Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

Multi-sensor data fusion based on the belief divergence measure of evidences and the belief entropy

Supplier selection is an important issue in supply chain management (SCM), and essentially is a multi-criteria decision-making problem. Supplier selection highly depends on experts' assessments. In the process of that, it inevitably involves various types of uncertainty such as imprecision, fuzziness and incompleteness due to the inability of human being's subjective judgment. However, the existing methods cannot adequately handle these types of uncertainties. In this paper, based on a new effective and feasible representation of uncertain information, called D numbers, a D-AHP method is proposed for the supplier selection problem, which extends the classical analytic hierarchy process (AHP) method. Within the proposed method, D numbers extended fuzzy preference relation has been involved to represent the decision matrix of pairwise comparisons given by experts. An illustrative example is presented to demonstrate the effectiveness of the proposed method.

https://isiarticles.com/bundles/Article/pre/pdf/46527.pdf

Supplier selection using AHP methodology extended by D numbers

Complex network approaches to nonlinear time series analysis

A common algorithm to solve the shortest path problem (SPP) is the Dijkstra algorithm. In this paper, a generalized Dijkstra algorithm is proposed to handle SPP in an uncertain environment. Two key issues need to be addressed in SPP with fuzzy parameters. One is how to determine the addition of two edges. The other is how to compare the distance between two different paths with their edge lengths represented by fuzzy numbers. To solve these problems, the graded mean integration representation of fuzzy numbers is adopted to improve the classical Dijkstra algorithm. A numerical example of a transportation network is used to illustrate the efficiency of the proposed method.

Short communication: Fuzzy Dijkstra algorithm for shortest path problem under uncertain environment

Dempster–Shafer evidence theory is widely used in information fusion. However, it may lead to an unreasonable result when dealing with high conflict evidence. In order to solve this problem, we put forward a new method based on the credibility of evidence. First, a novel belief entropy, Deng entropy, is applied to measure the information volume of the evidence and then the discounting coefficients of each evidence are obtained. Finally, weighted averaging the evidence in the system, the Dempster combination rule was used to realize information fusion. A weighted averaging combination role is presented for multi-sensor data fusion in fault diagnosis. It seems more reasonable than before using the new belief function to determine the weight. A numerical example is given to illustrate that the proposed rule is more effective to perform fault diagnosis than classical evidence theory in fusing multi-symptom domains.

https://journals.sagepub.com/doi/pdf/10.1177/1687814016641820

An evidential sensor fusion method in fault diagnosis

Performing risk analysis can be a challenging task for complex systems due to lack of data and insufficient understanding of the failure mechanisms. A semi quantitative approach that can utilize imprecise information, uncertain data and domain experts' knowledge can be an effective way to perform risk analysis for complex systems. Though the definition of risk varies considerably across disciplines, it is a well accepted notion to use a composition of likelihood of system failure and the associated consequences (severity of loss). A complex system consists of various components, where these two elements of risk for each component can be linguistically described by the domain experts. The proposed linguistic approach is based on fuzzy set theory and Dempster-Shafer theory of evidence, where the later has been used to combine the risk of components to determine the system risk. The proposed risk analysis approach is demonstrated through a numerical example.

Risk analysis in a linguistic environment: A fuzzy evidential reasoning-based approach

Contaminant intrusion in a water distribution network is a complex but a commonly observed phenomenon, which depends on three elements - a pathway, a driving force and a contamination source. However, the data on these elements are generally incomplete, non-specific and uncertain. In an earlier work, Sadiq, Kleiner, and Rajani (2006) have successfully applied traditional Dempster-Shafer theory (DST) to estimate the ''risk'' of contaminant intrusion in a water distribution network based on limited uncertain information. However, the method used for generating basic probability assignment (BPA) was not very flexible, and did not handle and process uncertain information effectively. In this paper, a more pragmatic method is proposed that utilizes ''soft'' computing flexibility to generate BPAs from uncertain information. This paper compares these two methods through numerical examples, and demonstrates the efficiency and effectiveness of modified method.

Modeling contaminant intrusion in water distribution networks: A new similarity-based DST method

Atanassov's intuitionistic fuzzy set (IFS) is a generalization of a fuzzy set that can express and process uncertainty much better. There are various averaging operators defined for IFSs. In this paper, a new type of operator called an intuitionistic fuzzy entropy weighted power average ggregation operator is proposed. The entropy among IFSs is taken into consideration to determine the weights. What's more, the similarity is considered to measure the support degree between two elements of the IFS. Compared with other classical power average operators, the proposed operator is completely driven by data and fully takes into account the relationship among values. Finally, an illustrative example of multiple attribute group decision making is presented to show that the proposed operator is effective and practical.

Intuitionistic Fuzzy Power Aggregation Operator Based on Entropy and Its Application in Decision Making

Z-number, a new concept describes both the restriction and the reliability of evaluation, is more applicable than fuzzy numbers in the fields of decision making, risk assessment etc. However, how to deal with the restriction and the reliability properly is still a problem which is discussed few and inadequately in the existing literatures. In this paper, firstly, a new improved method for ranking generalized fuzzy numbers where the weight of centroid points, degrees of fuzziness and the spreads of fuzzy numbers are taken into consideration is proposed, which can overcome some drawbacks of exiting methods and is very efficient for evaluating symmetric fuzzy numbers and crisp numbers. Then, a procedure for evaluating Znumbers with the method for ranking generalized fuzzy numbers is presented, which considers the status of two parts ((A,B)) of Z-numbers and gives the principles of ranking Z-numbers. The main advantage of the proposed method is utilization of Z-numbers which can express more vague information compared with the fuzzy number. In addition, instead of converting B to a crisp number as the existing methods of ranking Z-numbers did, the proposed method retains the fuzzy information of B which can reduce the loss of information. Finally, several numerical examples are provided to illustrate the superiority and the rationality of the proposed procedure. 6

Wen Jiang

Papers

An evidential sensor fusion method in fault diagnosis

Risk analysis in a linguistic environment: A fuzzy evidential reasoning-based approach

Modeling contaminant intrusion in water distribution networks: A new similarity-based DST method

Intuitionistic Fuzzy Power Aggregation Operator Based on Entropy and Its Application in Decision Making

Ranking Z-numbers with an improved ranking method for generalized fuzzy numbers