Research on effectiveness evaluation method and application of quality management system of manufacturing enterprise based on interval-valued hesitation fuzzy set

2.1. Definition on effectiveness of quality management system of manufacturing enterprise

Quality management system and effectiveness evaluation should be defined before effectiveness of quality management system of manufacturing enterprises is defined.

Quality management system can be defined by following words: the organization adopt series of management methods, such as organization, technology, economy, contract and so on, to achieve the goal of quality management, which include relevant government regulations, industry standards, and specific requirements.

Effectiveness evaluation can be defined by following words: the estimator can assess the value of activities and judge the outcome of activities by setting the target and measures.

Based on the definition of quality management system and effectiveness evaluation, evaluation on the effectiveness of the quality management system of manufacturing enterprises can be defined by following:

Evaluation on the effectiveness of the quality management system of manufacturing enterprises is an activity, which is used to analysis the positive influence in the process of normal operations by making evaluation standard, determining the size of the influence and getting the special judgment.

2.2. Overall thinking on construction of quality management effect evaluation index system of manufacturing enterprises

According to the above analysis, the evaluation on the effectiveness of the quality management system of manufacturing enterprises is an activity, which is used to analysis the positive influence in the process of normal operations by making evaluation standard, determining the size of the influence and getting the special judgment. And evaluation on the effectiveness of the quality management system of manufacturing enterprises mainly involves two aspects: one is the construction of evaluation index system on the effectiveness of the quality management system of manufacturing enterprises, the other is the construction of evaluation model on the effectiveness of the quality management system of manufacturing enterprises. Meanwhile the specific operation of effectiveness of the quality management system and feedback and summary of effectiveness evaluation results are involved in the evaluation on the effectiveness of the quality management system of manufacturing enterprises [3].

Thus the evaluation on the effectiveness of the quality management system of manufacturing enterprises should follow the following procedure: firstly, evaluation index system on the effectiveness of the quality management system of manufacturing enterprises should be built by analyzing the characters and affecting factors of quality management of manufacturing enterprise, combining with the relevant provisions of the existing, following the principles of establishing the index system and according to the first-class-second-class sequence; secondly, evaluation model of effectiveness on quality management system of manufacturing enterprise should be built. because many aspects are involve in the effectiveness of the quality management system of manufacturing enterprises, mathematical model of multiple index values should be built in the process of evaluation on the effectiveness of the quality management system of manufacturing enterprises; thirdly, evaluation on the effectiveness of the quality management system of manufacturing enterprises can be operating by building the mathematical model and evaluation index system of effectiveness of the quality management system of manufacturing enterprises; finally, analyzing the evaluation results of effectiveness on quality management system of manufacturing enterprise and reflecting the situation on the quality management system of manufacturing enterprises to improve the quality management system of manufacturing enterprise.

3.1. Establishment of index system

To ensure the reliability and practicability of the index system construction, the systematic principle, the typical principle, the principle of operation and quantification, and comprehensive principle should be followed and thinking of first-class index system - second-class index system should be followed in the process of developing the effectiveness evaluation index system of manufacturing enterprise quality management system.

3.2. Determination of weight of index system

This paper makes an attempt to determine the weight of indexes through GAHP. The basic idea of this method is to determine the weight of indexes using AHP by experts respectively based on which the arithmetic mean value of evaluation results from experts are taken as the final result. This method makes up for the traditional AHP can only be determined by a single index weight problem [4].

Although the GAHP method is able to achieve the goal of multi person decision weight, considering that when judging the relative importance weights of two indexes, decision makers may not judge through the numbers of “one to nine”, thus, judging from an interval-value may better reflect the intent of decision makers. It is necessary to clear each weight of every expert, because different experts have different experience, different status and different weight.

The core content of GAHP method is the determination of relative importance weights between two indexes, so the determination of relative importance weights between two indexes should be focused on the discussion.

Assuming that a total number of $K$ experts participates in the effectiveness of the quality management system of manufacturing enterprises, then in the weight determination process of index system, the relative importance interval-value between $x_g$ and $x_h$ in the same level gotten by $K$ expert ($k=\mathrm{1,2},...,K$) is $\left[d_{1e}^{\left(k\right)},d_{2e}^{\left(k\right)}\right]$$\left(d_{2e}^{\left(k\right)}\ge d_{1e}^{\left(k\right)}\right)$ and the weights of each experts are $c_k$ ($k=\mathrm{1,2},...,K$) respectively. Thus, the comparison value of relative importance of $x_g$ and $x_h$ is:

After determining the comparison value of relative importance of two indexes in the same level, according to the steps and requirements of AHP methods, the weight of evaluation index system of the effectiveness of the quality management system of manufacturing enterprises can be determined.

The weight of $X_i$ in the evaluation index system on the effectiveness of the quality management system of manufacturing enterprises is $X_i$ ($i=$1,2,…,7), first-class index weight vector$A=(w_1,w_2...,w_7)$ and meet the condition of $w_i\ge$0, and $\sum _{i=1}^7{w}_i=1\text{;}$ the set formed by the weight of second-class indexes to the target layers is $X_{is}$ ($i=$1,2,…,7; $s=$1,2,…, $n_i$), second-class index weight vector$W_{ij}=(w_{i1},w_{i2},...,w_{in})$ and meet the condition of $w_{is}\ge 0$ and $\sum _{s=1}^{n_i}{w}_{is}=1$.