Some hybrid aggregating operators in linguistic decision making with Dempster–Shafer belief structure

In this paper, we have studied the Dempster–Shafer theory of evidence in situations of decision making with linguistic information and we develop a new aggregation operator: belief structure generalized linguistic hybrid averaging (BS-GLHA) operator and a wide range of particular cases. we have developed the new decision making model with Dempster–Shafer belief structure that uses linguistic information in order to manage uncertain situations that cannot be managed in a probabilistic way. We have seen that all these approaches are very useful for representing the new approaches in a more complete way selecting for each situation the particular case that it is closest to our interests in the specific problem analyzed. Finally, a numerical example is used to illustrate the applicability and effectiveness of the proposed method. We have pointed out that the results and decisions are dependent on the linguistic aggregation operator used in the decision making process.     

A flexible rule for evidential combination in Dempster–Shafer theory of evidence

Dempster’s combination rule in Dempster–Shafer theory of evidence is widely used to combine multiple pieces of evidence. However, when the evidence is severely conflicting, the result could be counter-intuitive. Thus, many alternative combination rules have been proposed to address this issue. Nevertheless, the existing ones sometimes behave not very well. This may be because they do not hold some essential properties. To this end, this paper firstly identifies some of the important properties. Then, following the cues from these properties, we propose a novel evidential combination rule as a remediation of Dempster’s combination rule in Dempster–Shafertheory. Our new rule is based on the concept of complete conflict (we introduced in this paper), Dempster’s combination rule, and the concept of evidence weight. Moreover, we illustrate the effectiveness of our new rule by using it to successfully resolve well-known Zadeh’s counter-example, which is against Dempster’s combination rule. Finally, we confirm the advantages of our method over the existing methods through some examples.     

Partition belief median filter based on Dempster–Shafer theory for image processing

A novel median-type filter controlled by evidence fusion is proposed for removing noise from images. The fusion of evidence based on the Dempster–Shafer evidence theory, providing a way to deal with the uncertainty in the evidence fusion, indicates to what extent a noise is considered. The filter proposed here is obtained as a weighted sum of the current pixel value and the output of the median filter, and the weight is set based on the belief value of the input signal sequence. The efficient step-like function is used to partition the belief space, and the least mean square (LMS) algorithm is applied to obtain the optimal weight for each block. Moreover, to improve the performance, the new filter is recursively implemented. Experimental results have demonstrated that the proposed filter can outperform many well-accepted median-based filters in preserving image details while effectively suppressing impulsive noises, and it also works satisfactorily in reducing Gaussian as well as the mixture of Gaussian and impulsive noise.     

Dempster–Shafer structure based fuzzy logic system for stochastic modeling

The Dempster–Shafer (D–S) theory of evidence is introduced to improve fuzzy inference under the complex stochastic environment. The Dempster–Shafer based fuzzy set (DFS) is first proposed, together with its union and intersection operations, to capture the principal stochastic uncertainties. Then, the fuzzy inference will be modified based on the extensional Dempster rule of combination. This new approach is able to capture the stochastic disturbance acting on fuzzy membership function, and provide a more effective inference under strong stochastic uncertainty. Finally, the numerical simulation and the experimental prediction of the wind speed are conducted to show the potential of the proposed method in stochastic modeling.     

Chest X-ray enhancement to interpret pneumonia malformation based on fuzzy soft set and Dempster–Shafer theory of evidence

Image enhancement algorithms are commonly used to increase the contrast and visual quality of low-dose x-ray images. This paper proposes an automated enhancement method using soft fuzzy sets with a new decision-making scheme based on Dempster-Shafer theory of evidence for the visual interpretation of pneumonia malformation in low-dose x-ray images, called as XEFSDS. The XEFSDS model first generates an original source x-ray image into a complementary image, then each original and complement image is applied to the characterized image object and background areas of fuzzy space. The S-function is utilized to define fuzzy soft sets for the classification of gray level ambiguity in both images, and hence a decision criterion via Dempster-Shafer approach and fuzzy interval has been adapted to discriminate uncertainties on the pixel intensity and the spatial information. Modified membership grade operations have been performed on each object/background area, and Werner’s AND/OR operator (an aggregation operator) has been utilized to build a new membership function from two modified membership functions. Finally, an enhanced image is obtained from the new membership function via defuzzification. Experiments on different pneumonia X-ray images demonstrate that the XEFSDS scheme produces better results than the existing methods. To show the advantages of the XEFSDS scheme, we have executed a segmentation based examination on enhanced image for the detection of pneumonia malformation as well as abnormal lobe (lobar pneumonia) or bronchopneumonia.     

