A Novel Framework using Intuitionistic Fuzzy Logic with U-Net and U-Net++ Architecture: A case Study of MRI Bain Image Segmentation

Hanuman Verma; Kiho Im; Akshansh Gupta; M. Tanveer

eess.IVMar 15, 2026

A Novel Framework using Intuitionistic Fuzzy Logic with U-Net and U-Net++ Architecture: A case Study of MRI Bain Image Segmentation

Authors: Hanuman Verma, Kiho Im, Akshansh Gupta, M. Tanveer

Organizations: Department of Mathematics, Bareilly College, Bareilly (MJP Rohilkhand University), Uttar Pradesh, 243005, India · Fetal Neonatal Neuroimaging and Developmental Science Center, Boston Children’s Hospital, Harvard Medical School, Boston, MA 02115, USA · Division of Newborn Medicine, Boston Children’s Hospital, Harvard Medical School, Boston, MA 02115, USA · Department of Pediatrics, Harvard Medical School, Boston, MA, USA ·

Abstract

Accurate segmentation of brain images from magnetic resonance imaging (MRI) scans plays a pivotal role in brain image analysis and the diagnosis of neurological disorders. Deep learning algorithms, particularly U-Net and U-Net++, are widely used for image segmentation. However, it finds difficult to deal with uncertainty in images. To address this challenge, this work integrates intuitionistic fuzzy logic into U-Net and U-Net++, propose a novel framework, named as IFS U-Net and IFS U-Net++. These models accept input data in an intuitionistic fuzzy representation to manage uncertainty arising from vague ness and imprecise data. This approach effectively handles tissue ambiguity caused by the partial volume effect and boundary uncertainties. To evaluate the effectiveness of IFS U-Net and IFS U-Net++, experiments are conducted on two publicly available MRI brain datasets: the Internet Brain Segmentation Repository (IBSR) and the Open Access Series of Imaging Studies (OASIS). Segmentation performance is quantitatively assessed using Accuracy, Dice Coefficient, and Intersection over Union (IoU). The results demonstrate that the proposed architectures consistently improve segmentation performance by effectively addressing uncertainty

Figures & tables

Panel of Figure 1 — Fig. 1 : Intuitionistic fuzzy data in form of (a): membership, (b): non-membership and (c): hesitation degree. The image corresponding to the membership degree shows a higher degree of belonging, while the image corresponding to non-membership degree highlight the respective the degree of non-belongingness, observable through the image contrast value. The image corresponding to the hesitation degree highlights the boundary region, capturing the uncertainty.

Panel of Figure 2 — Fig. 2 : Gray-level histogram corresponding to (a): membership degree image (b): non-membership image and (c) hesitation image.

Fig. 3 : An overview of the proposed method in the deep learning architecture. The schematic overview of the training process of intuitionistic fuzzy set (IFS) system representation and deep learning architecture for segmentation of brain image. In this process, IFS system converted the input image into the triplet (intuitionistic fuzzy set) form that is membership $(\mu)$ , non-membership $(\nu)$ and hesitation degree $(\pi)$ . The uncertainty features in the image exploited the qualitative information using intuitionistic fuzzy logic in comparison to classical representation of an image. It utilizes the uncertainty during the training process.

Fig. 4 : IFS_U-Net framework with intuitionistic fuzzy logic systems. It accepts the input image in term of intuitionistic fuzzification of data and utilizes the uncertainty during the training process. And as a result, it able to segment the brain tissues in more accurate.

