A Generalization of Trapezoidal Fuzzy Numbers Based on Modal Interval Theory

A Heuristic Projection Pursuit Method Based on a Connection Cloud Model and Set Pair Analysis for Evaluation of Slope Stability

Determining the projection direction vector (PDV) is essential to the projection pursuit evaluation method for high-dimensional problems under multiple uncertainties. Although the PP method using a cloud model can facilitate interpretation of the fuzziness and randomness of the PDV, it ignores the asymmetry of the PDV and the fact that indicators are actually distributed over finite intervals; it quickly falls into premature defects. Therefore, a novel PP evaluation method based on the connection cloud model (CCM) is discussed to remedy these drawbacks. In this approach, adaptive numerical characteristics of the CCM are adopted to represent the randomness and fuzziness of the candidate PDV and evaluation indicators. Meanwhile, to avoid complex computing and to accelerate the convergence speed of the optimization procedure, an improved fruit fly optimization algorithm (FOA) is set up to find the rational PDV. Alternatively, candidate PDVs are mutated based on the mechanism “pick the best of the best” using set pair analysis (SPA) and chaos theory. Furthermore, the applicability and reliability are discussed based on an illustrative example of slope stability evaluation and comparisons with the neural network method and the PP evaluation method based on the other FOAs and the genetic algorithm. Results indicate that the proposed method with simpler code and quicker convergence speed has good global ergodicity and local searching capabilities, and can better explore the structure of high-dimensional data with multiple uncertainties and asymmetry of the PDV relative to other methods.