scholarly journals A New Formula for Calculating Uncertainty Distribution of Function of Uncertain Variables

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2429
Author(s):  
Yuxing Jia ◽  
Yuer Lv ◽  
Zhigang Wang
Keyword(s):  
Uncertainty Theory ◽  
Monotone Function ◽  
Uncertain Variable ◽  
Mathematical Tool ◽  
Human Beings ◽  
Uncertainty Distribution ◽  
Uncertain Variables ◽  
New Ideas ◽  
New Formula ◽  
Theory Uncertainty

As a mathematical tool to rationally handle degrees of belief in human beings, uncertainty theory has been widely applied in the research and development of various domains, including science and engineering. As a fundamental part of uncertainty theory, uncertainty distribution is the key approach in the characterization of an uncertain variable. This paper shows a new formula to calculate the uncertainty distribution of strictly monotone function of uncertain variables, which breaks the habitual thinking that only the former formula can be used. In particular, the new formula is symmetrical to the former formula, which shows that when it is too intricate to deal with a problem using the former formula, the problem can be observed from another perspective by using the new formula. New ideas may be obtained from the combination of uncertainty theory and symmetry.

A new measure of indeterminacy for uncertain variables with application to portfolio selection

2021 ◽  
pp. 1-5
Author(s):  
Jin Liu ◽  
Jinsheng Xie ◽  
Hamed Ahmadzade ◽  
Mehran Farahikia
Keyword(s):  
Probability Theory ◽  
Portfolio Selection ◽  
Uncertainty Theory ◽  
Random Variable ◽  
Uncertain Variable ◽  
Uncertainty Distribution ◽  
Uncertain Variables ◽  
Selection Problems ◽  
Exponential Entropy

Entropy is a measure for characterizing indeterminacy of a random variable or an uncertain variable with respect to probability theory and uncertainty theory, respectively. In order to characterize indeterminacy of uncertain variables, the concept of exponential entropy for uncertain variables is proposed. For computing the exponential entropy for uncertain variables, a formula is derived via inverse uncertainty distribution. As an application of exponential entropy, portfolio selection problems for uncertain returns are optimized via exponential entropy-mean models. For better understanding, several examples are provided.

scholarly journals Airline Overbooking Problem with Uncertain No-Shows

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Chunxiao Zhang ◽  
Congrong Guo ◽  
Shenghui Yi
Keyword(s):  
Historical Data ◽  
Uncertain Variable ◽  
Chance Constraint ◽  
Human Beings ◽  
Profit Rate ◽  
Uncertainty Distribution ◽  
Unexpected Events ◽  
Domain Experts ◽  
Social Reputation ◽  
Flight Capacity

This paper considers an airline overbooking problem of a new single-leg flight with discount fare. Due to the absence of historical data of no-shows for a new flight, and various uncertain human behaviors or unexpected events which causes that a few passengers cannot board their aircraft on time, we fail to obtain the probability distribution of no-shows. In this case, the airlines have to invite some domain experts to provide belief degree of no-shows to estimate its distribution. However, human beings often overestimate unlikely events, which makes the variance of belief degree much greater than that of the frequency. If we still regard the belief degree as a subjective probability, the derived results will exceed our expectations. In order to deal with this uncertainty, the number of no-shows of new flight is assumed to be an uncertain variable in this paper. Given the chance constraint of social reputation, an overbooking model with discount fares is developed to maximize the profit rate based on uncertain programming theory. Finally, the analytic expression of the optimal booking limit is obtained through a numerical example, and the results of sensitivity analysis indicate that the optimal booking limit is affected by flight capacity, discount, confidence level, and parameters of the uncertainty distribution significantly.

