Xin Gao

Economic globalization and the rapid development of the Internet make logistics systems more and more diversified, people and enterprises have greatly increased their requirements for logistics systems, and fourth party logistics has received more and more attention from people and related enterprises. In order to further study the routing problem under uncertain stochastic environments, this paper considers the fourth party logistics routing problem from a single manufacturer to multiple distributors with uncertain times and random supplies under the complete information symmetry scenario and symmetric transportation volume decision space. Then, an uncertain stochastic programming model is established with the minimum total cost as its core objective, and the total transportation time, manufacturer’s supply, and distributor’s demand as constraints. In order to solve the optimal path of the above problems, this paper transforms the uncertain stochastic programming model into a classical mathematical programming model based on the distribution functions of uncertain time and random supply. Finally, two numerical examples are given to verify the effectiveness of the proposed model.

With the rapid development of the economy, the fourth party logistics (4PL) has become an indispensable part of economic development, and the path optimization is an important topic in the research of 4PL routing problem. This paper studies the fourth party logistics routing problem with random demand and uncertain transportation time and transfer time by considering the randomness and uncertainty of the environment. In order to solve the path optimization strategy that minimizes the total transportation cost, this paper establishes an uncertain random programming model under the constraints of the total transportation time, the carrying capacity of the logistics provider, the transfer capacity of the transfer station, and the demand of the distributor. Subsequently, this paper transforms the uncertain random programming model into an equivalent deterministic programming model based on the distribution functions of random demand and uncertain time, and verifies the effectiveness of the model through two examples. The results show that the uncertain random programming model can give a reasonable path optimization strategy.

The existing parameter estimation methods of the uncertain moving average model are the least square method and ridge estimation. However, for some data with outliers, the least square method cannot eliminate the influence of outliers very well. In order to solve this problem, this paper discusses how to use the parameter estimation method of least absolute deviation to solve the uncertain moving average model, and calculate the mean and variance of the residuals, so as to find the confidence interval of the predicted value. Finally, two examples are given to demonstrate that the uncertain moving average model estimated by the least absolute deviation can predict closer values to the actual values than other estimation methods.

In practical applications of graph theory, indeterminacy factors always appear in graphs. Uncertain random graph was proposed via chance theory, in which some edges exist with degrees in probability measure and others exist with degrees in uncertain measure. This paper discusses the contributions of edges for connectivity of an uncertain random graph and proposes concepts about significance of edges, according to which edges are classified. In addition, this paper presents algorithms for calculating connectivity index and significance of edges of an uncertain random graph. Examples are given to illustrate algorithms and methods.

In many practical problems, randomness and uncertainty simultaneously appear in one complex system or network. When graph theory is applied to these problems, these complex systems or networks are usually represented by uncertain random graphs, in which some edges exist with degrees in probability measure, and some other edges exist with degrees in uncertain measure. In this paper, we focus on the connectivity of uncertain random graphs with respect to vertices. We propose the concepts of k- vertex-connectivity index and the connectivity of an uncertain random graph. The former is the chance measure that an uncertain random graph is k-vertex-connected, and the latter is an uncertain random variable, which characterizes the connectivity of the uncertain random graph with respect to vertices. We discuss some properties of these concepts. Methods and formulas are also presented for calculating the k-vertex-connectivity index, and the distribution and expected value of the connectivity of an uncertain random graph.

This paper proposes a new definition of cross entropy for uncertain random variables, and derives a formula. Moreover, this paper introduces generalized cross entropy for uncertain random variables, and discusses its properties. Based on the definition of cross entropy, a cross entropy chance distribution model of degree-constrained minimum spanning tree (DCMST) problem is proposed. An algorithm is designed here to solve the model. Finally, a numerical example is provided to illustrate the effectiveness of the proposed model and algorithm.

Uncertain partial differential equation is a type of partial differential equation driven by Liu processes. This paper first provides two methods for solving the first order linear uncertain partial differential equation and the inverse uncertainty distribution of solution is discussed. Moreover, on the basis of the study of uncertainty theory and the propagation process of internet public opinion, three types of internet public opinion (IPO) problem are proposed based on uncertain partial differential equation. Finally, some numerical examples are given.