A cloud computing framework for analysis of agricultural big data based on Dempster–Shafer theory

The Journal of Supercomputing - This paper aims to extract optimal location for cultivating orange trees. In order to reach this goal, a combination of Dempster-Shafer theory (DST) and cloud...     

A novel trust management scheme based on Dempster–Shafer evidence theory for malicious nodes detection in wireless sensor networks

With the development of Internet technology, social network has become an important application in the network life. However, due to the rapid increase in the number of users, the influx of a variety of bad information is brought up as well as the existence of malicious users. Therefore, it is emergent to design a valid management scheme for user’s authentication to ensure the normal operation of social networks. Node trust evaluation is an effective method to deal with typical network attacks in wireless sensor networks. In order to solve the problem of quantification and uncertainty of trust, a novel trust management scheme based on Dempster–Shafer evidence theory for malicious nodes detection is proposed in this paper. Firstly, by taking into account spatiotemporal correlation of the data collected by sensor nodes in adjacent area, the trust degree can be estimated. Secondly, according to the D–S theory, the trust model is established to count the number of interactive behavior of trust, distrust or uncertainty, further to evaluate the direct trust value and indirect trust value. Then, a flexible synthesis method is adopted to calculate the overall trust to identify the malicious nodes. The simulation results show that the proposed scheme has obvious advantages over the traditional methods in the identification of malicious node and data fusion accuracy, and can obtain good scalability.

     

Novel neutrality operation–based Pythagorean fuzzy geometric aggregation operators for multiple attribute group decision analysis

Pythagorean fuzzy sets (PFSs) accommodate more uncertainties than L_x the intuitionistic fuzzy sets and hence its applications are more extensive. Under the PFS, the objective of this paper is to develop some new operational laws and their corresponding weighted geometric aggregation operators. For it, we define some new neutral multiplication and power operational laws by including the feature of the probability sum and the interaction coefficient into the analysis to get a neutral or a fair treatment to the membership and nonmembership functions of PFSs. Associated with these operational laws, we define some novel Pythagorean fuzzy weighted, ordered weighted, and hybrid neutral geometric operators for Pythagorean fuzzy information, which can neutrally treat the membership and nonmembership degrees. The desirable relations and the characteristics of the proposed operators are studied in details. Furthermore, a multiple attribute group decision-making approach based on the proposed operators under the Pythagorean fuzzy environment is developed. Finally, an illustrative example is provided to show the practicality and the feasibility of the developed approach.     

Multi-SVM based Dempster–Shafer theory for gesture intention understanding using sparse coding feature

The Dempster–Shafer theory based on multi-SVM to deal with multimodal gesture images for intention understanding is proposed, in which the Sparse Coding (SC) based Speeded-Up Robust Features (SURF) are used for feature extraction of depth and RGB image. Aiming at the problems of the small sample, high dimensionality and feature redundancy for image data, we use the SURF algorithm to extract the features of the original image, and then perform their Sparse Coding, which means that the image is subjected to two-dimensional feature reduction. The dimensionally reduced gesture features are used by the multi-SVM for classification. A fusion framework based on D–S evidence theory is constructed to deal with the recognition of depth and RGB image to realize the gesture intention understanding. To verify the effectiveness of the proposal, the experiments on two RGB-D datasets (CGD2011 and CAD-60) are conducted. The results of 10-fold cross validation test show that the recognition rates were higher than those produced by other methods under the condition when each sensor was considered individually. Meanwhile, the preliminary experiments are also carried out in the developing emotional social robot system. The results indicate that the proposal can be applied to human–robot interaction.     

SAR target configuration recognition based on the Dempster–Shafer theory and sparse representation using a new classification criterion

Synthetic aperture radar (SAR) images are sensitive to target aspect angles. To weaken the influences of target aspect angle sensitivity on recognition, a new classification criterion is proposed for sparse representation (SR) based target configuration recognition in this paper. Different from the existing SR-based algorithms which utilize the reconstruction error of each class to identify the targets, the proposed algorithm establishes a supportive degree function to realize recognition. The supportive degree function can enhance the impacts of the samples with small reconstruction errors. Moreover, to further improve the performance of the proposed algorithm, the Dempster–Shafer theory (DST) is used to fuse the information of several similar samples. Experiments on the moving and stationary target acquisition and recognition (MSTAR) database verify the advantage of the proposed algorithm.     

