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

Handling Optimization Under Uncertainty Using Intuitionistic Fuzzy-Logic-Based Expected Value Model

2018 ◽  
pp. 750-776 ◽  
Author(s):  
Nagajyothi Virivinti ◽  
Kishalay Mitra
Keyword(s):  
Real Life ◽  
Expected Value ◽  
Optimization Under Uncertainty ◽  
Uncertain Parameters ◽  
Fuel Price ◽  
Deterministic Optimization ◽  
Fuzzy Variables ◽  
Intuitionistic Fuzzy ◽  
Expected Value Model ◽  
Value Model

Uncertainty in parameters during deterministic optimization studies can have large impact on the outcome of the optimization result. It is pragmatic that these parameters are uncertain as they have direct link with real life scenarios, e.g. fuel price appearing as a parameter in objective function or constraints. However, their variability is ignored while solving the problem in a deterministic optimization framework. While mitigating the above mentioned scenario, it is, therefore, necessary to investigate the development of uncertainty handling techniques for a realistic optimization problem. In this work, we propose intuitionistic fuzzy expected value model (IFEVM), which assumes uncertain parameters as intuitionistic fuzzy variables and derives the solution out of an equivalent transformed deterministic formulation while defining the expected values of the objective functions and constraints. Intuitionistic fuzzy parameters can be regarded as a superset of the conventional fuzzy set where the aspect of non-determinacy of a fuzzy member to a set is additionally taken into account. The proposed IFEVM technique has been applied on two examples: first, with the Binh-korn's multi-objective test function where uncertain parameters are linearly related and next with a real life case study of industrial grinding operation having multiple numbers of non-linearly related uncertain parameters. The technique has been further applied to these case studies considering three different levels of risk scenarios e.g. optimistic, pessimistic and intermediate approaches. The IFEVM technique is fairly generic and advantageous, can be applied to any kind of system for handling uncertainty in parameters.

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 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.

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 Credibility Measure for Intuitionistic Fuzzy Variables

Mathematics ◽  
2018 ◽  
Vol 6 (4) ◽  
pp. 50 ◽  
Author(s):  
Mohamadtaghi Rahimi ◽  
Pranesh Kumar ◽  
Gholamhossein Yari
Keyword(s):  
Credibility Measure ◽  
Fuzzy Variables ◽  
Intuitionistic Fuzzy

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.

Sign in / Sign up

Export Citation Format

Share Document