## 1 Introduction  
Rice direct seeding is used in paddy cultivation due to its low labor requirements and reduced production cost [1; 2]. Air-assisted direct seeding machines were studied by [PERSON] et al. [1], [PERSON] et al. [3], and [PERSON] et al. [4], showing many advantages and promising working efficiency. These machines can operate across 32 rows powered by a tractor power take-off PTO. The hardness of the soil surface is a factor affecting the depth of sowing. The accuracy of sowing is controlled by a float installed to increase the area of ground-surface contact. A series of seeding machines, such as those of Iseki, Kubota, and Yanmar, have been marketed to meet the needs of sowing seeds in flooded paddy fields. These sowing machines can sow 6-8 rows at the same time in clusters [5].  
The Tokyo University of Agriculture and Technology collaborated with the Vietnam National University of Agriculture to develop an air-assisted rice seeder for flooded paddy fields in Vietnam (Figure 1). This machine can sow 24 rows with an interval spacing of 20-25 cm. The experimental results showed that the seeding depth and seeding area precision were affected by the air-assisted velocity, internal diameter of the injection port, and distance between the injection port and soil surface. Seeding accuracy is one of the most important factors affecting the growth of paddy sprouts. In this study, a similarity measure using fuzzy sets was used to select the optimal plan for the sowing machines.  
Fuzzy logic was first introduced by [PERSON] in 1965 [6]. Fuzzy set theory allows researchers to flexibly handle practical problems, especially applied problems in engineering [7,8]. For example, the fuzzy multi-criteria decision-making (MCDM) method was used to select machines [9], as well as evaluate reconfigurable machines [10].  
In seeding machines, research studies have shown that the seeding depth allows ranges from 3-15 mm, preferably 5-10 mm for Vietnam rice variables, which is a prerequisite for seeds to thrive after sowing [11]. Trapezoidal fuzzy sets are considered the best option for the chosen situation, i.e., to select the optimal plan for sowing machines.  
The contributions of this study are as follows: (1) a new similarity measure using fuzzy sets is proposed; (2) this measure is compared with existing similarity measures; (3) the TOPSIS method using the new measure is applied to evaluate the best scenario with respect to specifications of the sowing machine; (4) analysis of the obtained results led to a determination of the correlation coefficient between factors and decision variables in MCDM to interpret/evaluate the identified specifications.  
The rest of this paper is organized as follows: Section 2 presents the problem to be solved, i.e., an estimation of the impact of technical parameters on the sowing machine. In this section, some important concepts regarding fuzzy sets and similarity measures of fuzzy sets are reviewed. Furthermore, the new similarity measures are proposed and compared with others from the literature. The TOPSIS model based on our proposed similarity measures is also introduced. In Section 3, the TOPSIS model is applied to evaluate the best scenario with respect to specifications of the sowing machine, and the results are presented. The results are discussed in Section 4, while Section 5 concludes the paper.