Type–reduction of Interval Type–2 fuzzy numbers via the Chebyshev inequality

Author(s):  
Juan Carlos Figueroa-García ◽  
Heriberto Román-Flores ◽  
Yurilev Chalco-Cano
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):  
Rimsha Umer ◽  
Muhammad Touqeer ◽  
Abdullah Hisam Omar ◽  
Ali Ahmadian ◽  
Soheil Salahshour ◽  
...  

AbstractThe Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is considered among the most frequently used techniques to deal with multi-criteria group decision-making (MCGDM) conflicts. In this article, we have presented an extended TOPSIS technique in the framework of interval type-2 trapezoidal Pythagorean fuzzy numbers (IT2TrPFN). We first projected a novel approach to evaluate the distance between them using ordered weighted averaging operator and $$(\alpha ,\beta )$$ ( α , β ) -cut. Subsequently, we widen the concept of TOPSIS method formed on the distance method with IT2TrPFNs and applied it on MCGDM dilemma by considering the attitudes and perspectives of the decision-makers. Lastly, an application of solar tracking system and numerous contrasts with the other existing techniques are presented to express the practicality and feasibility of our projected approach.


Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 140 ◽  
Author(s):  
Junhua Hu ◽  
Panpan Chen ◽  
Yan Yang

Patient-centered care is an essential part of the implementation of integrated medicine, integrating humanistic care into nursing services, enhancing communication between caregivers and patients, and providing personalized service to patients. Based on the similarity of interval type-2 fuzzy numbers (IT2FNs), a novel similarity-based methodology is presented for the selection of the most suitable medical treatment under a patient-centered environment. First, we propose a new similarity based on the geometric properties of interval type-2 fuzzy numbers and present a new property based on the center of gravity. Meanwhile, in order to better highlight the advantages of the proposed similarity, we selected 30 samples for comparative experiments. Second, considering the straightforward logic of the multi-attributive border approximation area comparison (MABAC) method, we extended it based on similarity to make the decision more accurate. Finally, a realistic patient-centered type-2 diabetes treatment selection problem is presented to verify the practicality and effectiveness of the proposed algorithm. A comparative analysis with existing methods is also described.


2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Pingping Gao ◽  
Yabin Gao

This paper presents a fuzzy regression analysis method based on a general quadrilateral interval type-2 fuzzy numbers, regarding the data outlier detection. The Euclidean distance for the general quadrilateral interval type-2 fuzzy numbers is provided. In the sense of Euclidean distance, some parameter estimation laws of the type-2 fuzzy linear regression model are designed. Then, the data outlier detection-oriented parameter estimation method is proposed using the data deletion-based type-2 fuzzy regression model. Moreover, based on the fuzzy regression model, by using the root mean squared error method, an impact evaluation rule is designed for detecting data outlier. An example is finally provided to validate the presented methods.


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