Fuzzy Module Research Articles

Fuzzy Classical Two-Absorbing Second (Secondary) Sub-modules and Strongly Classical Two-Absorbing Second Sub-modules

Fuzzy classical Two-Absorbing second sub-modules, Fuzzy classical Two-Absorbing secondary sub-modules and strongly classical Two-Absorbing second sub-modules are presented in this search under the names of comultiplication fuzzy modules, cocyclic fuzzy modules, and multiplication fuzzy modules, along with some basic traits and qualities of these concepts. The relationship between fuzzy classical Two-Absorbing second sub-modules, fuzzy classical Two-Absorbing secondary sub-modules, fuzzy strongly classical Two-Absorbing second sub-modules, and other fuzzy second sub-module concepts is also covered.

Support Based Essential and Core Based Superfluous Fuzzy Modules

In this paper, we introduce and explore several novel concepts within the framework of fuzzy module theory. First, we define the notion of a support based essential fuzzy module, establishing its foundational properties. We then investigate the essentiality of alpha cuts and the quotient fuzzy modules arising from support based essential fuzzy modules. Additionally, we demonstrate that under specific conditions, the product of a fuzzy ideal and a fuzzy module results in a support based essential fuzzy module. Further, we define the concept of a support based essential fuzzy monomorphism and provide a detailed characterization. We also introduce the fuzzy injective hull and prove that the direct sum of the fuzzy injective hulls of a class of fuzzy modules coincides with the fuzzy injective hull of the direct sum of the same class. Finally, we define the core based superfluous fuzzy module as a dual concept to the support based essential fuzzy module and establish corresponding dual results.

Essential Extensions and Injective Hulls of Fuzzy Modules

In this paper, we introduce the notion of essential extensions of fuzzy modules. We use these concepts to introduce the notion of injective hulls of fuzzy modules. It is known that every [Formula: see text]-module has an injective hull, where [Formula: see text] is a ring. We show that these corresponding results do not hold for fuzzy [Formula: see text]-modules, i.e. there exists a fuzzy [Formula: see text]-module that does not have an injective hull. Sufficient conditions are given for a fuzzy [Formula: see text]-module to have an injective hull.

Residual deep fuzzy system with randomized fuzzy modules for accurate time series forecasting

Residual deep fuzzy system with randomized fuzzy modules for accurate time series forecasting

Manju Varghese and Shery Fernandez

P. S. Das [Sivaramakrishna Das, P. Fuzzy groups and level subgroups. {\it J. Math. Anal. Appl.} {\bf 84} (1981), no. 1, 264--269.] proved that the level subgroups of any fuzzy subgroup of a finite group form a chain. In this paper we extend it to modules and showed that the level submodules of a fuzzy module also form a chain. With the help of these results we introduced fuzzy noetherian module for noetherian modules. Some results are proved for level submodules of any fuzzy module of modules with composition series.

TENSOR PRODUCT OF INTUITIONISTIC FUZZY MODULES

In this paper, we introduce the concept of tensor product between intuitionistic fuzzy submodules. We establish a formal framework for the tensor product operation, examining its properties and applications within the context of intuitionistic fuzzy modules. We then establish a relationship between the Hom functor and the tensor product in the category of intuitionistic fuzzy modules. The connection between tensor products and hom-functors in some algebraic structures, such as modules, is made possible via a natural isomorphism known as the HomTensor adjunction and it establishes a relationship between HomCR-IFM (B⊗A,C) and HomCR-IFM (A,HomCR-IFM (B,C)). An application of tensor product of intuitionistic fuzzy modules can be used in decision-making processes by embracing ambiguity and vagueness, making it a valuable tool when exact data is lacking.

Special types of morphisms in the category C_{R-IFM}

The aim of this paper is to introduce two special type of morphisms, namely Retraction and Coretraction in the category (CR-IFM) of intuitionistic fuzzy modules. We obtain the condition under which a morphism in CR-IFM, that is an intuitionistic fuzzy R-homomorphism, to be a retraction or a coretraction. Then, we acquire some equivalent statements for these two morphisms. Further, we study free, projective and injective objects in CR-IFM and establish their relation with morphism in CR-IFM and retraction, coretraction.

Fuzzy generator and fuzzy cogenerator

In this article, we introduce the fuzzy generator and fuzzy cogenerator and investigate some of their properties. Necessary and sufficient conditions for a fuzzy module to become a fuzzy generator and sufficient conditions for a fuzzy module to become a fuzzy cogenerator have also been established. We also discuss the behavior of fuzzy modules of finitely generated modules. Further, we introduce fuzzy trace and fuzzy reject and establish some specific results. Finally, we define a faithful fuzzy module and weave this notion with the concepts of fuzzy generator and fuzzy cogenerator.

