Centroid of a Type 2 Fuzzy Set: Type Reduction

Author(s):  
Abhijit Pandit
Keyword(s):  
2021 ◽  
pp. 1-18
Author(s):  
Le Jiang ◽  
Hongbin Liu

The use of probabilistic linguistic term sets (PLTSs) means the process of computing with words. The existing methods computing with PLTSs mainly use symbolic model. To provide a semantic model for computing with PLTSs, we propose to represent a PLTS by using an interval type-2 fuzzy set (IT2FS). The key step is to compute the footprint of uncertainty of the IT2FS. To this aim, the upper membership function is computed by aggregating the membership functions of the linguistic terms contained in the PLTS, and the lower membership function is obtained by moving the upper membership function downward with the step being total entropy of the PLTS. The comparison rules, some operations, and an aggregation operator for PLTSs are introduced. Based on the proposed method of computing with PLTSs, a multi-criteria group decision making model is introduced. The proposed decision making model is then applied in green supplier selection problem to show its feasibility.


Author(s):  
Mahamat Loutfi Imrane ◽  
Achille Melingui ◽  
Joseph Jean Baptiste Mvogo Ahanda ◽  
Fredéric Biya Motto ◽  
Rochdi Merzouki

Some autonomous navigation methods, when implemented alone, can lead to poor performance, whereas their combinations, when well thought out, can yield exceptional performances. We have demonstrated this by combining the artificial potential field and fuzzy logic methods in the framework of mobile robots’ autonomous navigation. In this article, we investigate a possible combination of three methods widely used in the autonomous navigation of mobile robots, and whose individual implementation still does not yield the expected performances. These are as follows: the artificial potential field, which is quick and easy to implement but faces local minima and robustness problems. Fuzzy logic is robust but computationally intensive. Finally, neural networks have an exceptional generalization capacity, but face data collection problems for the learning base and robustness. This article aims to exploit the advantages offered by each of these approaches to design a robust, intelligent, and computationally efficient controller. The combination of the artificial potential field and interval type-2 fuzzy logic resulted in an interval type-2 fuzzy logic controller whose advantage over the classical interval type-2 fuzzy logic controller was the small size of the rule base. However, it kept all the classical interval type-2 fuzzy logic controller characteristics, with the major disadvantage that type-reduction remains the main cause of high computation time. In this article, the type-reduction process is replaced with two layers of neural networks. The resulting controller is an interval type-2 fuzzy neural network controller with the artificial potential field controller’s outputs as auxiliary inputs. The results obtained by performing a series of experiments on a mobile platform demonstrate the proposed navigation system’s efficiency.


Author(s):  
Juan Carlos Figueroa-García ◽  
Heriberto Román-Flores ◽  
Yurilev Chalco-Cano

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