Mathematical Problems in Engineering

Volume 2017 (2017), Article ID 6781671, 7 pages

https://doi.org/10.1155/2017/6781671

## Crop Evaluation System Optimization: Attribute Weights Determination Based on Rough Sets Theory

^{1}College of Information Science & Technology, Agricultural University of Hebei, Baoding, China^{2}Agricultural University of Hebei, Baoding, China

Correspondence should be addressed to Ruihong Wang

Received 31 March 2017; Revised 9 July 2017; Accepted 15 August 2017; Published 14 September 2017

Academic Editor: Alessandro Lo Schiavo

Copyright © 2017 Ruihong Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The present study is mainly a continuation of our previous study, which is about a crop evaluation system development that is based on grey relational analysis. In that system, the attribute weight determination affects the evaluation result directly. Attribute weight is usually ascertained by decision-makers experience knowledge. In this paper, we utilize rough sets theory to calculate attribute significance and then combine it with weight given by decision-maker. This method is a comprehensive consideration of subjective experience knowledge and objective situation; thus it can acquire much more ideal results. Finally, based on this method, we improve the system based on ASP.NET technology.

#### 1. Introduction

Since Ju-Long proposed grey relational system in 1982 [1, 2], scholars have employed this theory making a lot of research works [3–6]. In the agricultural industry, Ma et al. utilize it to evaluate new self-cultivated sugarcane lines, Yan and Shen evaluate carding cashmere fiber and Zhang et al. evaluate new watermelon varieties [7–9]. Based on these previous works, we have developed a crop evaluation system based on grey relational analysis (GRA) [10]. The experiment results showed that the crop evaluation system is effective and could greatly improve the work efficiency of the researcher and expand the application scope. When we exploit GRA method to evaluate crops, attribute weight ascertainment plays an important role, because it affects the evaluation result directly.

In the management of multiple attribute decision-making system, people often take multiple indexes as evaluation standard for alternative scheme filtration. In the process of evaluation and decision-making, attribute weight is essential. It reflects the status or role of various factors and directly affects the final judgment and decision-making. We usually ascertain attribute weight based on the importance of each attribute. There are lots of classic decision methods, that is, AHP, TOPSIS, ELECTRE, and so forth [11, 12]. Although those methods promote the development of decision theory, the attribute weight is generally given by experts [10]. Potential uncertainty in expert judgment is the main disadvantage of the subjective methods. The weight determination is much affected by expert experience knowledge and sometimes is not able to objectively reflect the actual situation and even can distort the judgment and decision result [13].

In 1982, professor Pawlak proposed a theory of rough sets [14], which provides a formal tool for dealing with imprecise or incomplete information. Since its introduction, the theory has generated a great deal of interest along researchers [15–17], as well as among researchers dealing with machine learning and knowledge acquisition for expert systems [18–22]. It is used for knowledge acquisition and analysis without providing any a priori information and fully reflects the objectivity of data.

This paper presents a new method to determine attribute weights based on the theory of rough sets. First, objective weight value is derived by significance in the theory of rough sets [23–27]. And then, according to practical application background, we combine objective weight with subjective weight determined by expert experience knowledge and ascertain the final weight value so as to realize reasonable unification of subjective prior knowledge and objective situation. Finally, we utilize ASP.NET programming language to improve the crop evaluation system.

In this paper, first, in Section 2, we present preliminary and notation of the theory of rough sets. Section 3 is the algorithm of attribute weight determination. Section 4 is the real example in Fuji apple evaluation. In Section 5, we utilize ASP.NET to improve the system.

#### 2. Methods

##### 2.1. Theory of Rough Sets

The notion of equivalence is introduced first. is the equivalence relation defined on , where is the universe of objects. A binary relation which is reflexive (i.e., an object is in relation with itself, ), symmetric (if , then ), and transitive (if and , then ) is called an equivalence relation [28]. is a subset of . is the equivalence class generated by equivalence relation . The equivalence class of an element consists of all objects such that . Let be an information system and let and . We can approximate using only the information contained in by constructing the and approximations of , denoted as and , respectively, where and . The objects in can be with certainty classified as members of on the basis of knowledge in , where the objects in can be only classified as possible members of on the basis of knowledge in . If , set is said to be rough.

##### 2.2. Information System

Let be an information system such that denotes a nonempty finite set of objects, called universe. is attribute set; subsets and are called condition attribute set and decision attribute set, respectively. are the sets of attribute value. is information function, which specifies the attribute value of object of set . With any subsets , there is an associated equivalence relation : is called* B* relation and the subscript is usually omitted if it is clear which information system is meant. is obvious. The equivalence relation constitutes the partition of , denoted by and often abbreviated to .

##### 2.3. Attribute Significance

In this section, we will introduce basic definition of attribute significance [29–31]. We utilize the attribute reduction method of the theory of rough sets to ascertain each attribute’s significance. Using attribute reduction, we find core attribute and reduce unnecessary attribute and determine the important relation between attributes. On the other hand, after reducing one attribute, we define attribute contribution degree through judging the variation size of system structure. The bigger the variation size is, the greater the attribute weight is.

In an information system, we define as attribute significant for subset :where ; set ; then .

In practice, when we apply formula (2) to calculate the contribution degree, we may encounter this situation: some attribute contribution degrees are 0 or have same values, which do not accord with facts. In order to solve this problem, we define the improvement significance formula.where is subset of attribute set *, *, is an attribute, , and .

#### 3. Attribute Weight Ascertainment

We carry out the normalization processing of attribute significance to obtain the objective weight (OW) of each attribute. The calculation formulas, respectively, corresponding to formulas (2) and (3) are as follows:

Then combine the subjective weight (SW) and OW to get the final weight (FW) formula as follows:where is constant.

#### 4. The Analysis of Influence Factors in Fuji Apple

In order to verify the effectiveness of weight acquisition method, we still adopt the previous paper’s data for comprehensive evaluation: Fuji apple evaluation data [7] are shown in Table 1. Before analysis, we need to discrete the data according to the following method. First, calculate each attribute value interval as approximate distribution interval; then, set ideal variety data as objective value and suppose it has 5% fluctuation in random distribution interval; finally, judge whether each attribute value falls into ideal value interval and then assign discrete value of 1 or 0, respectively, and establish the decision table , as shown in Table 2, where and corresponding to eight attributes.