A novel hybrid deep fuzzy model based on gradient descent algorithm with application to time series forecasting

Deep fuzzy systems are widely used in time series forecasting tasks due to their excellent nonlinear transformation capabilities and interpretability. However, traditional optimization methods and fixed network structures cannot make the deep fuzzy system obtain the expected prediction accuracy and generalization ability. Therefore, a novel hybrid deep fuzzy model (HDFM) is proposed in this paper. Firstly, two types fuzzy modules, namely the type-1 TSK fuzzy module (T1TSKFM) and the interval type-2 TSK fuzzy module (IT2TSKFM), are respectively presented and designed in detail. And, the gradient expressions of the fuzzy parameters, including the antecedent and consequent parameters, are also derived in detail. Secondly, in order to optimize the fuzzy parameters and to further accelerate the module convergence, a novel parameter optimization strategy is presented, combining the gradient descent with the Regularization, the DropRule and the AdaBound algorithms. Thirdly, a new stacked hybrid deep fuzzy architecture is proposed, which can be automatically trained and constructed using the designed T1TSKFM and the IT2TSKFM. Then, the detailed data-driven learning and updating strategy are given in step by step way. In addition, both the layered structure interpretability and the fuzzy rule interpretability are respectively analyzed. This can guarantee that the proposed model not only has the better forecasting accuracy, but also has the higher interpretability. Finally, in order to verify the effectiveness of the proposed method, several comparative experiments are given. Experimental results show that the forecasting performance of the proposed model outperforms the other comparisons, such as the DIRM-DFM, the IT2DIRM-DFM, the DCFS, and the ANFIS method. At the same time, the proposed model has better interpretability and more flexible construction property.

Fully Fuzzy Visible Modules With Other Related Concepts

In previous our research, the concepts of visible submodules and fully visible modules were introduced, and then these two concepts were fuzzified to fuzzy visible submodules and fully fuzzy. The main goal of this paper is to study the relationships between fully fuzzy visible modules and some types of fuzzy modules such as semiprime, prime, quasi, divisible, F-regular, quasi injective, and duo fuzzy modules, where under certain conditions it has been proven that each fully fuzzy visible module is fuzzy duo. In addition, there are many various properties and important results obtained through this research, which have been illustrated. Also, fuzzy Artinian modules and fuzzy fully stable modules have been introduced, and we study the relationships between these kinds of modules and fully fuzzy visible modules. Many other intersecting results we found.

Research on a Three-Dimensional Fuzzy Active Disturbance Rejection Controller for the Mechanical Arm of an Iron Roughneck

In the position control of the mechanical arm of an iron roughneck (MAIR), a controller with high responsiveness, high accuracy, and high anti-interference capability is necessary. An MAIR consists of two proportional-valve-controlled single-extension (PVCSE) hydraulic cylinders, and a traditional proportional–integral–derivative (PID) controller cannot easily achieve the accuracy and robustness requirements of the hydraulic cylinders. In this paper, a three-dimensional fuzzy active disturbance rejection controller (TF-ADRC) is proposed for an MAIR, which adds a three-dimensional fuzzy module to a classical active disturbance rejection controller (ADRC) to adjust the controller output according to the tracking of differential deviation, deviation change rate, and deviation change acceleration rate. Firstly, the trajectory planning of the MAIR was carried out using the quintic polynomial interpolation method to improve the smoothness of the target trajectory. Then, the reliability of the established model was verified by experiments. Finally, the comprehensive performance of a PID controller, fuzzy PID controller, ADRC, and TF-ADRC were compared based on the AMESim-Simulink model. The system with the TF-ADRC exhibits higher position control accuracy and better anti-interference capability than the system with a PID or Fuzzy PID controller, and accuracy is higher compared with the common ADRC.

