Hamacher T-conorm Research Articles

Medical image enhancement using modified type II fuzzy membership function generated by Hamacher T-conorm

Medical image enhancement using modified type II fuzzy membership function generated by Hamacher T-conorm

Dual-hesitant fermatean fuzzy Hamacher aggregation operators and TOPSIS with their application to multi-criteria decision-making.

The concept of the Dual-hesitant fermatean fuzzy set (DHFFS) represents a significant advancement in practical implementation, combining Fermatean fuzzy sets and Dual-hesitant sets. This new structure uses membership and non-membership hesitancy and is more adaptable for arriving at values in a domain. Since it has the capability to treat multiple fuzzy sets over the degrees of membership and non-membership, the DHFFS greatly improves the flexibility of approaches to tackle multiple-criteria decision-making (MCDM) problems. By applying generalized T-norm (T) and T-conorm (T*) operation, improved union and intersection formulas are derived. The proposed work adopts Hamacher operations such as Hamacher T-conorm (HT*) and Hamacher T-norm (HT) that are more efficient than conventional techniques. New aggregation operators such as Hamacher weighted arithmetic, geometric, power arithmetic, and power geometric are developed for DHFFS. These operators are most beneficial when dealing with a MCDM issue. A case study is used to demonstrate the approachs' accuracy and effectiveness in real-world decision-making. The comparative and sensitivity analysis results show that these operators are more effective than traditional methods. These results show that the proposed methods are efficient and can be applied in large-scale decision-making processes, strengthening the solutions' practical implications.

Application of Hamacher Aggregation Operators in the Selection of the Cite for Pilot Health Project based on Complex T-spherical Fuzzy Information

The framework of complex T-spherical fuzzy set (CTSFS) deals with unclear and imprecise information with the help of membership degree (MD), abstinence degree (AD), nonmembership degree (NMD), and refusal degree (RD). Due to this characteristic, the CTSFSs can be applied to any phenomenon having the involvement of human opinions. This article aims to familiarize some Hamacher aggregation operators (HAOs) grounded on CTSFSs. To do so, we define some Hamacher operational laws in the environment of CTSFS by using Hamacher t-norm (HTNM) and Hamacher t-conorm (HTCNM). A few numbers of AOs are developed with the help of defined operational laws based on HTNM and HTCNM including the complex T-spherical fuzzy (CTSF), Hamacher weighted averaging (HWA) (CTSFHWA), CTSF Hamacher ordered weighted averaging (CTSFHOWA) operator, CTSF Hamacher hybrid weighted averaging (CTSFHHWA) operator, CTSF Hamacher weighted geometric (CTSFHWG) operator, CTSF Hamacher ordered weighted geometric (CTSFHOWG) operator, and CTSF Hamacher hybrid weighted geometric (CTSFHHWG) operator. Some interesting properties of developed HAOs are investigated and then these HAOs are applied to the multi-attribute decision making (MADM) problem. For the significance of these HAOs, the results obtained from these HAOs are compared with existing aggregation operators (AOs).

A Parametric Logarithmic Image Processing Framework Based on Fuzzy Graylevel Accumulation by the Hamacher T-Conorm.

It has been proven that Logarithmic Image Processing (LIP) models provide a suitable framework for visualizing and enhancing digital images acquired by various sources. The most visible (although simplified) result of using such a model is that LIP allows the computation of graylevel addition, subtraction and multiplication with scalars within a fixed graylevel range without the use of clipping. It is claimed that a generalized LIP framework (i.e., a parameterized family of LIP models) can be constructed on the basis of the fuzzy modelling of gray level addition as an accumulation process described by the Hamacher conorm. All the existing LIP and LIP-like models are obtained as particular cases of the proposed framework in the range corresponding to real-world digital images.

