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

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

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 an efficient tool in knowledge reasoning and decision-making under uncertain environments. Conflict management is an open issue in Dempster-Shafer evidence theory. In past decades, a large amount of research has been conducted on this issue. In this paper, we propose a new theory called generalized evidence theory (GET). In comparison with classical evidence theory, GET addresses conflict management in an open world, where the frame of discernment is incomplete because of uncertainty and incomplete knowledge. Within the presented GET, we define a novel concept called generalized basic probability assignment (GBPA) to model uncertain information, and provide a generalized combination rule (GCR) for the combination of GBPAs, and build a generalized conflict model to measure conflict among evidences. Conflicting evidence can be effectively handled using the GET framework. We present many numerical examples that demonstrate that the proposed GET can explain and deal with conflicting evidence more reasonably than existing methods.

https://link.springer.com/content/pdf/10.1007%2Fs10489-015-0661-2.pdf

Generalized evidence theory

The notion Z-number introduced by Zadeh in 2011 has more capability to describe the uncertain information. Now that the theories about Z-number is not mature, how to convert Z-number to classical fuzzy number is rather signicant for application. In this paper, a method of transforming Z-number to classical fuzzy number is proposed according to the Fuzzy Expectation of fuzzy set. At last, a simple example is used to illustrated the procedure of the proposed approach.

A Method of Converting Z-number to Classical Fuzzy Number

Research highlights? We proposed a method to deal with MCDM problem under the framework of Demspter-Shafer evidence theory. ? A new fuzzy evidential MCDM method under uncertain environments is proposed. ? The linguistic variables can be transformed into basic probability assignments. ? Data from different criteria can be combined based on the Demspter rule. Multiple-criteria decision-making (MCDM) is concerned with the ranking of decision alternatives based on preference judgements made on decision alternatives over a number of criteria. First, taking advantage of data fusion technology to comprehensively consider each criterion data is a reasonable idea to solve the MCDM problem. Second, in order to efficiently handle uncertain information in the process of decision making, some well developed mathematical tools, such as fuzzy sets theory and Dempster Shafer theory of evidence, are used to deal with MCDM. Based on the two main reasons above, a new fuzzy evidential MCDM method under uncertain environments is proposed. The rating of the criteria and the importance weight of the criteria are given by experts' judgments, represented by triangular fuzzy numbers. Then, the weights are transformed into discounting coefficients and the ratings are transformed into basic probability assignments. The final results can be obtained through the Dempster rule of combination in a simple and straight way. A numerical example to select plant location is used to illustrate the efficiency of the proposed method.

Ying Wu

Papers

A new linguistic MCDM method based on multiple-criterion data fusion