Table of contents
Classic set + characteristic function
Fuzzy set + membership function
How to determine the membership function
Using existing objective measures
Assignment method (if the question gives data)
Fuzzy comprehensive evaluation problem
First level fuzzy comprehensive evaluation
Example: First-level fuzzy evaluation (fuzzy statistics method to find membership degree)
Example: First-level fuzzy evaluation (obtaining membership function by assignment method)
Example: Level 2 fuzzy evaluation
Example: three-level fuzzy evaluation
Comprehensive evaluation methods: analytic hierarchy process, TOPSIS, gray relational analysis (can also be used for system analysis), fuzzy comprehensive evaluation
Classic set, fuzzy set
Classic set + characteristic function
Basic properties of classical sets: ① Mutual exclusivity; ② Determinism
Fuzzy set + membership function
Fuzzy set representation
Zade representation, vectors, ordinal pairs
Classification of fuzzy sets
Extremely small (decreasingly, the smaller it is, the more it belongs to this set), intermediate type, and extremely large (the larger it is, the more it belongs to this set)
How to determine the membership function
fuzzy statistics
Using existing objective measures
Assignment method (if the question gives data)
Choose the membership function yourself and determine the parameters:
Fuzzy comprehensive evaluation problem
Introduce three sets: factor set (evaluation indicators), comment set (evaluation results or alternative options), and weight set (weight of indicators)
Purpose: Select the review set with the largest degree of membership
First level fuzzy comprehensive evaluation
step
- determining factor set
- Determine the set of comments
- Determine the weight of each indicator in the factor set
- Form a fuzzy comprehensive judgment matrix: find the degree of membership of each indicator to each comment to form an n×m matrix (n: indicator; m: comment). One row of the matrix represents the degree of membership of the indicator to each comment. The greater the degree of membership, the more Close to this review/project
- Combined with the weight of the indicators, calculate and draw a conclusion on which review/plan to choose.
Example: First-level fuzzy evaluation (fuzzy statistics method to find membership degree)
Example: First-level fuzzy evaluation (obtaining membership function by assignment method)
Each row is an indicator, and each indicator has a membership function for the review.
Example: First-level fuzzy evaluation (implementing indicator forwarding by designing your own membership function) ⭐
Example: Level 2 fuzzy evaluation
The rows of matrix R are indicators, the columns are comments, and the elements are the degree of membership of indicator i to comment j;
the weight of each indicator is a row vector
Example: three-level fuzzy evaluation
