Ruiqing Zhao

Renewal process with fuzzy interarrival times and rewards

This paper considers a renewal process in which the interarrival times and rewards are characterized as fuzzy variables. A fuzzy elementary renewal theorem shows that the expected number of renewals per unit time is just the expected reciprocal of the interarrival time. Furthermore, the expected reward per unit time is provided by a fuzzy renewal reward theorem. Finally, a numerical example is presented for illustrating the theorems introduced in the paper.

Redundancy optimization problems with uncertainty of combining randomness and fuzziness

By using random fuzzy lifetimes as basic parameters, three types of system performance––expected system lifetime, (α,β)-system lifetime and system reliability––are presented. Some random fuzzy simulations are employed to estimate the system performance. Furthermore, a spectrum of random fuzzy models are constructed for redundancy optimization problems. In order to solve these models, a hybrid intelligent algorithm is used. Finally, some numerical examples are provided for the sake of illustration.

Standby redundancy optimization problems with fuzzy lifetimes

Three types of system performances--the expected system lifetime, α-system lifetime, and system reliability--characterized in the context of credibility are investigated in this paper. Some fuzzy simulations are designed to estimate these system performances. In order to formulate general standby redundancy optimization problems with fuzzy lifetimes, a spectrum of standby redundancy fuzzy programming models are proposed. Fuzzy simulation, neural network, and genetic algorithm are also integrated to produce a hybrid intelligent algorithm for solving those models. Finally, some numerical experiments on multi-stage system and network system are provided.

Pricing decisions for substitutable products with a common retailer in fuzzy environments

The pricing problem of substitutable products in a fuzzy supply chain is analyzed by using game theory in this paper. There are two substitutable products produced by two competitive manufacturers respectively and then sold by one common retailer to the consumers. Both the manufacturing cost and the customer demand for each product are characterized as fuzzy variables. How the two manufacturers and the common retailer make their own pricing decisions about wholesale prices and retail prices are explored under four different scenarios, and the corresponding expected value models are developed in this paper. Finally, a numerical example is given to illustrate the effectiveness of the proposed supply chain models.

Random fuzzy renewal process

Abstract This paper attempts to discuss a random fuzzy renewal process based on random fuzzy theory. The interarrival times are characterized as nonnegative random fuzzy variables which is a more reasonable consideration in the real world. Under this setting, the rate of the random fuzzy renewal process is discussed and a random fuzzy elementary renewal theorem is presented. Furthermore, the expected value of renewals in an arbitrary interval is investigated and Blackwell’s theorem in random fuzzy sense is also established.

Stochastic programming models for general redundancy-optimization problems

This paper provides a unified modeling idea for both parallel and standby redundancy optimization problems. A spectrum of redundancy stochastic programming models is constructed to maximize the mean system-lifetime, /spl alpha/-system lifetime, or system reliability. To solve these models, a hybrid intelligent algorithm is presented. Some numerical examples illustrate the effectiveness of the proposed algorithm. This paper considers both parallel redundant systems and standby redundant systems whose components are connected with each other in a logical configuration with a known system structure function. Three types of system performance-expected system lifetime, /spl alpha/-system lifetime and system reliability-are introduced. A stochastic simulation is designed to estimate these system performances. In order to model general redundant systems, a spectrum of redundancy stochastic programming models is established. Stochastic simulation, NN and GA are integrated to produce a hybrid intelligent algorithm for solving the proposed models. Finally, the effectiveness of the hybrid intelligent algorithm is illustrated by some numerical examples.

Risk model with fuzzy random individual claim amount

In this paper, we consider a risk model in which individual claim amount is assumed to be a fuzzy random variable and the claim number process is characterized as a Poisson process. The mean chance of the ultimate ruin is researched. Particularly, the expressions of the mean chance of the ultimate ruin are obtained for zero initial surplus and arbitrary initial surplus if individual claim amount is an exponentially distributed fuzzy random variable. The results obtained in this paper coincide with those in stochastic case when the fuzzy random variables degenerate to random variables. Finally, two numerical examples are presented.

Two-echelon supply chain games in a fuzzy environment

This paper considers a supply chain composed by a manufacturer and a retailer. It is assumed that the supply chain is operated in a fuzzy environment. The fuzziness is associated with the customers demand and the manufacturing cost. Two different game structures of the supply chain are considered: the manufacturer and the retailer cooperate with each other and behave as an integrated-firm; the manufacturer behaving as a Stackelberg leader dominates the supply chain. Expected value models as well as chance-constrained programming models are developed to determine the pricing strategies for the retailer and the manufacturer. Finally, a numerical example is given to illustrate the effectiveness of the proposed supply chain models.

Some properties of fuzzy random renewal processes

Fuzzy random variable is a measure function from a probability space to a collection of fuzzy variables. Based on the fuzzy random theory, this paper addresses some properties of fuzzy random renewal processes generated by a sequence of independent and identically distributed (iid) fuzzy random interarrival times. The relationship between the expected value of the fuzzy random renewal variable and the distribution functions of the alpha-pessimistic values and alpha-optimistic values of the interarrival times is discussed. Furthermore, the fuzzy random style of renewal equation is provided. Finally, fuzzy random Blackwells renewal theorem and Smiths key renewal theorem are also given

Fuzzy Programming Models for Vendor Selection Problem in a Supply Chain

Abstract This paper characterizes quality, budget, and demand as fuzzy variables in a fuzzy vendor selection expected value model and a fuzzy vendor selection chance-constrained programming model, to maximize the total quality level. The two models have distinct advantages over existing methods for selecting vendors in fuzzy environments. A genetic algorithm based on fuzzy simulations is designed to solve these two models. Numerical examples show the effectiveness of the algorithm.