Journal articles: 'Fuzzy partition'

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Mu, Yashuang, Lidong Wang, and Xiaodong Liu. "Dynamic programming based fuzzy partition in fuzzy decision tree induction." Journal of Intelligent & Fuzzy Systems 39, no. 5 (November 19, 2020): 6757–72. http://dx.doi.org/10.3233/jifs-191497.

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Fuzzy decision trees are one of the most popular extensions of decision trees for symbolic knowledge acquisition by fuzzy representation. Among the majority of fuzzy decision trees learning methods, the number of fuzzy partitions is given in advance, that is, there are the same amount of fuzzy items utilized in each condition attribute. In this study, a dynamic programming-based partition criterion for fuzzy items is designed in the framework of fuzzy decision tree induction. The proposed criterion applies an improved dynamic programming algorithm used in scheduling problems to establish an optimal number of fuzzy items for each condition attribute. Then, based on these fuzzy partitions, a fuzzy decision tree is constructed in a top-down recursive way. A comparative analysis using several traditional decision trees verify the feasibility of the proposed dynamic programming based fuzzy partition criterion. Furthermore, under the same framework of fuzzy decision trees, the proposed fuzzy partition solution can obtain a higher classification accuracy than some cases with the same amount of fuzzy items.

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Li, Chun Sheng, and Hong Liang Dai. "On the Measure of Compactness of Fuzzy Clustering." Advanced Materials Research 204-210 (February 2011): 1403–6. http://dx.doi.org/10.4028/www.scientific.net/amr.204-210.1403.

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This paper tested the measures of compactness of fuzzy partitions. Over the same labeled data, Fuzzy k-Means clustering algorithm generates the first partition, then the proposed revision function in (7) revises it several times to generate various fuzzy partitions with different pattern recognition rates computed by (6), finally the measures of compactness measure the compactness of each fuzzy partition. Experimental results on real data show that the measures of compactness in literatures fail to measure the compactness of a fuzzy clustering in some cases, for they argue that the fuzzy clustering with higher pattern recognition rate is less compact and worse than that with lower pattern recognition rate.

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Hyung Lee-Kwang and Keon-Myung Lee. "Fuzzy hypergraph and fuzzy partition." IEEE Transactions on Systems, Man, and Cybernetics 25, no. 1 (1995): 196–201. http://dx.doi.org/10.1109/21.362951.

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Honda, Katsuhiro, Shunnya Oshio, and Akira Notsu. "Fuzzy Co-Clustering Induced by Multinomial Mixture Models." Journal of Advanced Computational Intelligence and Intelligent Informatics 19, no. 6 (November 20, 2015): 717–26. http://dx.doi.org/10.20965/jaciii.2015.p0717.

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A close connection between fuzzyc-means (FCM) and Gaussian mixture models (GMMs) have been discussed and several extended FCM algorithms were induced by the GMMs concept, where fuzzy partitions are proved to be more useful for revealing intrinsic cluster structures than probabilistic ones. Co-clustering is a promising technique for summarizing cooccurrence information such as document-keyword frequencies. In this paper, a fuzzy co-clustering model is induced based on the multinomial mixture models (MMMs) concept, in which the degree of fuzziness of both object and item fuzzy memberships can be properly tuned. The advantages of the dual fuzzy partition are demonstrated through several experimental results including document clustering applications.

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Malik, D. S., John N. Mordeson, and M. K. Sen. "Admissible Partitions of Fuzzy Finite State Machines." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 05, no. 06 (December 1997): 723–32. http://dx.doi.org/10.1142/s021848859700052x.

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In this paper we introduce the concept of a covering of a ffsm by another, admissible partitions and relations of a ffsm, μ-orthogonality of admissible partitions, irreducibile ffsm, and the quotient of a ffsm induced by an admissible partition of the state set.

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Zuo, Yong Xia, Guo Qiang Wang, and Chun Cheng Zuo. "The Segmentation Algorithm for Pavement Cracking Images Based on the Improved Fuzzy Clustering." Applied Mechanics and Materials 319 (May 2013): 362–66. http://dx.doi.org/10.4028/www.scientific.net/amm.319.362.

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The segmentation technology of pavement cracking image is critical for identifying, quantifying and classifying pavement cracks. An improved fuzzy clustering algorithm is introduced to segment pavement cracking images. The algorithm makes no assumptions the initial position of clusters. For each value of the multiscale parameter, it obtains a corresponding hard partition. The different partitions values of the multiscale parameter indicate the structure of the image in different partitional scales. The algorithm was tested on actual pavement cracking images. We compared the results with FCM and OTSU to show that the improved fuzzy clustering algorithm can provide better crack edges.