Adaptive second order sliding mode guidance law for missile-target interception with fuzzy logic system

This paper presents the design of a 3D missile guidance law based on a second order sliding mode control technique employing an adaptive tuning law and a fuzzy gain scheduling. At the outset, the super-twisting sliding mode guidance law is obtained to overcome the chattering phenomenon. Then, without the knowledge about the bounds of disturbances, an adaptive law is used to determine the control gains. The results are enhanced using a fuzzy module that provides the controller parameters according to a set of linguistic rules. Finally, a comparative set of simulation results are given. To verify the performance and effectiveness of the proposed guidance law, we compare the performances of the traditional sliding mode (SM) guidance law, the traditional super-twisting sliding mode (STWSM) guidance law, the adaptive super-twisting sliding mode (ASTWSM) guidance law and the adaptive fuzzy super-twisting, sliding mode (AFSTWSM) guidance law. The simulation scenarios consider fundamental target movements. The results demonstrate that the proposed adaptive guidance laws display better performance in terms of miss distance, intercept time, and final closing velocity compared the alternatives considered in this study.

A hydroponic greenhouse fuzzy control system: design, development and optimization using the genetic algorithm

Aim of study: The design and development of a hydroponic greenhouse fuzzy control system. Area of study: The evaluation was performed using experimental data obtained from the literature. The construction and evaluation of the fuzzy control hydroponic greenhouse system was carried out in a greenhouse in Tehran, Iran. Material and methods: The greenhouse environmental conditions, including temperature, humidity, and carbon dioxide, were controlled. The design of a fuzzy controller begun with the selection of linguistic variables, process status, and input and output variables. The fuzzy control system consisted of three modules: 1) fuzzy module, 2) cost function, and 3) genetic algorithm for the adjustment of the greenhouse environmental conditions.The next step was to select a set of linguistic rules and the type of fuzzy inference process. The rules were set once, and the fuzzy set and output value needed to be specified after the inference, along with the development of a non-fuzzy strategy. Main results: The mean temperatures provided by the fuzzy control system during the day and night were 34.25°C and 23.22°C, respectively, which were improved to 31.17°C and 21.96°C after optimization. The mean humidity was 39.4% and 56.5% during the day and the night, respectively, which turned 60.22% and 74.59% after optimization. The control system also achieved desirable conditions in terms of CO2 amount. Research highlights: The results showed that the measured values of temperature and relative humidity of the greenhouse were improved after optimization with genetic algorithm.

Gradual and Fuzzy Modules: Functor Categories

The categorical treatment of fuzzy modules presents some problems, due to the well known fact that the category of fuzzy modules is not abelian, and even not normal. Our aim is to give a representation of the category of fuzzy modules inside a generalized category of modules, in fact, a functor category, Mod−P, which is a Grothendieck category. To do that, first we consider the preadditive category P, defined by the interval P=(0,1], to build a torsionfree class J in Mod−P, and a hereditary torsion theory in Mod−P, to finally identify equivalence classes of fuzzy submodules of a module M with F-pair, which are pair (G,F), of decreasing gradual submodules of M, where G belongs to J, satisfying G=Fd, and ∪αF(α) is a disjoint union of F(1) and F(α)\G(α), where α is running in (0,1].

Properties of Uniform Fuzzy Modules and Semiuniform Fuzzy Modules

In this research paper, the concepts of uniform fuzzy modules and semiuniform fuzzy modules were studied. We discussed the necessary and sufficient conditions between uniform fuzzy modules (and semiuniform fuzzy modules) in fuzzy set theory and uniform modules (and semiuniform modules) in module theory.

Compression and regularized optimization of modules stacked residual deep fuzzy system with application to time series prediction

The double-input-rule-modules stacked deep fuzzy method (DIRM-DFM) has attracted much attention because of its interpretability and prediction accuracy. However, when confronted with high-dimensional data and large numbers of fuzzy rules, the original DIRM-DFM has three limitations. First, the identity mapping that appears in the depth layer causes degradation of the prediction performance. Second, redundant fuzzy rules increase the complexity of the structure. Third, the overfitting phenomenon in the parameter-learning process imposes restrictions on the generalization ability of the system. Therefore, achieving structural simplification and high-accuracy prediction remains challenging. In this paper, a compression and regularized optimization scheme for the modules stacked residual deep fuzzy system (CDIRM-RDFS) is presented to address the above-mentioned limitations. To overcome the first limitation, a residual approximation mechanism was developed to approximate the actual output layer by layer. To obtain more compact fuzzy modules, singular value decomposition was conducted to eliminate the unimportant fuzzy rules, thus surmounting the second limitation. Finally, to prevent overfitting, regularization terms combining the l1 norm with the l2 norm were added to the loss function to penalize the parameters in the learning process and thereby solve the third problem. The performance of the proposed CDIRM-RDFS was validated using various types of datasets, including seasonal and non-seasonal as well as cyclical and non-cyclical time series. Compared with some existing popular shallow and deep models, the experimental results indicate that the proposed methodology can simplify the system architecture while improving the accuracy, effectiveness, and robustness of the prediction model.