SOME PROPERTIES OF CONTINUOUS UNCERTAIN MEASURE

2009 ◽  
Vol 17 (03) ◽  
pp. 419-426 ◽  
Author(s):  
XIN GAO
Keyword(s):  
Uncertainty Theory ◽  
Uncertain Variable ◽  
Expected Value ◽  
Critical Values ◽  
Uncertain Measure ◽  
Uncertainty Distribution ◽  
Convergence Theorems ◽  
Basic Properties

In this paper, we discuss some properties in uncertainty theory when uncertain measure is continuous. Firstly, the judgement conditions of continuous uncertain measure are proposed. Secondly, basic properties of uncertainty distribution and critical values of uncertain variable are proved. Finally, the convergence theorems for expected value are discussed.

Uncertainty Distribution of Some Composite Uncertain Variables

2017 ◽  
Vol 25 (04) ◽  
pp. 545-555
Author(s):  
Chongshuang Chen ◽  
Jiayin Tang ◽  
Jianbo Xiao ◽  
Lei Huang
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Measurable Function ◽  
Uncertain Variable ◽  
Uncertainty Distribution ◽  
Uncertain Variables ◽  
Convex Upward

In this paper, we named the composition by a real-valued measurable function and an uncertain variable as a composite uncertain variable. We focused on the uncertainty distribution for two kinds of composite uncertain variables. The conclusions show: (1) it exists a lower bound when the composed function is continuous and strictly monotonically decreasing at first and then strictly monotonically increasing (e.g. convex downward functions); (2) it exists an upper bound when the composed function is continuous and strictly monotonically increasing at first and then strictly monotonically decreasing (e.g. convex upward functions).

scholarly journals Some Theorems for Inverse Uncertainty Distribution of Uncertain Processes

Symmetry ◽  
2021 ◽  
Vol 14 (1) ◽  
pp. 14
Author(s):  
Xiumei Chen ◽  
Yufu Ning ◽  
Lihui Wang ◽  
Shuai Wang ◽  
Hong Huang
Keyword(s):  
Uncertainty Theory ◽  
Independent Increment ◽  
Monotone Function ◽  
Real Life ◽  
Uncertain Process ◽  
Uncertainty Distribution ◽  
Process With Independent Increments ◽  
Independent Increments ◽  
Independent Increment Process

In real life, indeterminacy and determinacy are symmetric, while indeterminacy is absolute. We are devoted to studying indeterminacy through uncertainty theory. Within the framework of uncertainty theory, uncertain processes are used to model the evolution of uncertain phenomena. The uncertainty distribution and inverse uncertainty distribution of uncertain processes are important tools to describe uncertain processes. An independent increment process is a special uncertain process with independent increments. An important conjecture about inverse uncertainty distribution of an independent increment process has not been solved yet. In this paper, the conjecture is proven, and therefore, a theorem is obtained. Based on this theorem, some other theorems for inverse uncertainty distribution of the monotone function of independent increment processes are investigated. Meanwhile, some examples are given to illustrate the results.

SINE ENTROPY FOR UNCERTAIN VARIABLES

2013 ◽  
Vol 21 (05) ◽  
pp. 743-753 ◽  
Author(s):  
KAI YAO ◽  
JINWU GAO ◽  
WEI DAI
Keyword(s):  
Maximum Entropy ◽  
Uncertainty Theory ◽  
Maximum Entropy Principle ◽  
Expected Value ◽  
Uncertain Variables ◽  
Entropy Principle

Entropy is a measure of the uncertainty associated with a variable whose value cannot be exactly predicated. In uncertainty theory, it has been quantified so far by logarithmic entropy. However, logarithmic entropy sometimes fails to measure the uncertainty. This paper will propose another type of entropy named sine entropy as a supplement, and explore its properties. After that, the maximum entropy principle will be introduced, and the arc-cosine distributed variables will be proved to have the maximum sine entropy with given expected value and variance.

