Intuitionistic fuzzy information aggregation plays an important part in Atanassov's intuitionistic fuzzy set theory, which has emerged to be a new research direction receiving more and more attention in recent years. In this paper, we first introduce some operations on intuitionistic fuzzy sets, such as Einstein sum, Einstein product, Einstein exponentiation, etc., and further develop some new geometric aggregation operators, such as the intuitionistic fuzzy Einstein weighted geometric operator and the intuitionistic fuzzy Einstein ordered weighted geometric operator, which extend the weighted geometric (WG) operator and the ordered weighted geometric (OWG) operator to accommodate the environment in which the given arguments are intuitionistic fuzzy values. We also establish some desirable properties of these operators, such as commutativity, idempotency and monotonicity, and give some numerical examples to illustrate the developed aggregation operators. In addition, we compare the proposed operators with the existing intuitionistic fuzzy geometric operators and get the corresponding relations. Finally, we apply the intuitionistic fuzzy Einstein weighted geometric operator to deal with multiple attribute decision making under intuitionistic fuzzy environments.

Based on the researches on ordered weighted average (OWA) operator, the weighted OWA operator (WOWA) and especially the quantifier guided aggregation method, with the generating function representation of regular increasing monotone (RIM) quantifier technique, we discuss the properties of WOWA operator with RIM quantifier in the respect of orness. With the continuous OWA and WOWA ideas recently proposed by Yager, an improvement on the continuous OWA and WOWA operator is proposed. The properties of WOWA are also extended from discrete to the continuous case. Based on these properties, two families of parameterized RIM quantifiers for WOWA operator are proposed, which have exponential generating function and piecewise linear generating function respectively. One interesting property of these two kinds of RIM quantifiers is that for any aggregated set (or variable) under any weighted (distribution) function, the aggregation values are always consistent with the orness (optimistic) levels, so they can be used to represent the decision maker's preference, and we can get the preference value of fuzzy sets or random variables with the orness level of RIM quantifier as their control parameter.

The Maclaurin symmetric mean (MSM) operator is a classical mean type aggregation operator used in modern information fusion theory, which is suitable to aggregate numerical values. The prominent characteristic of the MSM operator is that it can capture the interrelationship among the multi-input arguments. In this paper, we propose the dual Maclaurin symmetric mean (DMSM) operator and extend the DMSM operator to accommodate uncertain linguistic environment. Some new aggregation operators based on DMSM for aggregating uncertain linguistic information are developed, such as the uncertain linguistic dual Maclaurin symmetric mean (ULDMSM) operator, the uncertain linguistic weighted dual Maclaurin symmetric mean (ULWDMSM) operator and the uncertain linguistic Choquet dual Maclaurin symmetric mean (ULCDMSM) operator. Meanwhile, some desirable properties and special cases with respect to different parameter values of these operators are studied in detail. Furthermore, based on the ULWDMSM and ULCDMSM operators, two approaches to multiple attribute decision making with uncertain linguistic information are developed. Finally, a numerical example is provided to illustrate the feasibility of the proposed methods and deliver a comparative analysis with uncertain linguistic Bonferroni mean (ULBM) operator is also presented.

Failure mode and effect analysis (FMEA) is considered as a proactive risk prevention and control technique has been widely applied to identify, assess and eliminate the risk of failure modes in various fields. Nevertheless, the risk indicators interaction and decision maker’s psychological behavior character are seldom considered simultaneously in the current FMEA method. In this paper, we develop a hybrid FMEA framework integrating generalized TODIM (an acronym in Portuguese of Interactive and Multi-criteria Decision Making) method, Choquet integral and Shapley index to remedy this gap. In the proposed FMEA framework, the fuzzy measure and Shapley index are used to model the interaction relationships among risk indicators and to determine the weights of these indicators. The extended generalized TODIM method with fuzzy measure and Shapley index is present to simulate the psychological behavior character of FMEA team members. It is also applied to calculate the risk priority of each failure mode. The trapezoidal fuzzy numbers (TrFNs) are adopted to depict the uncertainty in the risk evaluation process. Furthermore, a new risk evaluation information fusion with TrFNs-WAIA (weighted arithmetic interaction averaging operator of the trapezoidal fuzzy numbers) operator based on Shapley Choquet is developed to aggregate individual risk evaluation information of FMEA team member into a group risk evaluation matrix, which considers the potential correlations among these members. Finally, a practical example of FMEA problem is presented to demonstrate the application and feasibility of the proposed hybrid FMEA framework, and comparison and sensitivity studies are also conducted to validate the effectiveness of the improved FMEA approach.