Intuitionistic fuzzy random variables

2011 ◽  
Author(s):  
Chao Wang ◽  
Ming-Hu Ha ◽  
Yi-Jun Fan ◽  
Ji-Qiang Chen
Keyword(s):  
Random Variables ◽  
Fuzzy Random Variables ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Random

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 Solving Capacitated Vehicle Routing Problem with Demands as Fuzzy Random Variable

2021 ◽  
Author(s):  
Vishnu Pratap Singh ◽  
Kirti Sharma ◽  
Debjani Chakraborty
Keyword(s):  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Real Life ◽  
Random Variables ◽  
Fuzzy Random Variables ◽  
Routing Problem ◽  
Capacitated Vehicle Routing Problem ◽  
Intuitionistic Fuzzy ◽  
Capacitated Vehicle ◽  
Fuzzy Random

Abstract Capacitated vehicle routing problem ( CVRP ) is a classical combinatorial optimization problem in which a network of customers with specified demands is given. The objective is to find a set of routes which originates as well as terminates at the depot node. These routes are to be traversed in such a way that the demands of all the customers in the network are satisfied and the cost associated with traversal of these routes come out to be a minimum. In real-world situations, the demand of any commodity depends upon various uncontrollable factors, such as, season, delivery time, market conditions and many more. Due to these factors, the demand can always not be told in advance and a precise information about the demand is nearly impossible to achieve. Hence, the demands of the customers always experience impreciseness and randomness in real-life. The decisions made by the customers about the demands may also have some scope of hesitation as well. In order to handle such demands of customers in the network, fuzzy random variables and intuitionistic fuzzy random variables are used in this work. The work bridges the gap between the classical version of CVRP and the real-life situation and hence makes it easier for the logistic management companies to determine the routes that should be followed for minimum operational cost and maximum profit. Mathematical models corresponding to CVRP with fuzzy stochastic demands ( CVRPFSD ) and CVRP with Intuitionistic fuzzy stochastic demands ( CVRPIFSD ) have been presented. A two-stage model has been proposed to find out the solution for the same. To explain the working of the methodology defined in this work, two different example of a network with fuzzy and intuitionistic fuzzy demands have been worked out. The proposed solution approach is also tested on modified fuzzy versions of some benchmark instances.

scholarly journals Several Limit Theorems on Fuzzy Quantum Space

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 438
Author(s):  
Viliam Ďuriš ◽  
Renáta Bartková ◽  
Anna Tirpáková
Keyword(s):  
Financial Markets ◽  
Incomplete Data ◽  
Extreme Values ◽  
Random Variables ◽  
Consumer Electronics ◽  
Financial Risks ◽  
Quantum Space ◽  
Fuzzy Random Variables ◽  
Scientific Disciplines ◽  
Fuzzy Random

The probability theory using fuzzy random variables has applications in several scientific disciplines. These are mainly technical in scope, such as in the automotive industry and in consumer electronics, for example, in washing machines, televisions, and microwaves. The theory is gradually entering the domain of finance where people work with incomplete data. We often find that events in the financial markets cannot be described precisely, and this is where we can use fuzzy random variables. By proving the validity of the theorem on extreme values of fuzzy quantum space in our article, we see possible applications for estimating financial risks with incomplete data.

scholarly journals Fuzzy random variables

1986 ◽  
Vol 114 (2) ◽  
pp. 409-422 ◽  
Author(s):  
Madan L Puri ◽  
Dan A Ralescu
Keyword(s):  
Random Variables ◽  
Fuzzy Random Variables ◽  
Fuzzy Random
Sign in / Sign up

Export Citation Format

Share Document