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Jung, Hye-Young, Woo-Joo Lee, and Seung Hoe Choi. "Fuzzy regression model using fuzzy partition." Journal of Physics: Conference Series 1334 (October 2019): 012019. http://dx.doi.org/10.1088/1742-6596/1334/1/012019.

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Ma, Ming, I. B. Turksen, and Abraham Kandel. "Fuzzy partition and fuzzy rule base." Information Sciences 108, no. 1-4 (July 1998): 109–21. http://dx.doi.org/10.1016/s0020-0255(97)10061-5.

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Pop, Horia F., Tudor L. Pop, and Costel Sarbu. "Assessment of Heart Disease using Fuzzy Classification Techniques." Scientific World JOURNAL 1 (2001): 369–90. http://dx.doi.org/10.1100/tsw.2001.64.

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In this paper we discuss the classification results of cardiac patients of ischemical cardiopathy, valvular heart disease, and arterial hypertension, based on 19 characteristics (descriptors) including ECHO data, effort testings, and age and weight. In this order we have used different fuzzy clustering algorithms, namely hierarchical fuzzy clustering, hierarchical and horizontal fuzzy characteristics clustering, and a new clustering technique, fuzzy hierarchical cross-classification. The characteristics clustering techniques produce fuzzy partitions of the characteristics involved and, thus, are useful tools for studying the similarities between different characteristics and for essential characteristics selection. The cross-classification algorithm produces not only a fuzzy partition of the cardiac patients analyzed, but also a fuzzy partition of their considered characteristics. In this way it is possible to identify which characteristics are responsible for the similarities or dissimilarities observed between different groups of patients.

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Gordon, A. D., and M. Vichi. "Fuzzy partition models for fitting a set of partitions." Psychometrika 66, no. 2 (June 2001): 229–47. http://dx.doi.org/10.1007/bf02294837.

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Cardone, Barbara, and Ferdinando Di Martino. "A Fuzzy Entropy-Based Thematic Classification Method Aimed at Improving the Reliability of Thematic Maps in GIS Environments." Electronics 11, no. 21 (October 28, 2022): 3509. http://dx.doi.org/10.3390/electronics11213509.

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Thematic maps of spatial data are constructed by using standard thematic classification methods that do not allow management of the uncertainty of classification and, consequently, evaluation of the reliability of the resulting thematic map. We propose a novel fuzzy-based thematic classification method applied to construct thematic maps in Geographical Information Systems. An initial fuzzy partition of the domain of the features of the spatial dataset is constructed using triangular fuzzy numbers; our method finds an optimal fuzzy partition evaluating the fuzziness of the fuzzy sets by using a fuzzy entropy measure. An assessment of the reliability of the final thematic map is performed according to the fuzziness of the fuzzy sets. We implement our method on a GIS framework, testing it on various vector and image spatial datasets. The results of these tests confirm that our thematic classification method provide thematic maps with a higher reliability with respect to that obtained through fuzzy partitions constructed by expert users.

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Samuel, A. Edward, and C. Kayalvizhi. "HAMILTONIAN FUZZY PARTITION COLORING." Far East Journal of Mathematical Sciences (FJMS) 99, no. 7 (April 14, 2016): 1061–79. http://dx.doi.org/10.17654/ms099071061.

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Li, Yu, Jianfeng Wu, Chunfu Lu, Zhichuan Tang, and Chengmin Li. "Pillow Support Model with Partitioned Matching Based on Body Pressure Distribution Matrix." Healthcare 9, no. 5 (May 12, 2021): 571. http://dx.doi.org/10.3390/healthcare9050571.

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(1) Objective: Sleep problems have become one of the current serious public health issues. The purpose of this research was to construct an ideal pressure distribution model for head and neck support through research on the partitioned support surface of a pillow in order to guide the development of ergonomic pillows. (2) Methods: Seven typical memory foam pillows were selected as samples, and six subjects were recruited to carry out a body pressure distribution experiment. The average value of the first 10% of the samples in the comfort evaluation was calculated to obtain the relative ideal body pressure distribution matrix. Fuzzy clustering was performed on the ideal matrix to obtain the support surface partition. The ideal body pressure index of each partition was calculated, and a hierarchical analysis of each partition was then performed to determine the pressure sensitivity weight of each partition. Using these approaches, the key ergonomic node coordinates of the partitions of four different groups of people were extracted. The ergonomic node coordinates and the physical characteristics of the material were used to design a pillow prototype. Five subjects were recruited for each of the four groups to repeat the body pressure distribution experiment to evaluate the pillow prototype. (3) Results: An ideal support model with seven partitions, including three partitions in the supine position and four partitions in the lateral position, was constructed. The ideal body pressure distribution matrix and ideal body pressure indicators and pressure sensitivity weights for each partition were provided. The pillow that was designed and manufactured based on this model reproduced the ideal pressure distribution matrix evaluated by various groups of people. (4) Conclusion: The seven-partition ideal support model can effectively describe the head and neck support requirements of supine and lateral positions, which can provide strong support for the development of related products.

