Rough analysis method of multi-attribute decision making with incomplete information
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Rule induction method based on rough set theory (RST) has received much attention recently since it may generate a minimal set of rules from the decision system for real-life applications by using of attribute reduction and approximations. The decision system may vary with time, e.g., the variation of objects, attributes and attribute values. The reduction and approximations of the decision system may alter on Attribute Values' Coarsening and Refining (AVCR), a kind of variation of attribute values, which results in the alteration of decision rules simultaneously. This paper aims for dynamic maintenance of decision rules w.r.t. AVCR. The definition of minimal discernibility attribute set is proposed firstly, which aims to improve the efficiency of attribute reduction in RST. Then, principles of updating decision rules in case of AVCR are discussed. Furthermore, the rough set-based methods for updating decision rules in the inconsistent decision system are proposed. The complexity analysis and extensive experiments on UCI data sets have verified the effectiveness and efficiency of the proposed methods.
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In this paper, we establish a dominance relation in interval-valued information systems. With respect to any subset of object set, attribute reduction methods are presented based on substitution of the indiscernibility relation by the dominance relation. Possible and certain decision rules can be derived by possible and uniform distribution functions, respectively. Any part of the decision rules can be identified by these attributes which obtained by the attribute reduction method. The usefulness of each method is illustrated by one example.
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Some of the rules derived by DRSA (Dominance-based Rough Set Approach) from incomplete decision systems may contain unknown values. To overcome the shortcoming, this paper proposes a new DRSA, which is based on novel dominance relation. The adapted relation is distinguished from traditional dominance relation by two roles, a subject and a reference. The subject played by an object from the universe leads to one-way comparison with the reference done by a virtual object from the virtual space. By the approach, virtual objects without unknown values, instead of objects that may carry unknown values, are used to extract decision rules from incomplete decision system, which brings about the induced rules without any unknown values. A numerical example is employed to substantiate the conceptual arguments.
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Dominance relations exist extensively in decision-making problems. Dominance-based neighborhood rough sets (DNRS) using fuzzy preference relations (FPRs) are presented in this article to deal with attribute reduction in the large-scale decision-making problems. In this model, FPR is elicited to quantify the dominance-based rough set model, which can efficiently deal with the under-fitting problem of classical dominance-based rough sets. First, by formulating a quantified dominance-based neighborhood relation which satisfies reflexivity, the propositions of the quantified DNRSs are analyzed. Second, we propose approaches to attribute reduction based on upper-approximate and lower-approximate discernibility matrices, respectively. Furthermore, we evaluate that the novel model performs efficiently and effectively in time consumption and space storage by experimental analysis. Finally, combining with parallel computing, we demonstrate that the new model can be used to deal with attribute reduction of large-scale datasets effectively.
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In the incomplete information system, no matter which dominance relation is being used to construct a rough set model the results would contain uncertainty. Considering three influence factors include the amount of information, the weight of attribute and the degree of different objects, a new grey dominance relation are defined in this paper. On this basis, a rough decision model is set up. The concept of difference coefficient is defined and optimized in the new model. An example is given to illustrate the efficiency and feasibility of the model.
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Methodologies for sorting problems have been developed from a variety of research disciplines, including statistics, artificial intelligence and operations research. Rough set theory has proved to be a useful tool for analysis of a large class of multi_attribute decision problems. But, the theory based on indiscernibility relation or similarity relation can not handle the decision problems with criterion. Greco et al have proposed a kind of extended rough set approach, in which the rough approximations of decision classes involve using dominance relation instead of using indiscernibility relation in the basic rough sets approach in the analysis of sorting examples. In order to construct preference models from decision examples, the dominance function is constructed to compute the minimal decision rules. Then, the methodology of rule simplification is presented to eliminate the redundancy in the rule set. In addition, the strategies of sorting decision based on the derived rules are put forward.
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In order to obtain probabilistic decision rules from multiple attribute decision systems with incomplete information,an extended rough sets methodology is proposed.Firstly,the concept of consistency degree based on the tolerance relation is presented.Secondly,rough approximations and region boundary of knowledge are put forward by giving out tolerant region value.Thirdly,the basic properties of rough approximations are discussed,and the probabilistic decision rules are acquired.Finally,the feasibility and effectiveness of this new method are demonstrated by a real example.
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The rough set theory plays an important role in such domains as multi-attribute decision making,data mining,machine learning and artificial intelligence,etc.According to the theory of classical rough set,the partition of complete information system classified by the indiscernibility relation is used to define the upper and lower approximation set for knowledge reduction,rule reasoning and decision making.While there are a large number of incomplete information systems in real life,According to incomplete information system of multiple attribute decision making problems proposed multi-attribute decision making based on rough set from the perspective of the nonsymmetric similarity relation.
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DRSA (Dominance-based Rough Set Approach) is an extension of rough set theory for dealing with multiple criteria decision analysis problems based on dominance principle. In this paper, we consider dominance-based approximation spaces based on a generalized dominance principle which are represented by indexed blocks of binary neighborhood systems. We introduce algorithms for updating approximation spaces of decision classes when decision examples are added to and removed from a multiple criteria decision table incrementally. The proposed algorithms are demonstrated by examples.
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