defined
cybernetics professor at the University of California bar too (L, A, Zadeh) After years of pondering, and finally first published in 1965 entitled "fuzzy sets" papers. He noted: If for any domain of (range studied) U is an element x, has a number A (x) ∈ [0,1] corresponding thereto, then A is a fuzzy set U, A (x ) referred to as x membership degree of a. When x changes in U, A (x) is a function, called the membership function A. A membership degree (x) becomes closer to 1, the higher the degree of x is A, A (x) becomes closer to 0 indicates a lower degree of x is A. With values in the interval [0,1] of the membership function A (x) A x is characterized by low degree of fuzziness describes more reasonable than the classical set theory.
categories
Application Foundation membership functions are fuzzy control, correct construct membership functions is the ability to control one of the key fuzzy good use. The process of determining the membership function, in essence should be objective, but for everyone with a vague understanding of the concept of understanding the differences there are, therefore, to determine the membership function and subjective.
establish the membership function does not have a mature and effective method to establish the method most systems still remain the basis of experience and experiments. For the same vague concept, different people will not establish membership function exactly the same, although not exactly the same form, as long as it reflects the same vague concept, still the same thing in practical problem-solving and processing fuzzy information. The following describes several commonly used methods.
fuzzy statistics
The basic idea of fuzzy statistical method is to make a clear judgment on a certain element vo whether a clear set of A3 a variation on the domain of the domain U . For different test subject, clearly set A3 may have different borders, but they all correspond to the same fuzzy set A. Fuzzy calculation step statistical method is: in each statistics, VO is the fixed value A3 is variable, for n tests, which can blur the statistics calculated by the following equation
v0 of times under the frequency of a = v0∈A / total number of test n
as n increases, the frequency will tend to be stable under this stable value vo is the membership degree of a. This method is more directly reflects the degree of membership in the fuzzy concept, but a large amount of calculation.
illustration
is the main idea of the exemplary method known finite values μA to estimate the fuzzy set membership function domain U of A. Such as domain U on behalf of all mankind, A is a "tall people." Clearly A is a fuzzy subset. To determine μA, first determine the value of a height h, and then select a few linguistic truth value (that is, the word of the true extent of) one to answer whether someone is considered as a "tall." Such as language true value can be divided into "real", "approximately true", "s real," "approximately false" and "false" five cases, and each digital 1,0.75,0.5,0.25, 0 to represent the true value of these languages. The n different heights h1, h2, ..., hn are the same as the query, which can obtain the membership function A discrete representation.
expertise
expert experience blurring method is given in equation corresponding weight coefficient values or information based on the actual experience of the expert to determine a method of membership function. In many cases, often initially determined rough membership function, and then through the "learning" and the test of practice and gradually modify and improve, but the actual effect is the basis for testing and adjusting the membership function.
Binary Comparison sorted
Binary Comparison ordering method is a more practical method of determining the membership function. It twenty-two of comparison between a plurality of things in order to determine certain characteristics through, thereby determining the general shape of the membership function characteristic things. Binary Comparison of different sorting method according to a comparative measure, can be divided into relatively, comparative average method, and the priority relationship sequencing method similar priority comparison method.
Example
an embodiment
A (x) = represents a fuzzy set "old" membership function, A represents a fuzzy set "old", when Age x≤50 when A (x) = 0 indicates that x does not belong to the fuzzy set A (i.e. "old"), while when x≥100, A (x) = 1 indicates that x entirely A, when 50
Example two
According to fuzzy comprehensive analysis, we evaluate the performance of a company. .
1 set of factors set U: U = {u1, u2, ...... u9}
my country's current comprehensive evaluation system and balanced scorecard (SEC), we choose u1 ( net earnings assets), u2 (assets operating conditions), u3 (long-term solvency), u4 (short-term solvency). U5 (sales growth conditions), u6 (market power), u7 (technical capacity), u8 (the development of innovative capability), u9 (learning) 9 indicators reflect the main indicators of firm performance. Which, u1, u2, u3, u4, u5 are financial indicators of financial performance, with all the original indicators reflect the exact ratio, but they are blurred more objectively reflect the real business performance appropriately. For example, in the evaluation of short-term solvency of the enterprise, the company current ratio of 1.8, but experts found a large amount of the company stock, accounting for a larger portion of current assets, indicating that the liquidity of its assets is not good, so still the assessment index to a lower level. U6 is the customer aspect of performance indicators, u7 internal business process aspects of performance indicators, u8, u9 is learning and growth performance indicators.
2. Evaluation provided set V = {v1, v2 ...... v4}. Simplicity, we set v1: Excellent, v2: good, v3: average, v4: poor.
3. We selected the company's certified public accountant, familiar with the business situation of experts judged group to obtain evaluation matrix
4. According to expert opinion, we determine the set of weights A is :
5 according to the M (,, +) model
Therefore, the maximum membership degree principle, the enterprise performance assessed as "satisfactory.". Later, the business leaders think the evaluation results more in line with the actual situation.