Multiple criteria decision making (MCDM) problems in practice may simultaneously contain both redundant and incomplete information and are difficult to solve. This paper proposes a new decision-making approach based on soft set theory to solve MCDM problems with redundant and incomplete information. Firstly, we give an incomplete soft set a precise definition. After that, the binary relationships of objects in an incomplete soft set are analyzed and some operations on it are provided. Next, some definitions regarding the incomplete soft decision system are also given. Based on that, an algorithm to solve MCDM problems with redundant and incomplete information based on an incomplete soft set is presented and illustrated with a numerical example. The results show that our newly developed method can be directly used on the original redundant and incomplete data set. There is no need to transform an incomplete information system into a complete one, which may lead to bad decision-making due to information loss or some unreliable assumptions about the data generating mechanism. To demonstrate its practical applications, the proposed method is applied to a problem of regional food safety evaluation in Chongqing, China.
<abstract><p>This paper proposes the concept of a neighborhood soft set and its corresponding decision system, named neighborhood soft decision system to solve decision-making (DM) problems with heterogeneous information. Firstly, we present the definition of a neighborhood soft set by combining the concepts of a soft set and neighborhood space. In addition, some operations on neighborhood soft sets such as "restricted/relaxed AND" operations and the degree of dependency between two neighborhood soft sets are defined. Furthermore, the neighborhood soft decision system and its parameter reduction, core attribute are also defined. According to the core attribute, we can get decision rules and make the optimal decision. Finally, the algorithm of DM with heterogeneous information based on the neighborhood soft set is presented and applied in the medical diagnosis, and the comparison analysis with other DM methods is made.</p></abstract>
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