Fund investment is a hot issue in today’s society. How to choose a project for investment is affected by many factors. In view of this problem, this paper starts from the granular computing point of view and combines the multigranulation rough set decision-making method to construct a fund investment decision information system; then, the fund investment decision information system is reduced under different thresholds, and the decision rules are extracted through reduction. And from the aspects of decision accuracy and rule accuracy, the rules are analyzed. Finally, decision rules are used to give the decision of the fund investment project. This study provides a new approach to fund management.

Fund investment management [

In order to enable investors to better invest in projects, many scholars have carried out many researches on investment methods in recent years. Lu [

Rough set theory [

In order to solve the problem of project investment fund, this paper constructs the fund investment decision information system from the perspective of granular computing and combined with multigranular rough set decision method. Then reduce the information table, extract the rules from the simplified information table, and perform the rule analysis. Finally, the decision conclusions of the fund investment are given. The main contributions of this article are as follows:

This paper proposes a method for constructing a project fund investment decision information system, which is the premise that we use rough sets to solve project investment problems

In this paper, the generalized multigranularity rough set model is used to reduce the fund project information system, and then the rules are extracted on the simplified information system. Finally, the fund investment decision is given from these rules

The remaining structure of this paper is shown as follows: in the second part, the related knowledge of multigranularity rough sets is introduced. In the third part, the cleaning information system of the fund investment project is constructed. In the fourth part, the fund investment decision based on the multigranularity rough set is studied. Finally, the conclusion is given in the fifth part.

The section recalls necessary concepts and preliminaries required in the sequel of our work. Detailed description of the theory can be found in [

An information system with decisions is an ordered quadruple

In an information system, the equivalence class of an object with respect to an attribute subset of

Let

The lower and upper approximation sets of

Considering further studies on multigranulation rough set, we now review the two basic forms of multigranulation rough set model.

Let

The set

From the above definition, the operators “

Let

The set

The uncertainty of a concept in a multigranulation rough set model is also due to the existence of a boundary region. The greater the boundary of a concept is, the lower its accuracy is, and the coarser the concept is. Similar to the measures in the Pawlak rough set model, the accuracy and roughness measures in optimistic multigranulation rough set and pessimistic multigranulation rough set were defined in the same way [

Let

In addition, there are many related properties as well as proof, please refer to [

In order to express generalized multigranulation rough sets, we first introduce a characteristic function, which is called support feature function.

Let

The optimistic multigranular rough set and the pessimistic multigranular rough set are generalizations of two multigranular rough set models. We will propose a new multigranular rough set model with the parameter

Let

The set

The multigranulation rough set is a generalization of the classical rough set. Since several attributes in the information system can have different effects on the decision-making effect, when these effects cannot be performed simultaneously, but separately and independently, we cannot use classical rough set theory to treat these attributes as a whole through an indistinguishable relationship for system reduction and rule extraction. Therefore, according to the general process of rough set decision, we can get the specific steps of multigranular rough set decision and provide a theoretical model for decision analysis of fund project investment in multigranular environment.

Fund has become an increasingly important source of financing for people. For a decision maker, one may need to adopt a better one from some possible fund projects or find some directions from existing successful fund projects before investing. How to do it? We will propose a novel decision-making fund investments based on multigranulation rough set. This section mainly focuses to build fund investment decision information system.

The flow chart of our multigranulation decision-making model for fund investment is shown in Figure

The flow chart of multigranulation decision-making model for fund investment.

As can be seen from the flow chart, the investment decision system model based on the multigranulation rough set fund is constructed according to the following steps.

Before investing in the fund project, we first carry out the essential project evaluation for each project. In this paper, we through the project interviews, questionnaires, and other methods to determine project evaluation factors, which are

According to the performance of market environment level, science and technology level, education level, management level, and culture level, a comprehensive overall evaluation of the items was conducted to be evaluated. In order to study conveniently, we only have a small research. So, we can simplify attribute values, which is divided into A, B, C, D, and E five grades for each factor. Moreover, five grades A, B, C, D, and E present mainly

According to the above analysis, the decision attribute is divided into

According to the knowledge of multigranulation rough sets and the above analysis, we regard these five conditional attributes as five granularities, i.e.,

Through this evaluation form, we obtained 6 valid data and formed 6 objects into the decision-making information system in Table

We mainly check the reduction and decision rule by designing multiple granularity rough set decision steps, and we can get more granular rough set decision-making application. In the paper, we do not set on a large scale data in detail and do not set testing for the rules, which will be our future research work.

