https://www.alaakhamis.org/teaching/MCT200/reading/Information%20Fusion.pdf

Multisensor data fusion: A review of the state-of-the-art

Despite the importance of decision-making (DM) techniques for construction of effective decision models for supplier selection, there is a lack of a systematic literature review for it. This paper provides a systematic literature review on articles published from 2008 to 2012 on the application of DM techniques for supplier selection. By using a methodological decision analysis in four aspects including decision problems, decision makers, decision environments, and decision approaches, we finally selected and reviewed 123 journal articles. To examine the research trend on uncertain supplier selection, these articles are roughly classified into seven categories according to different uncertainties. Under such classification framework, 26 DM techniques are identified from three perspectives: (1) Multicriteria decision making (MCDM) techniques, (2) Mathematical programming (MP) techniques, and (3) Artificial intelligence (AI) techniques. We reviewed each of the 26 techniques and analyzed the means of integrating these techniques for supplier selection. Our survey provides the recommendation for future research and facilitates knowledge accumulation and creation concerning the application of DM techniques in supplier selection.

Application of decision-making techniques in supplier selection: A systematic review of literature

Neighborhood rough set based heterogeneous feature subset selection

There has been great interest in developing methodologies that are capable of dealing with imprecision and uncertainty. The large amount of research currently being carried out in fuzzy and rough sets is representative of this. Many deep relationships have been established, and recent studies have concluded as to the complementary nature of the two methodologies. Therefore, it is desirable to extend and hybridize the underlying concepts to deal with additional aspects of data imperfection. Such developments offer a high degree of flexibility and provide robust solutions and advanced tools for data analysis. Fuzzy-rough set-based feature (FS) selection has been shown to be highly useful at reducing data dimensionality but possesses several problems that render it ineffective for large datasets. This paper proposes three new approaches to fuzzy-rough FS-based on fuzzy similarity relations. In particular, a fuzzy extension to crisp discernibility matrices is proposed and utilized. Initial experimentation shows that the methods greatly reduce dimensionality while preserving classification accuracy.

/pdf/new-approaches-to-fuzzy-rough-feature-selection-1cxy4aoqcm.pdf

New Approaches to Fuzzy-Rough Feature Selection

Relationship between generalized rough sets based on binary relation and covering

Rough sets and fuzzy sets have been proved to be powerful mathematical tools to deal with uncertainty, it soon raises a natural question of whether it is possible to connect rough sets and fuzzy sets. The existing generalizations of fuzzy rough sets are all based on special fuzzy relations (fuzzy similarity relations, T-similarity relations), it is advantageous to generalize the fuzzy rough sets by means of arbitrary fuzzy relations and present a general framework for the study of fuzzy rough sets by using both constructive and axiomatic approaches. In this paper, from the viewpoint of constructive approach, we first propose some definitions of upper and lower approximation operators of fuzzy sets by means of arbitrary fuzzy relations and study the relations among them, the connections between special fuzzy relations and upper and lower approximation operators of fuzzy sets are also examined. In axiomatic approach, we characterize different classes of generalized upper and lower approximation operators of fuzzy sets by different sets of axioms. The lattice and topological structures of fuzzy rough sets are also proposed. In order to demonstrate that our proposed generalization of fuzzy rough sets have wider range of applications than the existing fuzzy rough sets, a special lower approximation operator is applied to a fuzzy reasoning system, which coincides with the Mamdani algorithm.

On the generalization of fuzzy rough sets

Fuzzy rough sets are the generalization of traditional rough sets to deal with both fuzziness and vagueness in data. The existing researches on fuzzy rough sets are mainly concentrated on the construction of approximation operators. Less effort has been put on the attributes reduction of databases with fuzzy rough sets. This paper mainly focuses on the attributes reduction with fuzzy rough sets. After analyzing the previous works on attributes reduction with fuzzy rough sets, we introduce formal concepts of attributes reduction with fuzzy rough sets and completely study the structure of attributes reduction. An algorithm using discernibility matrix to compute all the attributes reductions is developed. Based on these lines of thought, we set up a solid mathematical foundation for attributes reduction with fuzzy rough sets. The experimental results show that the idea in this paper is feasible and valid.

Attributes Reduction Using Fuzzy Rough Sets

Fuzzy set theory has been used as a framework for interpreting imprecise linguistic expressions. In general, a linguistic term is described by the compatibility ordering induced in some universe of discourse (UoD). A membership function in fuzzy set theory serves to reflect this ordering by assignment of values in [0, 1] for objects in UoD. When we compute the meaning of a linguistic expression such as "young and tall" using fuzzy membership functions, two implicit assumptions are made. First, we assume the membership values have quantitative meaning so that they can be quantitatively manipulated, for example, by adding or subtracting (the extensive scale assumption). Second, we assume that the scales of the membership values used in describing the different linguistic terms are comparable and the same (the common scale assumption). In many cases, these assumptions cannot be justified. Some proposals have been made to address the first issue by using ordinal scale in defining fuzzy membership functions. However, the second issue has not been properly investigated. In this paper, we propose a framework that does not depend on both of these assumptions. Such framework will facilitate our understanding and investigation of qualitative reasoning without the extensive scale and common scale assumptions.

J.W.T. Lee

Papers

On the generalization of fuzzy rough sets

Attributes Reduction Using Fuzzy Rough Sets

Ordinal fuzzy sets