**Decision-Making Method based on Mixed Integer Linear Programming and Rough Set: A Case Study of Diesel Engine Quality and Assembly Clearance Data**

**Wenbing Chang 1,†, Xinglong Yuan <sup>1</sup> , Yalong Wu 2, Shenghan Zhou 1,† , Jingsong Lei <sup>1</sup> and Yiyong Xiao 1,\***


Received: 19 December 2018; Accepted: 22 January 2019; Published: 24 January 2019

**Abstract:** The purpose of this paper is to establish a decision-making system for assembly clearance parameters and machine quality level by analyzing the data of assembly clearance parameters of diesel engine. Accordingly, we present an extension of the rough set theory based on mixed-integer linear programming (MILP) for rough set-based classification (MILP-FRST). Traditional rough set theory has two shortcomings. First, it is sensitive to noise data, resulting in a low accuracy of decision systems based on rough sets. Second, in the classification problem based on rough sets, the attributes cannot be automatically determined. MILP-FRST has the advantages of MILP in resisting noisy data and has the ability to select attributes flexibly and automatically. In order to prove the validity and advantages of the proposed model, we used the machine quality data and assembly clearance data of 29 diesel engines of a certain type to validate the proposed model. Experiments show that the proposed decision-making method based on MILP-FRST model can accurately determine the quality level of the whole machine according to the assembly clearance parameters.

**Keywords:** data mining; decision-making system; rough set; mixed integer linear programming; assembly clearance; diesel engine quality