A fund investment information decision system.

A | A | C | B | C | G | |

B | A | C | C | D | Co | |

C | D | E | B | D | Co | |

B | B | A | B | A | G | |

A | B | D | A | B | G | |

C | C | C | D | E | Co |

In this section, based on the previous theories, the fund investment decisions are made with multigranulation rough sets. Firstly, generalized multigranulation rough set model is used to fund investment decision-making information system, and then some important rules are extracted based on the reduction of the information system. Finally, results of fund investment decision can be given from the obtained conclusion.

Starting from the data of the fund investment decision-making information system in Table

If we take information level

The support feature matrix table of lower approximation (

The support feature matrix table of upper approximation (

The support feature matrix table of upper approximation (

The support feature matrix table of lower approximation (

So, we can calculate the lower approximation and upper approximation of

In keeping the classification unchanged, all the reductions of the decision-making information system are obtained by MATLAB calculation as follows.

If we take information level

In the next, we extract the rules from two cases according to the reduction obtained above and give the quantitative results for the decision precision and rule precision of the rules.

The information level is

In this case, rule can be carried out in accordance with the system. In fact, each object is a decision rule, and the information cannot be simplified attributes in the system. So, we extract the rules directly, and the rules are in the following.

These rules are always valid and unique in decision information system of Table

The information level is

In the case, from the reductions, we can find that the decision system can be presented by partial not all attributes.

Thus, the decision system can be simplified in the following two decision tables which are Tables

Fund investment decision system after the reduction (I).

A | A | C | C | G | |

B | A | C | D | Co | |

C | D | E | D | Co | |

B | B | A | A | G | |

A | B | D | B | G | |

C | C | C | E | Co |

Fund investment decision system after the reduction (II).

A | C | B | C | G | |

A | C | C | D | Co | |

D | E | B | D | Co | |

B | A | B | A | G | |

B | D | A | B | G | |

C | C | D | E | Co |

From Table

From Table

As a result of our data on a smaller scale, the reduction of information system data has no duplication, so that we get 12 decision rules. When the data size is larger, reduction can make a lot of duplicate data merging, effectively reduce the number of decision rules, and improve the decision accuracy and precision of rules.

According to the calculation, the accuracy of the above 12 decision rules is 1/6 and the accuracy of the rules is 1. Although the decision-making accuracy is reduced, the rule accuracy does not decrease. So, we can have that reduction that simplifies the test of the data validation rules; decision conclusion can be obtained without a large scale of data validation.

From the rules obtained above, the conclusion of the decision making for fund investments can be got about the decision information system in Table

Decision results of the fund investment information system.

The serial number | Decision factors | Decision results | Decision accuracy | Information level |
---|---|---|---|---|

1 | 1 | (0.6,1] | ||

2 | 1 | (0.6,1] | ||

3 | 1 | (0.6,1] | ||

4 | 1 | (0.6,1] | ||

5 | 1 | (0.6,1] | ||

6 | 1 | (0.6,1] | ||

7 | 1 | (0.5,0.6] | ||

8 | 1 | (0.5,0.6] | ||

9 | 1 | (0.5,0.6] | ||

10 | 1 | (0.5,0.6] | ||

11 | 1 | (0.5,0.6] | ||

12 | 1 | (0.5,0.6] | ||

13 | 1 | (0.5,0.6] | ||

14 | 1 | (0.5,0.6] | ||

15 | 1 | (0.5,0.6] | ||

16 | 1 | (0.5,0.6] | ||

17 | 1 | (0.5,0.6] | ||

18 | 1 | (0.5,0.6] |

In this paper, a multigranulation rough set decision method is used to construct the fund investment decision information system; then, the fund investment decision information system is reduced at different thresholds, the decision rules are extracted by reduction and the rules are analyzed, and finally the decision rules are given using fund investment decision making. This study provides a new approach to fund management, enriching the application of multigranulation rough sets.

The data used to support the findings of this study are included within the article.

The authors declare no conflict of interest.

XY is the principal investigator of this work. He performed the experiments and wrote this manuscript. XS contributed to the framework and provided several suggestions for improving the quality of this manuscript. All authors revised and approved the publication.