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.

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 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.

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.

A SUFFICIENT AND NECESSARY CONDITION FOR CHANCE DISTRIBUTIONS OF RANDOM FUZZY VARIABLES

2007 ◽  
Vol 15 (supp02) ◽  
pp. 21-28 ◽  
Author(s):  
YUANGUO ZHU ◽  
BAODING LIU
Keyword(s):  
Mathematical Description ◽  
Fuzzy Variable ◽  
Random Variables ◽  
Necessary Condition ◽  
Random Fuzzy Variable ◽  
Fuzzy Variables ◽  
Chance Distribution ◽  
Random Fuzzy Variables ◽  
Sufficient And Necessary Condition

A random fuzzy variable is a function from a credibility space to the set of random variables. Chance distribution is a type of mathematical description of random fuzzy variables. This paper presents a sufficient and necessary condition for chance distributions of random fuzzy variables.

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.

scholarly journals A Scalar Expected Value of Intuitionistic Fuzzy Random Individuals and Its Application to Risk Evaluation in Insurance Companies

2018 ◽  
Vol 2018 ◽  
pp. 1-16
Author(s):  
Chunquan Li ◽  
Jianhua Jin
Keyword(s):  
Risk Evaluation ◽  
Random Variables ◽  
Expected Value ◽  
Insurance Companies ◽  
Claim Amount ◽  
Fuzzy Random Variables ◽  
Intuitionistic Fuzzy ◽  
The Mean ◽  
Fuzzy Random ◽  
Mean Chance

Randomness and uncertainty always coexist in complex systems such as decision-making and risk evaluation systems in the real world. Intuitionistic fuzzy random variables, as a natural extension of fuzzy and random variables, may be a useful tool to characterize some high-uncertainty phenomena. This paper presents a scalar expected value operator of intuitionistic fuzzy random variables and then discusses some properties concerning the measurability of intuitionistic fuzzy random variables. In addition, a risk model based on intuitionistic fuzzy random individual claim amount in insurance companies is established, in which the claim number process is regarded as a Poisson process. The mean chance of the ultimate ruin is investigated in detail. In particular, the expressions of the mean chance of the ultimate ruin are presented in the cases of zero initial surplus and arbitrary initial surplus, respectively, if individual claim amount is an exponentially distributed intuitionistic fuzzy random variable. Finally, two illustrated examples are provided.

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.

Truncation Method for Chance Measure

2013 ◽  
Vol 457-458 ◽  
pp. 974-978
Author(s):  
Chun Qin Zhang ◽  
Yang Fang
Keyword(s):  
Natural Extension ◽  
Additive Measure ◽  
Chance Measure ◽  
Truncation Method

Chance measure is a non-additive measure. In this paper, we derive the truncation method for chance measure. This result is a natural extension of the classical truncation method to the case where the measure tool is non-additive. The properties of chance measure are further discussed. Then the truncation method will be given on chance space. This work generalizes the research and applications of the truncation method.

Expected value based ranking of intuitionistic fuzzy variables

2017 ◽  
Author(s):  
Tanuj Kumar ◽  
Rakesh Kumar Bajaj ◽  
Rajeev Kaushik
Keyword(s):  
Expected Value ◽  
Fuzzy Variables ◽  
Intuitionistic Fuzzy

A FUZZY RELIABILITY ANALYSIS BASED ON THE TRANSFORMATION BETWEEN DISCRETE FUZZY VARIABLES AND DISCRETE RANDOM VARIABLES

2006 ◽  
Vol 13 (01) ◽  
pp. 25-35 ◽  
Author(s):  
YUGE DONG ◽  
AINAN WANG
Keyword(s):  
Reliability Analysis ◽  
Fuzzy Variable ◽  
Fuzzy Random Variable ◽  
Random Variable ◽  
Fuzzy Information ◽  
Discrete Random Variable ◽  
Fuzzy Reliability ◽  
Fuzzy Variables ◽  
Discrete Random Variables ◽  
Fuzzy Random

When fuzzy information is taken into consideration in design, it is difficult to analyze the reliability of machine parts because we usually must deal with random information and fuzzy information simultaneously. Therefore, in order to make it easy to analyze fuzzy reliability, this paper proposes the transformation between discrete fuzzy random variable and discrete random variable based on a fuzzy reliability analysis when one of the stress and strength is a discrete fuzzy variable and the other is a discrete random variable. The transformation idea put forwards in this paper can be extended to continuous case, and can also be used in the fuzzy reliability analysis of repairable system.

Sign in / Sign up

Export Citation Format

Share Document