Fig. 5 : Framework for IFS_U-Net++ with intuitionistic fuzzy logic systems, where the input image accepted in term of intuitionistic fuzzification of data and utilizes the uncertainty. The input image $(X\times Y\times 1)$ converted in form of $(X\times Y\times 3)$ ) as the input for IFS_U-Net++ architecture

Data	Metrics	U-Net	IFS_U-Net with Sugeno negation function
			$\lambda=0.5$	$\lambda=0.8$	$\lambda=0.9$	$\lambda=1.0$	$\lambda=1.2$	$\lambda=1.4$	$\lambda=1.5$	$\lambda=2.0$	$\lambda=2.5$
IBSR	AC	0.9888	0.9932	0.9971	0.9916	0.9964	0.9968	0.9964	0.9943	0.9976	0.9942
	DC	0.9829	0.9901	0.9956	0.9880	0.9947	0.9953	0.9946	0.9918	0.9964	0.9916
	IoU	0.9668	0.9807	0.9913	0.9765	0.9895	0.9908	0.9893	0.9840	0.9929	0.9835
OASIS	AC	0.9928	0.9950	0.9942	0.9945	0.9945	0.9954	0.9950	0.9952	0.9958	0.9954
	DC	0.9869	0.9905	0.9904	0.9900	0.9898	0.9909	0.9921	0.9909	0.9924	0.9913

TABLE I : Quantitative comparison of segmentation performance for U-Net, and IFS_U-Net with intuitionistic fuzzy logic with Sugeno negation function along with various value of

\lambda

for IBSR and OASIS data. We take the number of epochs 100 for IBSR data and use early stoppage for OASIS data and take the Batch size 2 for both brain data. The quantitative segmentation performances presented in term of accuracy

(AC)

, Dice coefficient

(DC)

and Intersection over Union

(IoU)

. Best respective results are marked in bold .

Data	Metrics	U-Net++	IFS_U-Net++ with Sugeno negation function
			$\lambda=0.5$	$\lambda=0.8$	$\lambda=0.9$	$\lambda=1.0$	$\lambda=1.2$	$\lambda=1.4$	$\lambda=1.5$	$\lambda=2.0$	$\lambda=2.5$
IBSR	AC	0.9853	0.9922	0.9914	0.9931	0.9912	0.9928	0.9912	0.9927	0.9914	0.9908
	DC	0.9785	0.9887	0.9877	0.9901	0.9874	0.9897	0.9875	0.9927	0.9877	0.9869
	IoU	0.9580	0.9779	0.9761	0.9806	0.9754	0.9797	0.9756	0.9793	0.9760	0.9746
OASIS	AC	0.9704	0.9774	0.9745	0.9795	0.9781	0.9751	0.9769	0.9775	0.9778	0.9778
	DC	0.9609	0.9682	0.9640	0.9710	0.9689	0.9647	0.9669	0.9683	0.9685	0.9681

TABLE II : Quantitative comparison of segmentation performance for U-Net++ and IFS_U-Net++ with intuitionistic fuzzy logic with Sugeno negation function, with various value of

\lambda

for IBSR and OASIS data. We take the number of epochs 100 for IBSR data and use early stoppage for OASIS data and Batch size 2 for both brain data. The segmentation performances represented in term of accuracy

(AC)

, Dice coefficient

(DC)

and Intersection over Union

(IoU)

. Best respective results are marked in bold .

Panel of Figure 8 — Fig. 6 : Ablation study for segmentation performance of U-Net, U-Net++ and proposed framework: IFS_U-Net , IFS_U-Net++ with Sugneo negation function in term of $(AC,DC,IoU)$ for IBSR and OASIS data with various value of $\lambda$ in Sugeno negation function. The proposed systems: IFS_U-Net , IFS_U-Net++ with Sugneo negation function for all considered value of $\lambda$ provide better consistent segmentation results in comparison to U-Net, U-Net++ utilizes the vague and qualitative information.

Data	Metrics	U-Net	IFS_U-Net with Yager negation function
			$\alpha=0.1$	$\alpha=0.2$	$\alpha=0.4$	$\alpha=0.6$	$\alpha=0.8$	$\alpha=0.9$
IBSR	AC	0.9888	0.9939	0.9928	0.9982	0.9945	0.9964	0.9923
	DC	0.9829	0.9912	0.9895	0.9972	0.9920	0.9947	0.9890
	IoU	0.9668	0.9827	0.9794	0.9945	0.9843	0.9895	0.9784
OASIS	AC	0.9928	0.9806	0.9921	0.9930	0.9835	0.9828	0.9827
	DC	0.9869	0.9721	0.9861	0.9882	0.9760	0.9752	0.9750