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Shyi-Ming Chen. "Interval-valued fuzzy hypergraph and fuzzy partition." IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics) 27, no. 4 (August 1997): 725–33. http://dx.doi.org/10.1109/3477.604121.

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Lee, Jeong-Gon, and Kul Hur. "Bipolar Fuzzy Relations." Mathematics 7, no. 11 (November 3, 2019): 1044. http://dx.doi.org/10.3390/math7111044.

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We introduce the concepts of a bipolar fuzzy reflexive, symmetric, and transitive relation. We study bipolar fuzzy analogues of many results concerning relationships between ordinary reflexive, symmetric, and transitive relations. Next, we define the concepts of a bipolar fuzzy equivalence class and a bipolar fuzzy partition, and we prove that the set of all bipolar fuzzy equivalence classes is a bipolar fuzzy partition and that the bipolar fuzzy equivalence relation is induced by a bipolar fuzzy partition. Finally, we define an ( a , b ) -level set of a bipolar fuzzy relation and investigate some relationships between bipolar fuzzy relations and their ( a , b ) -level sets.

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Szilágyi, László, László Lefkovits, and David Iclanzan. "A review on suppressed fuzzy c-means clustering models." Acta Universitatis Sapientiae, Informatica 12, no. 2 (December 1, 2020): 302–24. http://dx.doi.org/10.2478/ausi-2020-0018.

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Abstract Suppressed fuzzy c-means clustering was proposed as an attempt to combine the better properties of hard and fuzzy c-means clustering, namely the quicker convergence of the former and the finer partition quality of the latter. In the meantime, it became much more than that. Its competitive behavior was revealed, based on which it received two generalization schemes. It was found a close relative of the so-called fuzzy c-means algorithm with generalized improved partition, which could improve its popularity due to the existence of an objective function it optimizes. Using certain suppression rules, it was found more accurate and efficient than the conventional fuzzy c-means in several, mostly image processing applications. This paper reviews the most relevant extensions and generalizations added to the theory of fuzzy c-means clustering models with suppressed partitions, and summarizes the practical advances these algorithms can offer.

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Zoghlami, Mohamed Ali, Minyar Sassi Hidri, and Rahma Ben Ayed. "Consensus-Driven Cluster Analysis: Top-Down and Bottom-Up Based Split-and-Merge Classifiers." International Journal on Artificial Intelligence Tools 26, no. 04 (August 2017): 1750018. http://dx.doi.org/10.1142/s021821301750018x.

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Consensus clustering is used in data analysis to generate stable results out of a set of partitions delivered by stochastic methods. Typically, the goal is searching for the socalled median (or consensus) partition, i.e. the partition that is most similar, on average, to all the input partitions. In this paper we address the problem of combining multiple fuzzy clusterings without access to the underlying features of the data while basing on inter-clusters similarity. We are concerned of top-down and bottom-up based consensus-driven fuzzy clustering while splitting and merging worst clusters. The objective is to reconcile a structure, developed for patterns in some dataset with the structural findings already available for other related ones. The proposed classifiers consider dispersion and dissimilarity between the partitions as well as the corresponding fuzzy proximity matrices. Several illustrative numerical examples, using both synthetic data and those coming from available machine learning repositories, are also included. The experimental component of the study shows the efficiency of the proposed classifiers in terms of quality and runtime.

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Hamasuna, Yukihiro, Naohiko Kinoshita, and Yasunori Endo. "Comparison of Cluster Validity Measures Basedx-Means." Journal of Advanced Computational Intelligence and Intelligent Informatics 20, no. 5 (September 20, 2016): 845–53. http://dx.doi.org/10.20965/jaciii.2016.p0845.

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Thex-means determines the suitable number of clusters automatically by executingk-means recursively. The Bayesian Information Criterion is applied to evaluate a cluster partition in thex-means. A novel type ofx-means clustering is proposed by introducing cluster validity measures that are used to evaluate the cluster partition and determine the number of clusters instead of the information criterion. The proposedx-means uses cluster validity measures in the evaluation step, and an estimation of the particular probabilistic model is therefore not required. The performances of a conventionalx-means and the proposed method are compared for crisp and fuzzy partitions using eight datasets. The comparison shows that the proposed method obtains better results than the conventional method, and that the cluster validity measures for a fuzzy partition are effective in the proposed method.

