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.

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.

Triangular Interval Type-2 Interpolative Fuzzy Reasoning

2012 ◽  
Vol 198-199 ◽  
pp. 261-266
Author(s):  
Yang Chen ◽  
Tao Wang
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Inference ◽  
Fuzzy Reasoning ◽  
Membership Functions ◽  
Inference Models ◽  
Definition Of ◽  
Interval Type ◽  
Triangular Type

This paper first gives the definition of interval type-2 fuzzy sets,then investigates interval type-2 interpolative fuzzy reasoning under Triangular type membership functions. Two interpolative fuzzy reasoning algorithms responding to interval type-2 fuzzy inference models in the line of type-1 interpolative fuzzy reasoning algorithms are proposed.

Interval Type II Fuzzy Number Generation From Data Set Applied to Sedation Stage Classification

2020 ◽  
pp. 158-194
Author(s):  
Efendi Nasibov ◽  
Sinem Peker
Keyword(s):  
Membership Function ◽  
Fuzzy Number ◽  
Real Data ◽  
Classification Problem ◽  
Data Sets ◽  
Data Set ◽  
Number Generation ◽  
Interval Type ◽  
Function Construction

There are several ways to summarize the data set by using measures of locations, dispersions, charts, and so on. But how can the data set be represented or shown when uncertainty exists in the environment process? Usage of the fuzzy number can be a way to handle the uncertainty in the representation of the data set. This chapter focuses on the membership function construction from the data set and introduces the formulas for the interval Type-2 generalized bell-shaped fuzzy number generation based on the data set. The bispectral index scores (BIS) are processed to see the ability of the offered methods in the construction of the interval Type -2 generalized bell-shaped membership function in the real data set. The obtained membership functions are used for a classification problem of sedation stages according to BIS data sets. Classification accuracies are calculated.

scholarly journals Classification with Fuzzification Optimization Combining Fuzzy Information Systems and Type-2 Fuzzy Inference

2021 ◽  
Vol 11 (8) ◽  
pp. 3484
Author(s):  
Martin Tabakov ◽  
Adrian Chlopowiec ◽  
Adam Chlopowiec ◽  
Adam Dlubak
Keyword(s):  
Fuzzy Inference ◽  
Real Data ◽  
Fuzzy Rules ◽  
Fuzzy Information ◽  
Benchmark Data ◽  
System A ◽  
Footprint Of Uncertainty ◽  
Interval Type ◽  
Derived Rules

In this research, we introduce a classification procedure based on rule induction and fuzzy reasoning. The classifier generalizes attribute information to handle uncertainty, which often occurs in real data. To induce fuzzy rules, we define the corresponding fuzzy information system. A transformation of the derived rules into interval type-2 fuzzy rules is provided as well. The fuzzification applied is optimized with respect to the footprint of uncertainty of the corresponding type-2 fuzzy sets. The classification process is related to a Mamdani type fuzzy inference. The method proposed was evaluated by the F-score measure on benchmark data.

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.

scholarly journals Self-Adaptive K-Means Based on a Covering Algorithm

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-16 ◽  
Author(s):  
Yiwen Zhang ◽  
Yuanyuan Zhou ◽  
Xing Guo ◽  
Jintao Wu ◽  
Qiang He ◽  
...  
Keyword(s):  
Large Scale ◽  
Clustering Algorithm ◽  
Real Data ◽  
Second Phase ◽  
Data Sets ◽  
Number Of Clusters ◽  
Large Scale Data ◽  
Long Time ◽  
Two Phases ◽  
Selection Of

The K-means algorithm is one of the ten classic algorithms in the area of data mining and has been studied by researchers in numerous fields for a long time. However, the value of the clustering number k in the K-means algorithm is not always easy to be determined, and the selection of the initial centers is vulnerable to outliers. This paper proposes an improved K-means clustering algorithm called the covering K-means algorithm (C-K-means). The C-K-means algorithm can not only acquire efficient and accurate clustering results but also self-adaptively provide a reasonable numbers of clusters based on the data features. It includes two phases: the initialization of the covering algorithm (CA) and the Lloyd iteration of the K-means. The first phase executes the CA. CA self-organizes and recognizes the number of clusters k based on the similarities in the data, and it requires neither the number of clusters to be prespecified nor the initial centers to be manually selected. Therefore, it has a “blind” feature, that is, k is not preselected. The second phase performs the Lloyd iteration based on the results of the first phase. The C-K-means algorithm combines the advantages of CA and K-means. Experiments are carried out on the Spark platform, and the results verify the good scalability of the C-K-means algorithm. This algorithm can effectively solve the problem of large-scale data clustering. Extensive experiments on real data sets show that the accuracy and efficiency of the C-K-means algorithm outperforms the existing algorithms under both sequential and parallel conditions.

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