AN INCOMPLETE SOFT SET AND ITS APPLICATION IN MCDM PROBLEMS WITH REDUNDANT AND INCOMPLETE INFORMATION

Multiple criteria decision making (MCDM) problems in practice may simultaneously contain both redundant and incom-plete 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 il-lustrated 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.

Automated summary

This paper proposes a new decision-making approach based on soft set theory to solve MCDM problems with redundant and incomplete information. The proposed algorithm directly operates on the original data set without the need to transform incomplete information into complete one, avoiding potential bad decision-making due to information loss or unreliable assumptions about data generating mechanism. The practical application of the method in a regional food safety evaluation problem in Chongqing, China, demonstrates its effectiveness.