Fuzzy variables are functions from credibility spaces to the set of real numbers. Based on the expected value of a fuzzy variable, the expected value of function of a simple fuzzy variable is studied. In order further to discuss the mathematical properties of fuzzy variables, some inequalities for fuzzy variables are derived based on the concepts of credibility measures and expected value opera...

Credibility measure was created by Baoding Liu [5, 7] and his Chinese co workers [4] around 2004. Then, Baoding Liu designed a grand view of fuzzy process, hybrid process and uncertain process [6]. In response to his work, Dai [1] sketched how to create standard normal fuzzy process under credibility measure, which he called standard Liu process. Independently Kageyama and Iwamura [3] construct...

In this paper, a novel real number encoding method of Particle Swarm Optimization (PSO) for Vehicle Routing Problem is proposed. Objective is to solve the vehicle routing problem with fuzzy demands (FVRP) ,in FVRP, a fuzzy chance constrained program model is designed, based on fuzzy credibility theory. Firstly construct a suitable mapping between problem solution and PSO particle, and adopted a...

The failure possibility of transmission lines in power system may change from time to time since it will be affected by weather, environment and operating conditions, especially under short-time period. Impacts of various conditions on failure possibility can be described using fuzzy words. In this paper, credibility theory was introduced to model the short-term line maintenance-scheduling prob...

Abstract The classical credibility theory is a cornerstone of experience rating, especially in the field property and casualty insurance. An obstacle to putting into practice conversion available prior information precise choice crucial hyperparameters. In most real-world applications, necessary justify lacking, so we propose an imprecise estimator that honestly acknowledges imprecision hyperpa...

In economic order quantity models without backordering, both the stock cost of each unit quantity and the order cost of each cycle are characterized as independent fuzzy variables rather than fuzzy numbers as in previous studies. Based on an expected value criterion or a credibility criterion, a fuzzy expected value model and a fuzzy dependent chance programming (DCP) model are constructed. The...

We introduce a cardinality constrained multi-objective optimization problem for generating efficient portfolios within a fuzzy mean-absolute deviation framework. We assume that the return on a given portfolio is modeled by means of LR-type fuzzy variables, whose credibility distributions collect the contemporary relationships among the returns on individual assets. To consider credibility measu...

In practice, some special LR fuzzy numbers, like the triangular fuzzy number, the Gaussian fuzzy number and the Cauchy fuzzy number, are widely used in many areas to deal with various vague information. With regard to these special LR fuzzy numbers, called regular LR fuzzy numbers in this paper, an operational law is proposed for fuzzy arithmetic, providing a novel approach to analytically and ...