Type reduction techniques for two-dimensional interval type-2 fuzzy sets

Author(s):  
Vaibhav Saxena ◽  
Nikhil Yadala ◽  
Rishav Chourasia ◽  
Frank Chung-Hoon Rhee
2018 ◽  
Vol 26 (2) ◽  
pp. 1036-1039 ◽  
Author(s):  
Jiawei Li ◽  
Robert John ◽  
Simon Coupland ◽  
Graham Kendall

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Yang Chen

Interval type-2 fuzzy logic systems have favorable abilities to cope with uncertainties in many applications. While the block type-reduction under the guidance of inference plays the central role in the systems, Karnik-Mendel (KM) iterative algorithms are standard algorithms to perform the type-reduction; however, the high computational cost of type-reduction process may hinder them from real applications. The comparison between the KM algorithms and other alternative algorithms is still an open problem. This paper introduces the related theory of interval type-2 fuzzy sets and discusses the blocks of fuzzy reasoning, type-reduction, and defuzzification of interval type-2 fuzzy logic systems by combining the Nagar-Bardini (NB) and Nie-Tan (NT) noniterative algorithms for solving the centroids of output interval type-2 fuzzy sets. Moreover, the continuous version of NT (CNT) algorithms is proved to be accurate algorithms for performing the type-reduction. Four computer simulation examples are provided to illustrate and analyze the performances of two kinds of noniterative algorithms. The NB and NT algorithms are superior to the KM algorithms on both calculation accuracy and time, which afford the potential application value for designer and adopters of type-2 fuzzy logic systems.


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.


2021 ◽  
pp. 1-28
Author(s):  
Ashraf Norouzi ◽  
Hossein Razavi hajiagha

Multi criteria decision-making problems are usually encounter implicit, vague and uncertain data. Interval type-2 fuzzy sets (IT2FS) are widely used to develop various MCDM techniques especially for cases with uncertain linguistic approximation. However, there are few researches that extend IT2FS-based MCDM techniques into qualitative and group decision-making environment. The present study aims to adopt a combination of hesitant and interval type-2 fuzzy sets to develop an extension of Best-Worst method (BWM). The proposed approach provides a flexible and convenient way to depict the experts’ hesitant opinions especially in group decision-making context through a straightforward procedure. The proposed approach is called IT2HF-BWM. Some numerical case studies from literature have been used to provide illustrations about the feasibility and effectiveness of our proposed approach. Besides, a comparative analysis with an interval type-2 fuzzy AHP is carried out to evaluate the results of our proposed approach. In each case, the consistency ratio was calculated to determine the reliability of results. The findings imply that the proposed approach not only provides acceptable results but also outperforms the traditional BWM and its type-1 fuzzy extension.


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