Membership degree

Among the most important concepts associated with fuzzy sets are the concepts of an a-cut and a strong a-cut. Given a fuzzy set A defined on X and a number a in the unit interval [0,1], the a-cut of A, denoted by °A, is the crisp set that consists of all elements of A whose membership degrees in A are greater than or equal to a that is,... 

For each pair x,y eXxY, the membership degree R(x,y) indicates how strongly element x is related to element y according to R. The inverse of R, denoted by K", is a relation on YxA" defined by... 

Using this criterion function we can obtain the membership degrees thus ... 

The membership degrees are then computed using the distance d, where... 

Fuzzy comprehensive evaluation method which based on fuzzy mathematics is a method of quantitative evaluation. According to the features of Huanghua port and characteristics of storage coal, through the selection of evaluation subset, setting of remark set, and the decision of membership degree, establish evaluation system for this port coal. 

Table 2. Membership degree of different coal s evaluation factors. ...

ABSTRACT By analyzing the hierarchy of safety factors in purification plant of natural gas, they are divided into personnel, equipment, environment and management. After the study of safety index, evaluation methods and fuzzy arithmetic method for each hierarchy, its fuzzy evaluation flow is given. During the evaluation, the weight of the factors and each hierarchy is decided by analytical hierarchical process, and the operational criterion adapts maximum membership degree. And this model is exemplified in purification plant of natural gas. The results show that the second fuzzy evaluation is effective to assess purification plant of natural gas. 

Adopting the maximum membership degree principle of judgment, safety grade belongs to ... 

The single element , (i = 1-3) from set U can determine its membership degree for evaluation level set v, (y = 1-4) the ith single element. Evaluation set can be given. 

In the formula, bj indicates the membership degree of idler performance level in the j-th level. If... 

Considering the complexity of the affecting factors of idler s performance, the values given by the questionnaires from experts are used to determine weighted coefficients corresponding to each evaluation indicator. The membership degrees are adjusted according to practical experiences. The actual results of the evaluation are shown in Table land Table 2. 

The rows of i , indicate the membership degrees of fuzzy subset by single factor of first order indicators, To multiply row by the fuzzy weight vector ITj, the membership degree of each subset can be obtained, namely the result of the fuzzy comprehensive evaluation. 

It shows that the component quality of the idler rating of good and its membership degree is 57.75%. 

It can be seen that the main performance of the idler as good and its membership degree is... 

According to the highest degree of membership principle, we can determine the level of idler comprehensive performance evaluation as "good", the membership degree is 55.4%. 

In order to enhance the scientific nature, the rationality of the evaluation index, the theory of the evaluation indicators for membership degree analysis, correlation analysis, discrimination... 

If R, value is large, the evaluation indexes in the evaluation system is very important, which could be used as a formal evaluation index. On the other hand, the evaluation index is necessary to be deleted. Through the statistical analysis of 50 effective feedback reports, the membership degree was lower than 0.3 of 15 evaluation indexes were deleted, and the 41 indicators were retained, which formed the second round safety, quality, progress, investment risk index system. 

The project performance evaluation based on fuzzy membership degree evaluation analysis... 

Among them, the maximum value of membership degree for the index is selected as the judge value. If the same value of appears, the lower values is selected. 

Fuzzy control is reahzed within 3 processes fuzzification, inference and defuzzification. The fuzzification process describes variables by means of input values. Thus a fuzzy set is represented by a membership function. The membership function is constructed based on the variable s input values (laanineh Maijohann 1996). Accordingly every input value obtains a membership degree between one and zero. If the input value is clearly assigned to the description of the variable, it receives a membership degree one. It is a fiiU membership to a related fuzzy set. The membership degree zero means that an input value does not belong to the fuzzy set. Membership values between zero and one indicate a partial membership of an input value to the certain fuzzy set. 

Once the rule basis has been determined, the evaluation operators can be selected. Presently a Max-Min operator is used. Thus the decision maker prefers the manpower to be simultaneously determined on the basis of task quantity, level of knowledge and personnel costs. Hereby the decision maker considers, by any fired rule, the smallest membership degree of input values. For example possible input values for task quantity, personnel costs and level of knowledge are the following 7 months, 3056 Euros and 3 years of task-related experience. These input values fire 4 rules, see Table 8. 

As the input value of the task quantity has a partial membership degree at the fuzzy sets very low and low, two rules are fired. Further on the input value of the personnel costs has a partial membership degree at the fuzzy sets high-price and very high-price. So, two further rules are fired. 

At the rule 10, 28 and 31, the input value of the task quantity reaches, at each of those rules, the lowest membership degree. Within these rules the membership degree of task quantity and related fuzzy set determinate the actual mnnber of a possible manpower. Later on only the highest membership degree... 

Data collected using both applications were analysed using an application developed using Matlab. A detail of this Application is depicted in Fig. 13.6, where the membership functions used in this work are presented. The marks on the plot represent the different membership degrees for the different points. 

The truth value of a proposition is calculated by a combination of membership degrees. For... 

P(fp) is considered as the weight of the pth rule (Wrp) where P(fp) is PAE of fp (continuous path in the pth rule). Fire strength or membership degree of the pth rule, is equal to the truth value of the proposition which is ... 

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