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Buşoniu, Lucian, Damien Ernst, Bart De Schutter, and Robert Babuška. "Fuzzy Partition Optimization for Approximate Fuzzy Q-iteration." IFAC Proceedings Volumes 41, no. 2 (2008): 5629–34. http://dx.doi.org/10.3182/20080706-5-kr-1001.00949.

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Hu, Yi-Chung, Ruey-Shun Chen, and Gwo-Hshiung Tzeng. "Discovering fuzzy association rules using fuzzy partition methods." Knowledge-Based Systems 16, no. 3 (April 2003): 137–47. http://dx.doi.org/10.1016/s0950-7051(02)00079-5.

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LIN, CHENG-JIAN. "A FUZZY ADAPTIVE LEARNING CONTROL NETWORK WITH ON-LINE STRUCTURE AND PARAMETER LEARNING." International Journal of Neural Systems 07, no. 05 (November 1996): 569–90. http://dx.doi.org/10.1142/s0129065796000567.

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This paper addresses a general connectionist model, called Fuzzy Adaptive Learning Control Network (FALCON), for the realization of a fuzzy logic control system. An on-line supervised structure/parameter learning algorithm is proposed for constructing the FALCON dynamically. It combines the backpropagation learning scheme for parameter learning and the fuzzy ART algorithm for structure learning. The supervised learning algorithm has some important features. First of all, it partitions the input state space and output control space using irregular fuzzy hyperboxes according to the distribution of training data. In many existing fuzzy or neural fuzzy control systems, the input and output spaces are always partitioned into “grids”. As the number of input/output variables increase, the number of partitioned grids will grow combinatorially. To avoid the problem of combinatorial growing of partitioned grids in some complex systems, the proposed learning algorithm partitions the input/output spaces in a flexible way based on the distribution of training data. Second, the proposed learning algorithm can create and train the FALCON in a highly autonomous way. In its initial form, there is no membership function, fuzzy partition, and fuzzy logic rule. They are created and begin to grow as the first training pattern arrives. The users thus need not give it any a priori knowledge or even any initial information on these. In some real-time applications, exact training data may be expensive or even impossible to obtain. To solve this problem, a Reinforcement Fuzzy Adaptive Learning Control Network (RFALCON) is further proposed. The proposed RFALCON is constructed by integrating two FALCONs, one FALCON as a critic network, and the other as an action network. By combining temporal difference techniques, stochastic exploration, and a proposed on-line supervised structure/parameter learning algorithm, a reinforcement structure/parameter learning algorithm is proposed, which can construct a RFALCON dynamically through a reward/penalty signal. The ball and beam balancing system is presented to illustrate the performance and applicability of the proposed models and learning algorithms.

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Domingo-Ferrer, Josep, and Vicenç Torra. "Fuzzy Microaggregation for Microdata Protection." Journal of Advanced Computational Intelligence and Intelligent Informatics 7, no. 2 (June 20, 2003): 153–59. http://dx.doi.org/10.20965/jaciii.2003.p0153.

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In this work we describe a microdata protection method based on the use of fuzzy clustering and, more specifically, using fuzzy c-means. Microaggregation is a well-known masking method for microdata protection used by National Statistical Offices. Given a set of objects described in terms of a set of variables, this method consists on building a partition of the objects and then replace the original evaluation for each variable by the aggregates of each partition. This is, the values in a given cluster are aggregated –fused– and used instead of the original ones. As the problem of finding the best partition for microdata protection is an NP problem, heuristic methods are considered in the literature. Our approach uses fuzzy c-means for building a fuzzy partition, instead of a crisp one.

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Guo, Jia Mei, and Yin Xiang Pei. "Association Rules Mining Based on Adaptive Fuzzy Clustering Algorithm." Advanced Materials Research 998-999 (July 2014): 842–45. http://dx.doi.org/10.4028/www.scientific.net/amr.998-999.842.

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Association rules extraction is one of the important goals of data mining and analyzing. Aiming at the problem that information lose caused by crisp partition of numerical attribute , in this article, we put forward a fuzzy association rules mining method based on fuzzy logic. First, we use c-means clustering to generate fuzzy partitions and eliminate redundant data, and then map the original data set into fuzzy interval, in the end, we extract the fuzzy association rules on the fuzzy data set as providing the basis for proper decision-making. Results show that this method can effectively improve the efficiency of data mining and the semantic visualization and credibility of association rules.