A novel approach to MADM problems using Fermatean fuzzy Hamacher aggregation operators

The intuitionistic fuzzy set, briefly as; IFS and its extension involving Pythagorean fuzzy set (PFS) and Fermatean fuzzy set (FFS), are all effective tools to express uncertain and incomplete cognitive information with membership, nonmembership, and hesitancy degrees. The FFS introduced by Senapati and Yager, carries out uncertain and imprecise information smartly in exercising decision-making than IFS and PFS. A generalized form of union and intersection on FFS can be formulated from a generalized T-norm and T-conorm. Hamacher operations such as Hamacher product and Hamacher sum, are good alternatives to product and sum. In this course of this article, we first device new operations on Fermatean fuzzy information by employing Hamacher T-conorm and T-norm and discuss basic operations. Induced by the Hamacher operations and FFS, we propose Fermatean fuzzy Hamacher arithmetic and also geometric aggregation operators. In the first section, we introduce the concepts of a Fermatean fuzzy Hamacher weighted average operator, a Fermatean fuzzy Hamacher ordered weighted average operator, and a Fermatean fuzzy Hamacher hybrid weighted operator and discuss their basic properties in detail. In the second part, we develop Fermatean fuzzy Hamacher weighted geometric operator, Fermatean fuzzy Hamacher ordered weighted geometric operator, and Fermatean fuzzy Hamacher hybrid geometric operator. We study essential properties and a few special cases of our newly introduced operators. Then, we make use of these proposed operators in developing tools which are key factors in solving the Fermatean fuzzy multiattribute decision-making situations. The cyclone disaster assessment phenomena is considered as a direct application for analysis and to demonstrate the practicality and efficacy of our model. Further, comparison analysis is conducted for the authenticity of our proposed operators.

Contrast Enhancement of Digital Images Using an Improved Type-II Fuzzy Set-Based Algorithm

Contrast is a distinctive image feature that tells if it has adequate visual quality or not. On many occasions, images are captured with low-contrast due to inevitable obstacles. Therefore, an improved type-II fuzzy set-based algorithm is developed to enhance the contrast of various color and grayscale images properly while preserving the brightness and providing natural colors. The proposed algorithm utilizes new upper and lower ranges, amended Hamacher t-conorm, and a transform-based gamma correction method to provide the enhanced images. The proposed algorithm is assessed with artificial and real contrast distorted images, compared with twelve specialized methods, and the outcomes are evaluated using four advanced metrics. From the obtained results of experiments and comparisons, the developed algorithm demonstrated the ability to process various color and grayscale images, performed the best among the comparative methods, and scored the best in all four quality evaluation metrics. The findings of this study are significant because the proposed algorithm has low-complexity and can adjust the contrast of different images expeditiously, which enables it to be used with different imaging modalities especially those with limited hardware resources or produce high-resolution images.

A novel fuzzy approach for segmenting medical images

In various medical imaging studies, the segmentation of the medical image is a crucial step. Due to the inherent behavior of the images, the computerized tomography (CT) scan/magnetic resonance imaging (MRI) images are not clear. As the medical images are captured using electronic devices, these images are ambiguous and unclear. This ambiguity in the images is due to factors related to noise and the environment while capturing images. A fuzzy set is a valuable method to deal with data uncertainty. In this paper, a novel clustering approach based upon a fuzzy concept is proposed, which enhances the vague MRI/CT scan image before segmentation. Initially, the image noise is minimized by processing eight immediate neighborhood pixels around each pixel in an image. After noise processing, upper and lower membership levels of the image are computed. Hamacher T-conorm is used as an aggregation operator to construct a new membership function using upper and lower membership levels. The enhanced image, created using the new membership function, is then segmented using Gaussian kernel-based fuzzy c means clustering. The experiment is performed on MRI/CT scan brain tumor images. Real data experiments demonstrate that the proposed algorithm has better performance when compared with existing methods both quantitatively and qualitatively. It is observed that even in the presence of noise, the proposed method exhibits better efficiency.

