Fuzzy E-Bayesian and Hierarchical Bayesian Estimations on the Kumaraswamy Distribution Using Censoring Data

2016 ◽  
Vol 5 (2) ◽  
pp. 74-95 ◽  
Author(s):  
Ramin Gholizadeh ◽  
Manuel J.P. Barahona ◽  
Mastaneh Khalilpour
Keyword(s):  
Original Problem ◽  
Model Parameters ◽  
Hierarchical Bayesian ◽  
Nonlinear Programming Problem ◽  
Membership Functions ◽  
Fuzzy Random Variables ◽  
Kumaraswamy Distribution ◽  
Bayesian Estimations ◽  
Resolution Identity ◽  
Fuzzy Random

The main purpose of this paper is to provide a methodology for discussing the fuzzy. This approach will be used to create the fuzzy E-Bayesian and Hierarchical Bayesian estimations of Kumaraswamy Distribution under censoring data by introducing and applying a theorem called “Resolution Identity” for fuzzy sets. In other words, model parameters are assumed to be fuzzy random variables. The authors also use computational methods Wu (2003). For this purpose, the original problem is transformed into a nonlinear programming problem which is then divided up into four sub-problems to simplify computations. Finally, the results obtained for the sub-problems can be used to determine the membership functions of the fuzzy E-Bayesian and Hierarchical Bayesian estimations.

Reliability computation for an uncertain PVC window production system using a modified bayesian estimation

2021 ◽  
Vol 40 (1) ◽  
pp. 179-189
Author(s):  
Hadi Gholizadeh ◽  
Hamed Fazlollahtabar ◽  
Mohammad Khalilzadeh
Keyword(s):  
Bayesian Estimation ◽  
System Reliability ◽  
Production System ◽  
Safety Management ◽  
Reliability Assessment ◽  
Model Parameters ◽  
Repairable Systems ◽  
Bayesian Estimations ◽  
Resolution Identity ◽  
Reliability Computation

Nowadays, Industries have been receiving much attention in Failure modelling and reliability assessment of repairable systems due to the fact that it plays a crucial role in risk and safety management of process. The primary purpose of this article is to present a methodology for discussing uncertainty in the reliability assessment if the production system. In fact, we discuss the fuzzy E-Bayesian estimation of reliability for PVC window production system. This approach is used to create the fuzzy E-Bayesian estimations of system reliability by introducing and applying a theorem called “Resolution Identity” for fuzzy sets. To be more specific, the model parameters are assumed to be fuzzy random variables. For this purpose, the original problem is transformed into a nonlinear programming problem which is divided into four sub-problems to simplify the computations. Finally, the results obtained for the sub-problems can be used to determine the membership functions of the fuzzy E-Bayesian estimation of system reliability. To clarify the proposed model, a practical example for PVC window production system is conducted.

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

Hierarchical Bayesian Parameter Estimation for Modeling and Analysis of User Affective Influence

2013 ◽  
Author(s):  
Feng Zhou ◽  
Jianxin (Roger) Jiao
Keyword(s):  
Decision Making ◽  
Interior Design ◽  
Computational Models ◽  
Human Perception ◽  
Model Parameters ◽  
Hierarchical Bayesian ◽  
Affective States ◽  
Modeling And Analysis ◽  
Human Decision

Traditional user experience (UX) models are mostly qualitative in terms of its measurement and structure. This paper proposes a quantitative UX model based on cumulative prospect theory. It takes a decision making perspective between two alternative design profiles. However, affective elements are well-known to have influence on human decision making, the prevailing computational models for analyzing and simulating human perception on UX are mainly cognition-based models. In order to incorporate both affective and cognitive factors in the decision making process, we manipulate the parameters involved in the cumulative prospect model to show the affective influence. Specifically, three different affective states are induced to shape the model parameters. A hierarchical Bayesian model with a technique called Markov chain Monte Carlo is used to estimate the parameters. A case study of aircraft cabin interior design is illustrated to show the proposed methodology.

Sign in / Sign up

Export Citation Format

Share Document