Algorithm Explanations and Examples for 15 Mathematical Modeling Approaches

This article provides comprehensive explanations of 15 mathematical modeling algorithms implemented in MATLAB, accompanied by practical examples. The covered models include:

- Grey Prediction: Forecasting method using grey system theory with MATLAB's gm() function implementation

- Grey Relational Analysis: Measuring relationships between factors using relational degree calculations

- Principal Component Analysis: Dimensionality reduction technique via covariance matrix eigendecomposition

- Fuzzy Clustering Analysis: Data grouping using fuzzy c-means algorithm with MATLAB's fcm() function

- Stochastic Simulation: Monte Carlo methods for probabilistic system modeling

- Multiple Regression Models: Multivariable linear regression analysis with least squares estimation

- Orthogonal Experimental Design: Efficient experimental arrangement using orthogonal arrays

- Graph Theory: Network analysis including shortest path and maximum flow algorithms

- Goal Programming Models: Multi-objective optimization with priority-based goal achievement

- Markov Prediction Methods: State transition probability matrices for future state forecasting

- Time Series Analysis: ARIMA modeling and seasonal decomposition techniques

- Fuzzy Comprehensive Evaluation Models: Multi-factor assessment using fuzzy mathematics

- Analytic Hierarchy Process: Decision-making framework with pairwise comparison matrices

- Fuzzy Mathematics Methods: Fuzzy logic operations and membership function applications

- Simulated Annealing Algorithm: Global optimization inspired by metallurgical annealing process

Each model will be thoroughly explained with its mathematical foundation, implementation approach, and practical MATLAB code examples to help readers master mathematical modeling methodologies and techniques.