An entropy-based global sensitivity analysis for the structures with both fuzzy variables and random variables

2012 ◽  
Vol 227 (2) ◽  
pp. 195-212 ◽  
Author(s):  
Tang Zhangchun ◽  
Lu Zhenzhou ◽  
Pan Wang ◽  
Zhang Feng
Keyword(s):  
Failure Probability ◽  
Uncertainty Propagation ◽  
Random Variables ◽  
Uncertain Variable ◽  
Importance Measure ◽  
Similar Measure ◽  
Practical Applications ◽  
Fuzzy Variables ◽  
Global Sensitivity ◽  
Uncertain Variables

Based on the entropy of the uncertain variable, a novel importance measure is proposed to identify the effect of the uncertain variables on the system, which is subjected to the combination of random variables and fuzzy variables. For the system with the mixture of random variables and fuzzy variables, the membership function of the failure probability can be obtained by the uncertainty propagation theory first. And then the effect of each input variable on the output response of the system can be evaluated by measuring the shift between entropies of two membership functions of the failure probability, obtained before and after the uncertainty elimination of the input variable. The intersecting effect of the multiple input variables can be calculated by the similar measure. The mathematical properties of the proposed global sensitivity indicators are investigated and proved in detail. A simple example is first employed to demonstrate the procedure of solving the proposed global sensitivity indicators and then the influential variables of four practical applications are identified by the proposed global sensitivity indicators.

Belief in the Human

2018 ◽  
pp. 250-281
Author(s):  
Ethan H. Shagan
Keyword(s):  
Seventeenth Century ◽  
Social World ◽  
Human Beings ◽  
The Social ◽  
New Ideas ◽  
Suspension Of Disbelief

This chapter cites Samuel Taylor Coleridge's concept of the “willing suspension of disbelief” in order to describe the timeless process by which human beings believe in their own creations. As seen before, Europeans influenced by new ideas in the seventeenth century were freed to believe in spiritual objects in much the same way they believed in mundane ones, as acts of sovereign judgment. With the category so perforated, there was no intrinsic reason why belief had to remain bound to objects judged “true” in a transcendent or universal sense; it might also alight upon objects judged true in more provisional or instrumental ways. Crucially, this included the social world: ephemeral human creations, the ideas and things that humans themselves make.

An Uncertain Single-Server Queueing Model

2021 ◽  
pp. 2150001
Author(s):  
Kai Yao
Keyword(s):  
Queueing Theory ◽  
Busy Period ◽  
Queueing System ◽  
Single Server ◽  
Queueing Model ◽  
Uncertainty Distribution ◽  
Uncertain Variables ◽  
Service Efficiency ◽  
Service Times ◽  
Interarrival Times

In the queueing theory, the interarrival times between customers and the service times for customers are usually regarded as random variables. This paper considers human uncertainty in a queueing system, and proposes an uncertain queueing model in which the interarrival times and the service times are regarded as uncertain variables. The busyness index is derived analytically which indicates the service efficiency of a queueing system. Besides, the uncertainty distribution of the busy period is obtained.

Analysis of Fault Tree Base on Uncertain Optimistic Value

2011 ◽  
Vol 50-51 ◽  
pp. 140-144
Author(s):  
Jian Jun Liu ◽  
Yu Fu Ning
Keyword(s):  
Internal Combustion Engine ◽  
Empirical Data ◽  
Uncertainty Theory ◽  
Statistical Data ◽  
Combustion Engine ◽  
Fault Tree ◽  
Internal Combustion ◽  
Uncertain Variable ◽  
Simulation Technology ◽  
Optimistic Value

Based on uncertainty theory, this paper proposes a method that constructs and analyzes fault tree. In this paper, it would be characterized as crisp number if fault rate of bottom event is obtained from reliable handbook, empirical data and so on; it would be characterized as uncertain variable if fault rate of bottom event has no statistical data but is obtained from expert's subjective judgment. The optimistic value of overall system’s top event is calculated by using uncertain simulation technology. Finally feasibility and validity of this method is confirmed by taking fault tree of internal combustion engine as example.

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