Hesitant fuzzy C-means algorithm and its application in image segmentation†

2020 ◽  
Vol 39 (3) ◽  
pp. 3681-3695
Author(s):  
Wenyi Zeng ◽  
Rong Ma ◽  
Qian Yin ◽  
Xin Zheng ◽  
Zeshui Xu
Keyword(s):  
Image Segmentation ◽  
Fuzzy Set ◽  
Distance Measure ◽  
Hesitant Fuzzy Set ◽  
Natural Image ◽  
Membership Degree ◽  
Fuzzy C Means ◽  
Comprehensive Performance ◽  
Multi Attribute Decision Making ◽  
Fuzzy C Means Algorithm

Image segmentation plays an important role in many fields such as computer vision, pattern recognition, machine learning and so on. In recent years, many variants of standard fuzzy C-means (FCM) algorithm have been proposed to explore how to remove noise and reduce uncertainty. In fact, there are uncertainty on the boundary between different patches in images. Considering that hesitant fuzzy set is a useful tool to deal with uncertainty, in this paper, we merge hesitant fuzzy set with fuzzy C-means algorithm, introduce a new kind of method of fuzzification and defuzzification of image and the distance measure between hesitant fuzzy elements of pixels, present a method to establish hesitant membership degree of hesitant fuzzy element, and propose hesitant fuzzy C-means (HFCM) algorithm. Finally, we compare our proposed HFCM algorithm with some existing fuzzy C-means (FCM) algorithms, and apply HFCM algorithm in natural image, BSDS dataset image, different size images and multi-attribute decision making. These numerical examples illustrate the validity and applicability of our proposed algorithm including its comprehensive performance, reducing running time and almost without loss of accuracy.

Type-2 Fuzzy C-Means Algorithm with Spatial Informations and Membership Constrains for Liver Segmentation

2013 ◽  
Vol 746 ◽  
pp. 570-574
Author(s):  
Qin Li Zhang ◽  
Ya Fan Yue ◽  
Zhao Zhuang Guo
Keyword(s):  
Image Segmentation ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Spatial Information ◽  
Target Area ◽  
Fuzzy C Means ◽  
Liver Image ◽  
Fuzzy C Means Algorithm

The Fuzzy C-Means algorithm with spatial informations and membership constrains is a very effective and efficient image segmentation method. However£¬it is founded with Type-1 fuzzy sets, which can not handle the uncertainties existing in liver image well.The type-2 fuzzy sets have better performance on handling uncertainties than Type-1 fuzzy set. In this paper, a new robust Type-2 FCM image segmentation algorithm is proposed aiming to improve the segmentation precision and robustness of liver image by introducing the type-2 fuzzy set into FCM with spatial information and membership constrains. We extend the type-1 fuzzy set of membership to interval type-2 fuzzy set using two fuzzifiers and which create a footprint of uncertainty (FOU). The experimental results show that the target area of the liver in CT images can be segmented well by the proposed method.

scholarly journals Approach to Multi-Attribute Decision-Making Methods for Performance Evaluation Process Using Interval-Valued T-Spherical Fuzzy Hamacher Aggregation Information

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 145
Author(s):  
Yun Jin ◽  
Zareena Kousar ◽  
Kifayat Ullah ◽  
Tahir Mahmood ◽  
Nimet Yapici Pehlivan ◽  
...  
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Evaluation Process ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Membership Degree ◽  
Operational Laws ◽  
Multi Attribute Decision Making ◽  
Interval Valued ◽  
Do So

