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We devote to study the arithmetic operator of fuzzy regular prismoid numbers as well as the degree of similarity between fuzzy regular prismoid numbers, and then the arithmetic operator and the degree of similarity are applied in risk analysis. Firstly, the arithmetic operator of fuzzy regular prismoid numbers are researched, and some properties of the arithmetic operators are discussed. At the same time, the fuzzy regular prismoid numbers approximation of 2-dimensional fuzzy numbers is discussed as an indispensable part to study the fuzzy risk analysis. Then, the degree of similarity between fuzzy regular prismoid numbers are deeply researched, which are the basic work of studying the fuzzy risk analysis. Finally, the proposed results are applied in risk analysis of a company.

Taking into account that interval-valued fuzzy numbers can provide more flexibility to represent the imprecise information and interval-valued trapezoidal fuzzy numbers are widely used in practice, this paper devotes to seek an approximation operator that produces an interval-valued trapezoidal fuzzy number which is the nearest one to the given interval-valued fuzzy number, and the approximation operator preserves the core of the original interval-valued fuzzy number with respect to the weighted distance. As an application, we use the interval-valued trapezoidal approximation to handle fuzzy risk analysis problems, which overcome the drawback of existing fuzzy risk analysis methods.

It is well-known that the cooperative communication and error control technology can improve the network performance, but most existing cooperative MAC protocols have not focused on how to cope with the contention process caused by cooperation and how to reduce the bad influence of channel packet error rate on the system performance. Inspired by this, this paper first modifies and improves the basic rules of the IEEE 802.11 Medium Access Control (MAC) protocol to optimize the contention among the multi-relay in a cooperative ARQ scheme. Secondly, a hybrid ARQ protocol with soft combining is adopted to make full use of the effective information in the error data packet and hence improve the ability of the receiver to decode the data packet correctly. The closed expressions of network performance including throughput and average packet transmission delay in a saturated network are then analyzed and derived by establishing a dedicated two-dimensional Markov model and solving its steady-state distribution. Finally, the performance evaluation and superiority of the proposed protocol are validated in different representative study cases through MATLAB simulations. [ABSTRACT FROM AUTHOR]