Showing papers by "Jian Zhou published in 2018"

Ruin Time of Uncertain Insurance Risk Process

Abstract: An insurance risk process usually describes the risk of an insurance company via many criteria, such as ruin index, ruin time, and deficit. So far, the insurance risk process involving random factors has been extensively investigated. As a complement, considering the human uncertainty in running an insurance company, this paper studies an insurance risk process involving human uncertainty. The inverse uncertainty distribution of the uncertain insurance risk process is obtained, and the uncertainty distribution of the ruin time is also derived. Some numerical experiments are performed to illustrate the results.

Affordable levels of house prices using fuzzy linear regression analysis: the case of Shanghai

Abstract: The house prices in China have been growing nearly twice as fast as national income over the last decade. Such an irrational soaring of house prices, not only puts the Chinese economy in danger, but also the country’s social interconnectedness and stability are at risk. Under this background, assuming that the affordable level of house prices from a consumer perspective is an uncertain parameter, which can be modelled, respectively, as symmetric and asymmetric triangular fuzzy number, several types of fuzzy linear regression models are introduced. A survey for the city of Shanghai was conducted, where three major policy and an equal number of non-policy variables have been selected to facilitate the analysis. The results derived show that the real estate tax policy had a key role for retaining the house prices in Shanghai in short run, whereas the two non-policies variables, annual household income and housing size, have even greater influence on consumers than policy variables. Additionally, it was observed that the family population and the affordable level of house prices are correlated negatively.

Reliability Analysis of Uncertain Weighted $k$ -Out-of- $n$ Systems

Abstract: The uncertain variable is used to model a quantity under human uncertainty, and the weighted $k$ -out-of- $n$ system is used to model a system of $n$ components, which functions if and only if the total weights of functioning components is greater than $k$ . Considering the human uncertainty in operating the system, this paper introduces the uncertain variable to the weighted $k$ -out-of- $n$ system, and proposes a concept of uncertain weighted $k$ -out-of- $n$ system. Some formulas are derived to calculate the reliability index of such a system. As a generalization, this paper also studies an uncertain weighted $k$ -out-of- $n$ system whose weights are estimated by experts and modeled by uncertain variables instead of crisp numbers. In addition, this paper analyzes the importance measure of the components in the uncertain weighted $k$ -out-of- $n$ systems.

Solving High-Order Uncertain Differential Equations via Runge–Kutta Method

Abstract: High-order uncertain differential equations are used to model differentiable uncertain systems with high-order differentials, and how to solve the high-order uncertain differential equations is a core issue in practice. This paper aims at proposing a numerical method to solve the high-order uncertain differential equations based on the Runge–Kutta recursion formula, which is of high precision degree. A procedure is designed and some numerical experiments are performed to illustrate the effectiveness and efficiency of the Runge–Kutta method. In addition, this paper also presents a numerical method to calculate the expected value of a function of the solution.

Renewal Reward Process With Uncertain Interarrival Times and Random Rewards

Abstract: Renewal reward process is used to measure the cumulative occasional rewards up to some given time. So far, two basic types of renewal reward processes with only random parameters or with only uncertain parameters have been proposed. This paper aims at proposing a new type of renewal reward process, which has uncertain interarrival times and random rewards in the framework of the chance theory. The chance distribution of such an uncertain random renewal reward process is obtained, and the reward rate is derived. A renewal reward theorem is verified to show that the reward rate converges in distribution to an uncertain variable, which is highly related to the interarrival times and the expected values of random rewards.

The Operational Law of Uncertain Variables With Continuous Uncertainty Distributions

Abstract: As we know, the classical operational law of uncertain variables initiated by Liu, which gives a major push to the development of uncertainty theory, restricts the uncertain variables being dealt with to those with regular uncertainty distributions. This restriction makes the operational law no longer applicable when some uncertain variables whose distributions are not regular are involved. Therefore, a generalized operational law is proposed in this paper, for uncertain variables with continuous distributions, of which regular distributions can be treated as special cases. By utilizing this extended operational law, the uncertainty distributions of strictly monotonic functions of uncertain variables with continuous (not necessarily regular) distributions can be analytically deduced, similarly to that suggested by the classical one. Furthermore, some new conclusions on the expected values of uncertain variables with continuous distributions are presented as well. Finally, as an important application of the generalized operational law, it is proved that some types of uncertain programming involving uncertain parameters with continuous distributions can be translated into deterministic counterparts, and then be handled by classic optimization techniques without any other additional efforts.