Interval-valued T-spherical fuzzy set (IVTSFS) handles uncertain and vague information by discussing their membership degree (MD), abstinence degree (AD), non-membership degree (NMD), and refusal degree (RD). MD, AD, NMD, and RD are defined in terms of closed subintervals of that reduce information loss compared to the T-spherical fuzzy set (TSFS), which takes crisp values from intervals; hence, some information may be lost. The purpose of this manuscript is to develop some Hamacher aggregation operators (HAOs) in the environment of IVTSFSs. To do so, some Hamacher operational laws based on Hamacher t-norms (HTNs) and Hamacher t-conorms (HTCNs) are introduced. Using Hamacher operational laws, we develop some aggregation operators (AOs), including an interval-valued T-spherical fuzzy Hamacher (IVTSFH) weighted averaging (IVTSFHWA) operator, an IVTSFH-ordered weighted averaging (IVTSFHOWA) operator, an IVTSFH hybrid averaging (IVTSFHHA) operator, an IVTSFH-weighted geometric (IVTSFHWG) operator, an IVTSFH-ordered weighted geometric (IVTSFHOWG) operator, and an IVTSFH hybrid geometric (IVTSFHHG) operator. The validation of the newly developed HAOs is investigated, and their basic properties are examined. In view of some restrictions, the generalization and proposed HAOs are shown, and a multi-attribute decision-making (MADM) procedure is explored based on the HAOs, which are further exemplified. Finally, a comparative analysis of the proposed work is also discussed with previous literature to show the superiority of our work.

Extended TOPSIS method based on the entropy measure and probabilistic hesitant fuzzy information and their application in decision support system

2021 ◽  
pp. 1-12
Author(s):  
Muhammad Naeem ◽  
Muhammad Ali Khan ◽  
Saleem Abdullah ◽  
Muhammad Qiyas ◽  
Saifullah Khan
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Distance Measure ◽  
Group Decision ◽  
Hesitant Fuzzy Set ◽  
Entropy Measure ◽  
Fuzzy Information ◽  
Score Functions ◽  
Fuzzy Environment ◽  
Basic Operating

Probabilistic hesitant fuzzy Set (PHFs) is the most powerful and comprehensive idea to support more complexity than developed fuzzy set (FS) frameworks. In this paper, it can explain a novel, improved TOPSIS-based method for multi-criteria group decision-making (MCGDM) problem through the Probabilistic hesitant fuzzy environment, in which the weights of both experts and criteria are completely unknown. Firstly, we discuss the concept of PHFs, score functions and the basic operating laws of PHFs. In fact, to compute the unknown weight information, the generalized distance measure for PHFs was defined based on the Probabilistic hesitant fuzzy entropy measure. Second, MCGDM will be presented with the PHF information-based decision-making process.

scholarly journals A NOVEL IMAGE SEGMENTATION APPROACH BASED ON NEUTROSOPHIC SET AND IMPROVED FUZZY C-MEANS ALGORITHM

2011 ◽  
Vol 07 (01) ◽  
pp. 155-171 ◽  
Author(s):  
H. D. CHENG ◽  
YANHUI GUO ◽  
YINGTAO ZHANG
Keyword(s):  
Image Segmentation ◽  
Point Of View ◽  
Neutrosophic Set ◽  
Convergence Criterion ◽  
Complex Objects ◽  
Fuzzy C Means ◽  
Segmentation Methods ◽  
Segmentation Algorithms ◽  
Segmentation Approach ◽  
Fuzzy C Means Algorithm

Image segmentation is an important component in image processing, pattern recognition and computer vision. Many segmentation algorithms have been proposed. However, segmentation methods for both noisy and noise-free images have not been studied in much detail. Neutrosophic set (NS), a part of neutrosophy theory, studies the origin, nature, and scope of neutralities, as well as their interaction with different ideational spectra. However, neutrosophic set needs to be specified and clarified from a technical point of view for a given application or field to demonstrate its usefulness. In this paper, we apply neutrosophic set and define some operations. Neutrosphic set is integrated with an improved fuzzy c-means method and employed for image segmentation. A new operation, α-mean operation, is proposed to reduce the set indeterminacy. An improved fuzzy c-means (IFCM) is proposed based on neutrosophic set. The computation of membership and the convergence criterion of clustering are redefined accordingly. We have conducted experiments on a variety of images. The experimental results demonstrate that the proposed approach can segment images accurately and effectively. Especially, it can segment the clean images and the images having different gray levels and complex objects, which is the most difficult task for image segmentation.

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