An FA-SegNet Image Segmentation Model Based on Fuzzy Attention and Its Application in Cardiac MRI Segmentation

Aiming at the medical images segmentation with low-recognition and high background noise, a deep convolution neural network image segmentation model based on fuzzy attention mechanism is proposed, which is called FA-SegNet. It takes SegNet as the basic framework. In the down-sampling module for image feature extraction, a fuzzy channel-attention module is added to strengthen the discrimination of different target regions. In the up-sampling module for image size restoration and multi-scale feature fusion, a fuzzy spatial-attention module is added to reduce the loss of image details and expand the receptive field. In this paper, fuzzy cognition is introduced into the feature fusion of CNNs. Based on the attention mechanism, fuzzy membership is used to re-calibrate the importance of the pixel value in local regions. It can strengthen the distinguishing ability of image features, and the fusion ability of the contextual information, which improves the segmentation accuracy of the target regions. Taking MRI segmentation as an experimental example, multiple targets such as the left ventricles, right ventricles, and left ventricular myocardium are selected as the segmentation targets. The pixels accuracy is 92.47%, the mean intersection to union is 86.18%, and the Dice coefficient is 92.44%, which are improved compared with other methods. It verifies the accuracy and applicability of the proposed method for the medical images segmentation, especially the targets with low-recognition and serious occlusion.

Towards an Efficient Big Data Indexing Approach under an Uncertain Environment

It is generally accepted that data production has experienced spectacular growth for several years due to the proliferation of new technologies such as new mobile devices, smart meters, social networks, cloud computing and sensors. In fact, this data explosion should continue and even accelerate. To find all of the documents responding to a request, any information search system develops a methodology to confirm whether or not the terms of each document correspond to those of the user's request. Most systems are based on the assumption that the terms extracted from the documents have been certain and precise. However, there are data in which this assumption is difficult to apply. The main objective of the work carried out within the framework of this article is to propose a new model of data service indexing in an uncertain environment, meaning that the data they contain can be untrustworthy, or they can be contradictory to another data source, due to failure in collection or integration mechanisms. The solution we have proposed is characterized by its Intelligent side ensured by an efficient fuzzy module capable of reasoning in an environment of uncertain and imprecise data. Concretely, our proposed approach is articulated around two main phases: (i) a first phase ensures the processing of uncertain data in a textual document and, (ii) the second phase makes it possible to determine a new method of uncertain syntactic indexing. We carried out a series of experiments, on different bases of standard tests, in order to evaluate our solution while comparing it to the approaches studied in the literature. We used different standard performance measures, namely precision, recall and F_measure. The results found showed that our solution is more efficient and more efficient than the main approaches proposed in the literature. The results show that the proposed approach realizes an efficient Big Data indexing solution in an Uncertain Environment that increases the Precision, the Recall and the F_measure measurements. Experimental results present that the proposed uncertain model obtained the best precision accuracy 0.395 with KDD database and the best recall accuracy 0.254 with the same database.

The Properties of Intuitionistic Anti Fuzzy Module t-norm and t-conorm

Zadeh have introduced fuzzy set in 1965 and Atanassov have introduced intuitionistic fuzzy set in 1986 in theirs paper. Now, many of researcher connecting intuitionistic fuzzy set with algebraic structure. We interested to combine some concepts over intuitionistic fuzzy set, module of a ring, t-norm, t-conorm, and intuitionistic anti fuzzy. In this paper, we discusses about intuitionistic anti fuzzy module t-norm and t-conorm (IAFMTC) and their properties with respect to module homomorphism, maps, pre-image, and anti-image from intuitionistic fuzzy sets. We have investigate all properties of IAFMTC.

Category of Intuitionistic Fuzzy Modules

We study the relationship between the category of R-modules (CR-M) and the category of intuitionistic fuzzy modules (CR−IFM). We construct a category CLat(R−IFM) of complete lattices corresponding to every object in CR−M and then show that, corresponding to each morphism in CR−M, there exists a contravariant functor from CR−IFM to the category CLat (=union of all CLat(R−IFM), corresponding to each object in CR−M) that preserve infima. Then, we show that the category CR−IFM forms a top category over the category CR−M. Finally, we define and discuss the concept of kernel and cokernel in CR−IFM and show that CR−IFM is not an Abelian Category.