated by some numerical experiments.

scholarly journals Modeling Portfolio Optimization Problem by Probability-Credibility Equilibrium Risk Criterion

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
Ye Wang ◽  
Yanju Chen ◽  
YanKui Liu
Keyword(s):  
Convex Programming ◽  
Portfolio Selection ◽  
Optimization Problem ◽  
Fuzzy Variable ◽  
Optimization Method ◽  
General Purpose ◽  
Convex Programming Problem ◽  
Fuzzy Variables ◽  
Return Rates ◽  
Fuzzy Expected Value

This paper studies the portfolio selection problem in hybrid uncertain decision systems. Firstly the return rates are characterized by random fuzzy variables. The objective is to maximize the total expected return rate. For a random fuzzy variable, this paper defines a new equilibrium risk value (ERV) with credibility level beta and probability level alpha. As a result, our portfolio problem is built as a new random fuzzy expected value (EV) model subject to ERV constraint, which is referred to as EV-ERV model. Under mild assumptions, the proposed EV-ERV model is a convex programming problem. Furthermore, when the possibility distributions are triangular, trapezoidal, and normal, the EV-ERV model can be transformed into its equivalent deterministic convex programming models, which can be solved by general purpose optimization software. To demonstrate the effectiveness of the proposed equilibrium optimization method, some numerical experiments are conducted. The computational results and comparison study demonstrate that the developed equilibrium optimization method is effective to model portfolio selection optimization problem with twofold uncertain return rates.

scholarly journals The Scalar Mean Chance and Expected Value of Regular Bifuzzy Variables

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1428
Author(s):  
Guang Wang ◽  
Yixuan Shen ◽  
Yujiao Jiang ◽  
Jiahao Chen
Keyword(s):  
Fuzzy Variable ◽  
Natural Extension ◽  
Expected Value ◽  
Monotone Functions ◽  
Chance Measure ◽  
Fuzzy Variables ◽  
Chance Distribution ◽  
Analytical Formulas ◽  
Bifuzzy Variable ◽  
Mean Chance

As a natural extension of the fuzzy variable, a bifuzzy variable is defined as a mapping from a credibility space to the collection of fuzzy variables, which is an appropriate tool to model the two-fold fuzzy phenomena. In order to enrich its theoretical foundation, this paper explores some important measures for regular bifuzzy variables, the most commonly used type of bifuzzy variables. Firstly, we introduce the regular bifuzzy variables’ mean chance measure and some properties, including self-duality and its calculation formulas. Furthermore, we also investigate the mean chance distribution for strictly monotone functions of regular bifuzzy variables based on the proposed operational law. Finally, we present the expected value operator as well as equivalent analytical formulas of the expected value of regular bifuzzy variables and their strictly monotone functions.

Fuzzy-based approach for determination of characteristic values of measured geotechnical parameters

2000 ◽  
Vol 37 (5) ◽  
pp. 1131-1140 ◽  
Author(s):  
N O Nawari ◽  
R Liang
Keyword(s):  
Fuzzy Variable ◽  
Fuzzy Model ◽  
Mean Value ◽  
Geotechnical Properties ◽  
Distribution Functions ◽  
Safety Level ◽  
Geotechnical Parameters ◽  
Fuzzy Variables ◽  
Characteristic Values

Determination of the nominal (characteristic) values of geotechnical properties plays a crucial role within the limits states design (LSD or LRFD) concepts. The interrelationship between the process of the selection of the nominal value and the safety level is not clearly addressed in most of the new limits states design codes of practice for geotechnical engineering. Estimation of the characteristic values (p% fractile or the mean value) using the stochastic models is often linked up with some assumptions regarding the probability distribution functions. Probability theory has been perceived as a unique methodology to handle uncertainty in these geotechnical parameters despite the fact that some of the uncertainties associated with these geotechnical properties may be nonstochastic in nature. In this paper, the uncertainty connected with measured geotechnical properties is modeled using the fuzzy-reliability techniques. The measured parameters are rendered into fuzzy variables and the nominal values are characterized by fuzziness. The procedure presented is proposed as an alternative or complementary method to the estimate of the nominal values of geomaterials. The approach is illustrated with computational algorithms and a numerical example.Key words: characteristic value, nominal value, fuzzy model, fuzzy variable, resistance factor, probability.