Context-dependent combination of sensor information in Dempster–Shafer theory for BDI

There has been much interest in the belief–desire–intention (BDI) agent-based model for developing scalable intelligent systems, e.g. using the AgentSpeak framework. However, reasoning from sensor information in these large-scale systems remains a significant challenge. For example, agents may be faced with information from heterogeneous sources which is uncertain and incomplete, while the sources themselves may be unreliable or conflicting. In order to derive meaningful conclusions, it is important that such information be correctly modelled and combined. In this paper, we choose to model uncertain sensor information in Dempster–Shafer (DS) theory. Unfortunately, as in other uncertainty theories, simple combination strategies in DS theory are often too restrictive (losing valuable information) or too permissive (resulting in ignorance). For this reason, we investigate how a context-dependent strategy originally defined for possibility theory can be adapted to DS theory. In particular, we use the notion of largely partially maximal consistent subsets (LPMCSes) to characterise the context for when to use Dempster’s original rule of combination and for when to resort to an alternative. To guide this process, we identify existing measures of similarity and conflict for finding LPMCSes along with quality of information heuristics to ensure that LPMCSes are formed around high-quality information. We then propose an intelligent sensor model for integrating this information into the AgentSpeak framework which is responsible for applying evidence propagation to construct compatible information, for performing context-dependent combination and for deriving beliefs for revising an agent’s belief base. Finally, we present a power grid scenario inspired by a real-world case study to demonstrate our work.     

Designing high-level decision making systems based on fuzzy if–then rules for a point-to-point car racing game

In this paper, fuzzy rule-based systems are applied to a point-to-point car racing game. In the point-to-point car racing game, two car agents compete with each other for taking waypoints. There are three waypoints in the car racing field, each of which is assigned a number that indicates the order to take. The control process of car agents is modeled as a non-holonomic system where there are two input variables (acceleration and steering) for controlling the position, angle and velocity of the car agents. Fuzzy rule-based systems are used to make a high-level decision where the target waypoint to take is determined. Since a fuzzy rule-based system for the high-level decision making is generated in the manner of supervised learning, a set of training patterns should be given for the construction of the fuzzy rule-based systems. In this paper we examine two methods to obtain such a set of training patterns. We also examine two representations of input vectors for the fuzzy rule-based systems. We discuss the effect of obtained training patterns and the input representation on the performance of the fuzzy rule-based systems. After discussing and analyzing the experimental results, we present an adaptive framework of fuzzy rule-based systems. The performance of adaptive fuzzy rule-based systems is then examined based on the results of their non-adaptive version. A series of computational experiments are performed to show the learning ability of the adaptive fuzzy rule-based systems.     

Human–robot communication for collaborative decision making — A probabilistic approach

Humans and robots need to exchange information if the objective is to achieve a task collaboratively. Two questions are considered in this paper: what and when to communicate. To answer these questions, we developed a human–robot communication framework which makes use of common probabilistic robotics representations. The data stored in the representation determines what to communicate, and probabilistic inference mechanisms determine when to communicate. One application domain of the framework is collaborative human–robot decision making: robots use decision theory to select actions based on perceptual information gathered from their sensors and human operators. In this paper, operators are regarded as remotely located, valuable information sources which need to be managed carefully. Robots decide when to query operators using Value-Of-Information theory, i.e. humans are only queried if the expected benefit of their observation exceeds the cost of obtaining it. This can be seen as a mechanism for adjustable autonomy whereby adjustments are triggered at run-time based on the uncertainty in the robots’ beliefs related to their task. This semi-autonomous system is demonstrated using a navigation task and evaluated by a user study. Participants navigated a robot in simulation using the proposed system and via classical teleoperation. Results show that our system has a number of advantages over teleoperation with respect to performance, operator workload, usability, and the users’ perception of the robot. We also show that despite these advantages, teleoperation may still be a preferable driving mode depending on the mission priorities.     

