scholarly journals An Interval Type-2 Possibilistic C-Means Clustering Algorithm and Its Application

2021 ◽  
Vol 2132 (1) ◽  
pp. 012016
Author(s):  
Haihua Xing ◽  
Huannan Chen ◽  
Hongyan Lin ◽  
Xinghui Wu
Keyword(s):  
Image Segmentation ◽  
Fuzzy Sets ◽  
Clustering Algorithm ◽  
High Order ◽  
Data Sets ◽  
Fuzzy Uncertainty ◽  
Penalty Factor ◽  
Interval Type

Abstract In this paper, we aim at the fuzzy uncertainty caused by noise in pattern data. The advantages of PCM algorithm to deal with noise and interval type-2 fuzzy sets to deal with high-order uncertainties are used, respectively. An interval type-2 probability C-means clustering (IT2-PCM) based on penalty factor is proposed. The performance of the algorithm is evaluated by two sets of data sets and two groups of images segmentation experiments. The results show that IT2-PCM algorithm can assign proper membership degrees to clustering samples with noise, and it can detect noise points effectively, and it has good performance in image segmentation.

A NEW DISTANCE FOR INTERVAL TYPE-2 FUZZY SETS WITH AN APPLICATION TO CLUSTERING

2014 ◽  
Vol 13 (04) ◽  
pp. 1450020
Author(s):  
ARMAGHAN HEIDARZADE ◽  
NEZAM MAHDAVI-AMIRI ◽  
IRAJ MAHDAVI
Keyword(s):  
Fuzzy Sets ◽  
Clustering Algorithm ◽  
Real Data ◽  
Data Sets ◽  
Fuzzy Data ◽  
Fuzzy Membership Functions ◽  
Definition Of ◽  
Interval Type ◽  
Distance Formula

Type-2 fuzzy sets are generalizations of ordinary fuzzy sets, in which membership grades are characterized by fuzzy membership functions. Here, a problem of finding distance between two interval type-2 fuzzy sets (IT2-FSs) was considered. Based on a new definition of centroid for an IT2-FS, a formulation for calculation of the distance between two IT2-FSs was introduced, and an algorithm was explained to obtain it. The proposed distance formula was incorporated in Yang and Shih's clustering algorithm to reach a clustering method for interval type-2 fuzzy data sets. The applicability of the proposed distance formula was evaluated using two artificial and real data sets, and reasonable results were obtained.

An interval type-2 hesitant fuzzy best-worst method

2021 ◽  
pp. 1-28
Author(s):  
Ashraf Norouzi ◽  
Hossein Razavi hajiagha
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Group Decision Making ◽  
Group Decision ◽  
Fuzzy Ahp ◽  
Uncertain Data ◽  
Interval Type ◽  
Best Worst Method

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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