The covariance of uncertain variables: definition and calculation formulae

Abstract: Uncertainty theory as a branch of axiomatic mathematics has been widely used to deal with human uncertainty. The two commonly used numerical characteristics of uncertain variables, the expected value and the variance together with their mathematical properties have been discussed and applied to real optimization problems in an uncertain environment. As a further study, in this paper, we focus on the covariance and correlation coefficient of uncertain variables. The definitions and calculation formulae of covariance and correlation coefficient of two uncertain variables are suggested by means of their inverse distributions. Then we show that the correlation coefficient of uncertain variables is essentially a measure of the relevance of distributions of uncertain variables. Finally, the relation between variance and covariance is analysed and represented with some equalities and inequalities.

An Effective Solution Approach to Fuzzy Programming with Application to Project Scheduling

Abstract: In the present paper, a novel solution approach is proposed for a class of fuzzy programming models. In this direction, we prove that the lower and upper bounds of their fuzzy optimal objective values at a possibility level, $$\alpha \in [0,1]$$ , can be calculated solving a pair of crisp mathematical programming models. Thus, their membership functions are simulated enumerating the upper and lower bounds obtained from a series of $$\alpha$$ -level calculations. Motivated from real-world project scheduling applications, several numerical examples are considered to evaluate the accuracy, efficiency and applicability of our treatment. The results derived are compared with those of Chen and Tsai (Eur J Oper Res 212(2):386–397, 2011) to demonstrate that our method is easier to be utilized, with lower computational complexity, nonetheless without losing its effectiveness. Finally, the new approach does not suffer from the limitation to be applicable only to linear programming models that makes it suitable for a wider range of models and applications.

Establishing the relationship matrix in QFD based on fuzzy regression models with optimized h values

Abstract: In quality function deployment (QFD), establishing the relationship matrix is quite an important step to transform ambiguous and qualitative customer requirements into concrete and quantitative technical characteristics. Owing to the inherent imprecision and fuzziness of the matrix, the fuzzy linear regression (FLR) is gradually applied into QFD to establish it. However, with regard to an FLR model, the h value is a critical parameter whose setting is always an aporia and it is commonly determined by decision makers. To a certain extent, this subjective assignment fades the effectiveness of FLR in the application of QFD. Aiming to this problem, FLR models with optimized parameters h obtained by maximizing system credibility are introduced into QFD in this paper, in which relationship coefficients are assumed as asymmetric triangular fuzzy numbers. Moreover, a systematic approach is developed to identify the relationship matrix in QFD, whose application is demonstrated through a packing machine example. The final results show that FLR models with optimized h values can always achieve a more reliable relationship matrix. Besides, a comparative study on symmetric and asymmetric cases is elaborated detailedly.

Arithmetic operations on triangular fuzzy numbers via credibility measures: An inverse distribution approach

Abstract: With extensive applications of fuzzy numbers, many methods for fuzzy arithmetics especially the basic operations have been developed based on Zadeh’s extension principle. Among these methods, the interval arithmetic approach and the standard approximation method are the most important and commonly used exact and approximate methods, respectively. In this paper, regarding the continuous and strictly monotone functions of triangular fuzzy numbers, we propose an inverse distribution approach to deriving the exact or well approximate membership functions for arithmetic results by embedding the credibility measure of fuzzy sets into fuzzy arithmetics. Besides, some non-complicated and complicated examples are given to illustrate the performance of the new approach, together with a detailed comparison with the interval arithmetic approach and the standard approximate method. Furthermore, the inverse distribution approach is also applied to the fuzzy system reliability calculation based on fault tree compared with serval current related researches.