scholarly journals Analytical Expressions of Hydro-Seismic Forces on Dams

2018 ◽  
Author(s):  
Abdelmadjid Tadjadit ◽  
Boualem Tiliouine
Keyword(s):  
Viscous Fluid ◽  
Linear Combination ◽  
Upstream Face ◽  
Compressible Viscous Fluid ◽  
Natural Modes ◽  
Boundary Method ◽  
Complete Sets ◽  
Seismic Forces ◽  
Analytical Expressions

Analytical expressions for the determination of hydro-seismic forces acting on a rigid dam with irregular upstream face geometry in presence of a compressible viscous fluid are derived through a linear combination of the natural modes of water in the reservoir based on a boundary method making use of complete sets of complex T-functions.Analytical expressions for the determination of hydro-seismic forces acting on a rigid dam with irregular upstream face geometry in presence of a compressible viscous fluid are derived through a linear combination of the natural modes of water in the reservoir based on a boundary method making use of complete sets of complex T-functions. The formulas obtained for distributions of both shear forces and overturning moments are simple, computationally effective and useful for the preliminary design of dams. They show clearly the separate and combined effects of compressibility and viscosity of water. They also have the advantage of being able to cover a wide range of excitation frequencies even beyond the cut-off frequencies of the natural modes of the reservoir. Key results obtained using the proposed analytical expressions of the hydrodynamic forces are validated using numerical and experimental solutions published for some particular cases available in the specialized literature.

Computing the Risk Indicators in Fuzzy Systems

2012 ◽  
Vol 5 (4) ◽  
pp. 63-84 ◽  
Author(s):  
Irina Georgescu
Keyword(s):  
Risk Aversion ◽  
Risk Premium ◽  
Stochastic Dominance ◽  
Probabilistic Models ◽  
Fuzzy Variable ◽  
Risk Indicators ◽  
Credibility Theory ◽  
Fuzzy Variables ◽  
Risk Situation ◽  
Definition Of

The modeling of complex risk situations imposes the existence of multiple ways to represent the risk and compare the risk situations between them. In probabilistic models, risk is described by random variables and risk situations are compared by stochastic dominance. In possibilistic or credibilistic models, risk is represented by fuzzy variables. This paper concerns three indicators of dominance associated with fuzzy variables. This allows the definition of three notions of fuzzy dominance: dominance in possibility, dominance in necessity and dominance in credibility. These three types of dominance are possibilistic and credibilistic versions of stochastic dominance. Each type offers a modality of ranking risk situations modeled by fuzzy variables. In the paper some properties of the three indicators of dominance are proved and relations between the three types of fuzzy dominance are established. For triangular fuzzy numbers formulas for the computation of these indicators are obtained. The paper also contains a contribution on a theory of risk aversion in the context of credibility theory. Using the credibilistic expected utility a notion of risk premium is defined as a measure of risk aversion of an agent in front of a risk situation described by a fuzzy variable and an approximate calculation formula of this indicator is proved.

On Some Classes of Idempotent Operators

1997 ◽  
Vol 05 (04) ◽  
pp. 401-410 ◽  
Author(s):  
G. Mayor ◽  
J. Torrens
Keyword(s):  
Linear Combination ◽  
Representation Theorem ◽  
Special Kind ◽  
Classical Representation ◽  
Aggregation Functions ◽  
Idempotent Operators ◽  
Special Cases ◽  
Convex Linear Combination

In this paper we deal with the idempotency equation H(x,x)=x for all x∈[0,1]. In particular we solve it for two special cases. First when H is a convex linear combination of a strict t-norm and its (1-j)-dual and second, when H is a convex linear combination of a special kind of aggregation functions F=<(f,N)> and its N-dual, being these aggregation functions, called L-representable aggregation functions, a kind of functions verifying a similar representation theorem to the classical representation theorem for non strict Archimedean t-norms.

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