Let two finite universes: U={u 1, u2, …, un}, V={v 1, v2, …, vm}. Here u is a set of comprehensive evaluation factors, and v represents a set of comments. Fuzzy comprehensive evaluation is a fuzzy transformation problem: x? R=Y
Where "?" Represents the synthesis operation, X is a fuzzy subset on U, the evaluation result Y is a fuzzy subset on V, and the fuzzy relation R can be regarded as a fuzzy transformer (see figure). Given y and r, find x; Or know x and y, and find r; It constitutes the inverse problem of fuzzy comprehensive evaluation, and it is necessary to solve the fuzzy relation equation. The fuzzy relation equation was put forward by French scholar E. Sanjay in 1976 according to the needs of medical diagnosis. This kind of problem is equivalent to knowing the evaluation results and fuzzy relations, and finding the weight distribution of various factors by the judges. This kind of problem has great practical significance and plays a guiding role in the development of expert system.
Taking the evaluation of TV set as an example, the method of fuzzy comprehensive evaluation is explained. U={u 1, u2, u3}, V={v 1, v2, v3, v4}. Here u 1 stands for image, u2 stands for sound, and u3 stands for price; V 1 means very good, v2 means good, v3 means ok, and v4 means bad. Designate experts or customers to judge. For example, for the image, 50% people feel good, 40% people feel good, 10% people feel ok, and no one feels bad. All results are recorded as follows:
For image: Vu 1=(0.5, 0.4, 0. 1, 0)
For acoustics: Vu2=(0.4, 0.3, 0.2, 0. 1)
For the price: vu3 = (0 0,0.1,0.3, 0.6)
In this way, a fuzzy matrix is formed: assuming that when a customer buys a TV set, the image is clear, the price is cheap, and it doesn't matter if the sound is slightly poor, then the weight distribution of the three factors of the TV set by the customer is X =0.5 0.2 0.3.
The result of judging the TV set is obtained according to the maximum and minimum operation and needs to be normalized. Because 0.5+0.4+0.3+0.3= 1.5, divide by 1.5 to get 0.330.27 0. According to the results of fuzzy comprehensive evaluation, image, sound and price account for the largest proportion, reaching 33%.