Comment on ‘ Tolerance analysis using fuzzy sets ’ and ‘ A procedure for multiple aspect decision making ’

The problem of tracking a reference vector variable from a given class is considered for discrete time linear multiple input-output plants. The plant and the reference are both described by an input-output relation and the objective is to track so that a quadratic criterion is minimized. This tracking problem is solved by reformulating it as a regulator problem for an augmented system. The optimal control law is shown to contain both feedback and feedforward terms and it is obtained by applying polynomial matrix techniques. The design procedure consists in spectral factorization and the solution of linear equations in polynomial matrices. The case of unstable references is included and a natural solvability condition is derived in the form of divisibility of polynomial matrices.     

A verified realization of a Dempster–Shafer based fault tree analysis

Fault tree analysis is a method to determine the likelihood of a system attaining an undesirable state based on the information about its lower level parts. However, conventional approaches cannot process imprecise or incomplete data. There are a number of ways to solve this problem. In this paper, we will consider the one that is based on the Dempster–Shafer theory. The major advantage of the techniques proposed here is the use of verified methods (in particular, interval analysis) to handle Dempster–Shafer structures in an efficient and consistent way. First, we concentrate on DSI (Dempster–Shafer with intervals), a recently developed tool. It is written in MATLAB and serves as a basis for a new add-on for Dempster–Shafer based fault tree analysis. This new add-on will be described in detail in the second part of our paper. Here, we propagate experts’ statements with uncertainties through fault trees, using mixing based on arithmetic averaging. Furthermore, we introduce an implementation of the interval scale based algorithm for estimating system reliability, extended by new input distributions.     

A calibration approach based on Takagi–Sugeno fuzzy inference system for digital electronic compasses

Recently, the development of industrial processes brought on the outbreak of technologically complex systems. This development generated the necessity of research relative to the mathematical techniques that have the capacity to deal with project complexities and validation. Fuzzy models have been receiving particular attention in the area of nonlinear systems identification and analysis due to it is capacity to approximate nonlinear behavior and deal with uncertainty. A fuzzy rule-based model suitable for the approximation of many systems and functions is the Takagi–Sugeno (TS) fuzzy model. TS fuzzy models are nonlinear systems described by a set of if then rules which gives local linear representations of an underlying system. Such models can approximate a wide class of nonlinear systems. In this paper a performance analysis of a system based on TS fuzzy inference system for the calibration of electronic compass devices is considered. The contribution of the evaluated TS fuzzy inference system is to reduce the error obtained in data acquisition from a digital electronic compass. For the reliable operation of the TS fuzzy inference system, adequate error measurements must be taken. The error noise must be filtered before the application of the TS fuzzy inference system. The proposed method demonstrated an effectiveness of 57% at reducing the total error based on considered tests.     

Supplier selection in a fuzzy group setting: A method using grey related analysis and Dempster–Shafer theory

Supplier selection in a fuzzy group setting is a very important strategic decision involving decisions balancing a number of conflicting criteria and opinions from different experts. This paper uses grey related analysis and Dempster–Shafer theory to deal with this fuzzy group decision making problem. First, in the individual aggregation, grey related analysis is employed as a means to reflect uncertainty in multi-attribute models through interval numbers. Second, in the group aggregation, the Dempster–Shafer (D–S) rule of combination is used to aggregate individual preferences into a collective preference, by which the candidate alternatives are ranked and the best alternative(s) are obtained. The proposed approach uses both quantitative and qualitative data for international supplier selection. It provides alternative tools to evaluate and improve supplier selection decisions in an uncertain global market.     

Generalized Atanassov’s intuitionistic fuzzy power geometric operators and their application to multiple attribute group decision making

In this paper, we extend the power geometric (PG) operator and the power ordered weighted geometric (POWG) operator [Z.S. Xu, R.R. Yager, Power-geometric operators and their use in group decision making, IEEE Transactions on Fuzzy Systems 18 (2010) 94–105] to Atanassov’s intuitionistic fuzzy environments, i.e., we develop a series of generalized Atanassov’s intuitionistic fuzzy power geometric operators to aggregate input arguments that are Atanassov’s intuitionistic fuzzy numbers (IFNs). Then, we study some desired properties of these aggregation operators and investigate the relationships among these operators. Furthermore, we apply these aggregation operators to develop some methods for multiple attribute group decision making with Atanassov’s intuitionistic fuzzy information. Finally, two practical examples are provided to illustrate the proposed methods.