International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

Atanassov (Intuitionistic fuzzy set, Fuzzy Sets and Systems 20 (1986) 87–96) proposed the intuitionistic fuzzy set (A-IFS) that is a generalization of Zadeh's fuzzy set. The essential elements of an A-IFS are intuitionistic fuzzy values (IFVs), each of which is depicted by a membership degree and a non-membership degree. The existing literature only gives the explanation of the meaning and the aggregation operators of IFVs, which is very hard and non-visualized for us to comprehend. To overcome the above shortcomings, this paper puts forward the diagram method to analyze the structures of the basic aggregation operations of IFVs. In addition, this paper utilizes the diagram method which is similar to joint probability distribution to describe the components of aggregation operations of IFVs, and each IFV depicts a 3-dimensional vector which is regarded as the marginal distributions of the joint probability distribution.

The purpose of this paper is to propose a new approach to interactive multi-attribute group decision making with triangular Atanassov's intuitionistic fuzzy numbers (TAIFNs). The contribution of this study is fivefold: (1) Minkowski distance between TAIFNs is firstly defined; (2) We define the possibility attitudinal expected values of TAIFNs and thereby present a novel risk attitudinal ranking method of TAIFNs which can sufficiently consider the risk attitude of decision maker; (3) The weighted average operator (TAIFWA) and generalized ordered weighted average (TAIFGWA) operator of TAIFNs are defined as well as the hybrid ordered weighted average (TAIFHOWA) operator; (4) To study the interaction between attributes, we further develop the generalized Choquet (TAIF-GC) integral operator and generalized hybrid Choquet (TAIF-GHC) integral operator of TAIFNs. Their desirable properties are also discussed; (5) The individual overall value of alternative is obtained by TAIF-GC operator and the collective one is derived through TAIFWA operator. Fuzzy measures of attribute subsets and expert weights are objectively derived through constructing multi-objective optimization model which is transformed into the goal programming model to solve. The system analyst selection example verifies effectiveness of the proposed approach.

The problem of distributivity was posed many years ago and it has been investigated for families of certain operations, such as t-norms, t-conorms, uninorms and nullnorms. In this paper, we continue to investigate the same topic as the above by focusing on semi-nullnorms and semi-t-operators, which are generalization of nullnorms and t-operators by omitting commutativity and associativity, and commutativity, respectively. The obtained results are not only the full characterization of this kind of distributivity equation, but also extensions of distributivity for nullnorms and for semi-nullnorms. Moreover, this paper finishes the full characterization of distributivity between semi-nullnorms and semi-t-operators together with Refs. 6 and 20.

Uncertainty and its imposed risk have significant impacts on decision-making. However, both are disregarded in many trust-based applications. In this paper, we propose a risk-aware approach to explicitly take uncertainty of trust and its effects into account. Our approach consists of a trust, a confidence, and a risk model. We do not prescribe a specific trust model, and any probabilistic trust model can be empowered by our approach. The confidence model calculates the uncertainty of the trust model in the form of a confidence interval, and is independent of the inner-workings of the trust model. This interval is used by the utility-based risk model which assesses the effects of uncertainty on trust-based decisions. We evaluated our approach by a four-state HMM-based simulated trustee, and employed the Beta, HMM and evidence-based trust models. We proposed and compared different methods for calculating confidence intervals, as well as methods for determining the risk and opportunity of a trust-based interaction. The results demonstrate how our approach should be used to improve the correctness of decision-making in trust-based applications. According to the statistical analysis of the simulation results, confidence intervals can properly represent the trust value and its uncertainty, and strongly improve trust-based decisions.

Existing distance-based outlier mining methods do not consider the impact of each attribute's importance degree, thereby resulting in poor mining accuracies. To address this problem, we propose a new outlier mining algorithm – Miner* – that makes use of information entropy and Weighted Distance Sum to substantially improve mining accuracies. Miner* employs information entropy to determine weight values indicating the importance degrees of data attributes. An input dataset is reduced by Miner* through the neighbour-radius-based pruning technologies. Thus, Miner* obtains a candidate outlier set by removing any data objects that are unlikely to be outliers. Miner* calculates the weighted distance sum value W_k of each object in the candidate outlier set; W_k value ranks the top n to be regarded as outliers. Due to the sum of distance, which takes full advantage of the clustering characteristics of the dataset, edge distribution data objects and local outliers can be effectively mined out. To demonstrate the effectiveness of the Miner* algorithm, we implement Miner* in a prototype system to detect star spectrum data objects with abnormal characteristic lines. Our experimental results show that the algorithm in Miner* achieves high accuracy, high scalability, and low man-made influence by utilizing UCI and star spectrum dataset. Our results also confirm that Miner* is feasible and effective in mining spectrum data with abnormal characteristic lines from massive star spectrum dataset.

In this paper, a self-adaptive PD (SAPD) is employed for motion control of omni-directional robots. The method contains a PD controller that can be tuned online using a fuzzy logic system (FLS). Fast and accurate positioning is one of significant challenges in robot platforms. In addition, some uncertainties have adverse effects on traditional control system's performance during the robot's motion. Slow responses, low accuracy and instability are the most important drawbacks of widespread controllers in presence of uncertain dynamics. Since the fuzzy algorithm can deal with uncertainties and nonlinearities, the proposed method can tackle the mentioned problems. The controller is designed based on an uncertain model and implemented on a four wheeled omni-directional fast robot. The novelty of this article is proposing an enhanced version of well-known gain scheduling PD controller to improve positioning performance of the robot in different circumstances. Experimental results show that the method can provide a desirable performance in the presence of uncertainties.

Energy Management Systems have become an imperative aspect of smart grids, owing to the enormous challenges imposed due to real-time pricing, distributed generation and integration of intermittent renewables. Due to the uncertainty associated with renewable sources and prominent fluctuations in the load demand, it is extremely important to maintain the overall energy balance in such grids. In this paper, the distributed energy management is achieved using a Multi-agent System which provides a flexible and reliable solution to control and manage smart grids. Adaptive fuzzy systems are designed to instill intelligent decision making capability in the agents of multi-agent system. When renewable sources are inadequate, the sustainability of the system is not guaranteed and multi-agent system is capable of deciding the mode of operation such that the system reliability and performance is not compromised. The proposed algorithm maintains power balance in the system and also sustains desired values for the State of Charge of storage units in order to guarantee extended battery life. The Energy management system also implements a cost optimization algorithm based on the Particle Swarm Optimization technique, to minimize operating costs and maximize profits earned by the grid. The proposed energy management algorithm is tested and validated on a practical test system which inherits most of the features of a small-scale smart grid.