Basic Formal Properties of Triangular Norms and Conorms

Summary In the article we present in the Mizar system [1], [8] the catalogue of triangular norms and conorms, used especially in the theory of fuzzy sets [13]. The name triangular emphasizes the fact that in the framework of probabilistic metric spaces they generalize triangle inequality [2]. After defining corresponding Mizar mode using four attributes, we introduced the following t-norms: minimum t-norm minnorm (Def. 6), product t-norm prodnorm (Def. 8), Łukasiewicz t-norm Lukasiewicz_norm (Def. 10), drastic t-norm drastic_norm (Def. 11), nilpotent minimum nilmin_norm (Def. 12), Hamacher product Hamacher_norm (Def. 13), and corresponding t-conorms: maximum t-conorm maxnorm (Def. 7), probabilistic sum probsum_conorm (Def. 9), bounded sum BoundedSum_conorm (Def. 19), drastic t-conorm drastic_conorm (Def. 14), nilpotent maximum nilmax_conorm (Def. 18), Hamacher t-conorm Hamacher_conorm (Def. 17). Their basic properties and duality are shown; we also proved the predicate of the ordering of norms [10], [9]. It was proven formally that drastic-norm is the pointwise smallest t-norm and minnorm is the pointwise largest t-norm (maxnorm is the pointwise smallest t-conorm and drastic-conorm is the pointwise largest t-conorm). This work is a continuation of the development of fuzzy sets in Mizar [6] started in [11] and [3]; it could be used to give a variety of more general operations on fuzzy sets. Our formalization is much closer to the set theory used within the Mizar Mathematical Library than the development of rough sets [4], the approach which was chosen allows however for merging both theories [5], [7].

A Novel Multiple Attribute Decision Making Framework based on Hamacher Operations in Patron Driven Acquisitions Mode of Library Management

As a fuzzy set extension, the hesitant set is effectively used to model situations where it is allowable to determine several possible membership degrees of an element to a set due to the ambiguity between different values. Some new hesitant fuzzy operational rules are introduced based on the Hamacher t-conorm and t-norm, whereby we present a multi attribute decision making method under hesitant fuzzy information. In the daily management of library, book selection problem usually is very complex and unstructured, because variety of uncontrollable and unpredictable factors affects the evaluation and decision-making process at different levels. By integrating the multiple attribute decision making method with (Patron Driven Acquisitions, PDA) mode, a novel multiple attribute decision making framework based on Hamacher operations in PDA mode is proposed to select the best book providing the highest satisfaction for the attributes determined in this paper. Finally, a case study is so demonstrated to verify the reliability and applicability of the proposed framework.

Rank-ordered filter for edge enhancement of cellular images using interval type II fuzzy set.

An edge-enhancement technique using an interval type II fuzzy set that uses rank-ordered filter to enhance the edges of cellular images is proposed. When cellular images from any laboratory are digitized, scanned, and stored, some kind of degradation occurs, and directly using a rank-ordered filter may not produce clear edges. These images contain uncertainties, present in edges or boundaries of the image. Fuzzy sets that take into account these uncertainties may be a good tool to process these images. However, a fuzzy set sometimes does not produce better results. We used an interval type II fuzzy set, which considers the uncertainty in a different way. It considers the membership function in the fuzzy set as "fuzzy," so the membership values lie within an interval range. A type II fuzzy set has upper and lower membership levels, and with the two levels, a new membership function is computed using Hamacher t-conorm. A new fuzzy image is formed. A rank-ordered filter is applied to the image to obtain an edge-enhanced image. The proposed method is compared with the existing methods visually and quantitatively using entropic method. Entropy of the proposed method is higher (0.4418) than the morphology method (0.2275), crisp method (0.3599), and Sobel method (0.2669), implying that the proposed method is better.

Generalizing inference rules in a coherence-based probabilistic default reasoning

In this paper we first recall some notions and results on the coherence-based probabilistic treatment of uncertainty. Then, we deepen some probabilistic aspects in nonmonotonic reasoning, by generalizing OR, CM, and Cut rules. We also illustrate the degradation of these inference rules when the number of premises increases. Finally, we show that the lower bounds obtained when applying OR and Quasi-Conjunction inference rules coincide, respectively, with Hamacher and Lukasiewicz t-norms; the upper bounds in both rules coincide with Hamacher t-conorm.