The Scalar Mean Chance and Expected Value of Regular Bifuzzy Variables

As a natural extension of the fuzzy variable, a bifuzzy variable is defined as a mapping from a credibility space to the collection of fuzzy variables, which is an appropriate tool to model the two-fold fuzzy phenomena. In order to enrich its theoretical foundation, this paper explores some important measures for regular bifuzzy variables, the most commonly used type of bifuzzy variables. Firstly, we introduce the regular bifuzzy variables’ mean chance measure and some properties, including self-duality and its calculation formulas. Furthermore, we also investigate the mean chance distribution for strictly monotone functions of regular bifuzzy variables based on the proposed operational law. Finally, we present the expected value operator as well as equivalent analytical formulas of the expected value of regular bifuzzy variables and their strictly monotone functions.

A Counterfactual Analysis of Causation

A counterfactual analysis of causation is developed by distinctive notion of chance-raising characterized by probabilistic Σ‎-dependence, when a causal chain is complete appealing to chance-raising at a time just before the time of the effect, and a requirement that the causal chain is made up of actual events to avoid the standard problems with conditional analyses, due to potential changes in the circumstances when the antecedents are true. Although the development takes the form of a consideration of difficult cases of causation (especially probabilistic cases of pre-emption), the resulting idea has independent motivation and simplicity. It is that causes of a target event are those which (independently of its competitors) both make the mean chance of an effect very much greater than its mean background chance, and actually influence the probability of the effect in this way, at the time at which the effect occurred via a complete causal chain.

A Scalar Expected Value of Intuitionistic Fuzzy Random Individuals and Its Application to Risk Evaluation in Insurance Companies

Randomness and uncertainty always coexist in complex systems such as decision-making and risk evaluation systems in the real world. Intuitionistic fuzzy random variables, as a natural extension of fuzzy and random variables, may be a useful tool to characterize some high-uncertainty phenomena. This paper presents a scalar expected value operator of intuitionistic fuzzy random variables and then discusses some properties concerning the measurability of intuitionistic fuzzy random variables. In addition, a risk model based on intuitionistic fuzzy random individual claim amount in insurance companies is established, in which the claim number process is regarded as a Poisson process. The mean chance of the ultimate ruin is investigated in detail. In particular, the expressions of the mean chance of the ultimate ruin are presented in the cases of zero initial surplus and arbitrary initial surplus, respectively, if individual claim amount is an exponentially distributed intuitionistic fuzzy random variable. Finally, two illustrated examples are provided.

Optimization Model of Loan Portfolio Based on Mean Chance

This paper discusses the problem of loan portfolio in fuzzy random environment, in real life, because of the influence of random and fuzzy factors, the return rates of loan in bank often have fuzzy random characteristic. Mean chance is a measure of fuzzy random variable, based on mean chance, a new optimization model of loan portfolio is provided. To give a general solution to the new model, a hybrid intelligent algorithm is designed. The algorithm integrates fuzzy random simulation, neural network and genetic algorithm. Neural network is employed to calculate the expected value and the mean chance value, it greatly reduce the computational work. At last, a numerical example is presented to illustrate the new model and the proposed new algorithm.