TABLE III : The quantitative comparison of segmentation performance with various value of

\alpha

for IBSR and OASIS data for U-Net, and IFS_U-Net with intuitionistic fuzzy logic using Yager negation function to handle the uncertainty. We take the number of epochs 100 for IBSR data and use early stoppage for OASIS data and Batch size 2 for both brain data. The segmentation performances evaluated in term of

AC,DC

, and

IoU

Data	Metrics	U-Net++	IFS_U-Net++ with Yager negation function
			$\alpha=0.1$	$\alpha=0.2$	$\alpha=0.4$	$\alpha=0.6$	$\alpha=0.8$	$\alpha=0.9$
IBSR	AC	0.9853	0.9919	0.9931	0.9921	0.9918	0.9928	0.9929
	DC	0.9785	0.9883	0.9901	0.9887	0.9883	0.9897	0.9898
	IoU	0.9580	0.9772	0.9805	0.9778	0.9772	0.9797	0.9801
OASIS	AC	0.9704	0.9805	0.9812	0.9782	0.9793	0.9792	0.9804
	DC	0.9609	0.9727	0.9733	0.9691	0.9709	0.9702	0.9721

TABLE IV : The quantitative segmentation performance

(AC,DC,

and

IoU)

for U-Net++ and suggested IFS_U-Net++ with intuitionistic fuzzy logic using Yager negation function with various value of

\alpha

for IBSR and OASIS data. We take the number of epochs 100 for IBSR data and use early stoppage for OASIS data and take the Batch size 2 for both brain data.

Panel of Figure 11 — Fig. 7 : Ablation study of segmentation performance $(AC,DC,IoU)$ for U-Net, U-Net++ and IFS_U-Net , IFS_U-Net++ with Yager negation function for IBSR and OASIS data with various value of $\alpha$ . The proposed framework: IFS_U-Net , IFS_U-Net++ with Yager negation function for all considered value of $\alpha$ provide better segmentation results in comparison to U-Net, U-Net++ with utilizing the vague and qualitative information for IBSR data. On OASIS data, IFS_U-Net , results are equal or less than U-Net architecture, however the IFS_U-Net++ results is better in comparison to U-Net++.

Fig. 8 : Visual representation of OASIS brain image segmentation of a particular slice (2D image) using deep learning architecture into different classes like BG (background), CSF, GM and WM. Figure shows image segmentation with original and intuitionistic fuzzy logics using Sugeno and Yager negation function, architectures: (a) U-Net, (b) IFS_U-Net ( $\lambda=2.0$ ), (c) IFS_U-Net ( $\alpha=0.4$ ), (d) U-Net++, (e) IFS_U-Net++ ( $\lambda=0.9$ ) (f) IFS_U-Net++ ( $\alpha=0.4$ ). The deep learning architectures with intuitionistic fuzzy logic handle the partial volume effect and provide the better segmentation.

Medical Image Segmentation

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Medical Image Segmentation Segmentation Uncertainty Estimation Fuzzy Logic

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Accurate brain image segmentation, particularly for distinguishing various tissues from magnetic resonance imaging (MRI) images, plays a pivotal role in finding the neurological dis ease and medical image computing. In deep learning approaches, loss functions are very crucial for optimizing the model. In this study, we introduce a novel loss function integrating fuzzy logic to deals uncertainty issues in brain image segmentation into various tissues. It integrates the well-known categorical cross-entropy (CCE) loss function and fuzzy entropy based on fuzzy logic. By employing fuzzy logic, this loss function accounts for the inherent uncertainties in pixel classifications. The proposed loss function has been evaluated on two publicly available benchmark datasets, IBSR and OASIS, using two widely recognised architectures, U-Net and U-Net++. Experimental results demonstrate that the trained model with proposed loss function provided better results in comparison to the CCE optimisation function in terms of various performance metrics. Additionally, it effectively enhances segmentation performance while handling meaningful uncer tainty during training. The findings suggest that this approach not only improves segmentation outcomes but also contributes to the reliability of model predictions.

Abstract

Medical Image Segmentation

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