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Shu'aibu, D. S., S. K. Syed Yusof, N. Fisal, S. H. S. Ariffin, R. A. Rashid, N. M. Abdul Latiff, and Y. S. Baguda. "Fuzzy Logic Partition-Based Call Admission Control for Mobile WiMAX." ISRN Communications and Networking 2011 (June 1, 2011): 1–9. http://dx.doi.org/10.5402/2011/171760.

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The unpredictable nature of the wireless network and exponential growth in traffics with different quality of service requirements has led hardware complexity to escalate. In order to effectively control and manage the network traffics, there is a need for intelligent call admission control (CAC) in admitting traffics into the wireless network that provides necessary quality of service. In this paper, we propose a fuzzy logic partition-based call admission control (FZ CAC). The scheme primarily partitions the total link bandwidth into three which corresponds to constant bit rate (CBR), variable bit rate (VBR) and handover (HO) services. The fuzzy logic admission control scheme was implemented in the HO portion to intelligently keep dropping probability as low as possible based on the available bandwidth. Simulation results showed that the proposed approach outperformed both partition-based CAC (PB CAC) and conventional bandwidth allocation CAC (CB CAC).

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Umayahara, Kazutaka, Yoshiteru Nakamori, and Sadaaki Miyamoto. "Fuzzy Clustering for Detecting Linear Structures with Different Dimensions." Journal of Advanced Computational Intelligence and Intelligent Informatics 3, no. 1 (February 20, 1999): 13–20. http://dx.doi.org/10.20965/jaciii.1999.p0013.

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One recent interest in fuzzy clustering is the simultaneous determination of a fuzzy partition of a given dataset and parameters of assumed models having different shapes that explain partitioned datasets. We propose an objective function to detect linear varieties with different dimensionalities. The noise cluster suggested by Dave is introduced. Since this is not all-purpose method, some techniques are suggested using artificial examples to show how to implement clustering successfully.

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Matsushita, Yutaka, and Hiroshi Kambara. "Partition Type Fuzzy Integral Model for Evaluation Process." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 05, no. 05 (October 1997): 531–45. http://dx.doi.org/10.1142/s0218488597000415.

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This paper formulates "partition type fuzzy integral" which is a fuzzy integral of functions on a partition of the set of all attributes. The identity of it is the set of intermediate fuzzy integrals between the linear form and the usual multilinear fuzzy integrals. In this fuzzy integral, any combination of attributes in the same macro-attribute yields no interactions, but any set of attributes, each member of which belongs to a distinct macro-attribute, causes an interaction. Therefore, we can extract only the essential interactions from the evaluation process by discovering the best expressive partition. An application to a concrete evaluation problem shows the effectiveness of this model.

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Urumov, Georgy, and Panagiotis Chountas. "Clustering stock price volatility using intuitionistic fuzzy sets." Notes on Intuitionistic Fuzzy Sets 28, no. 3 (September 8, 2022): 343–52. http://dx.doi.org/10.7546/nifs.2022.28.3.343-352.

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Clustering involves gathering a collection of objects into homogeneous groups or clusters, such that objects in the same cluster are more similar when compared to objects present in other groups. Clustering algorithms that generate a tree of clusters called dendrogram which can be either divisive or agglomerative. The partitional clustering gives a single partition of objects, with a predefined K number of clusters. The most popular partition clustering approaches are: k-means and fuzzy C-means (FCM). In k-means clustering, data are divided into a number of clusters where data elements belong to exactly one cluster. The k-means clustering works well when data elements are well separable. To overcome the problem of non-separability, FCM and IFCM clustering algorithm were proposed. Here we review the use of FCM/IFCM with reference to the problem of market volatility.

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LIN, CHENG-JIAN, and CHIN-TENG LIN. "ADAPTIVE FUZZY CONTROL OF UNSTABLE NONLINEAR SYSTEMS." International Journal of Neural Systems 06, no. 03 (September 1995): 283–98. http://dx.doi.org/10.1142/s0129065795000214.

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This paper addresses the structure and an associated on-line learning algorithm of a feedforward multilayer connectionist network for realizing the basic elements and functions of a traditional fuzzy logic controller. The proposed Fuzzy Adaptive Learning Control Network (FALCON) can be contrasted with the traditional fuzzy logic control systems in their network structure and learning ability. An on-line structure/parameter learning algorithm, called FALCON-ART, is proposed for constructing the FALCON dynamically. The FALCON-ART can partition the input/output space in a flexible way based on the distribution of the training data. Hence it can avoid the problem of combinatorial growing of partitioned grids in some complex systems. It combines the backpropagation learning scheme for parameter learning and the fuzzy ART algorithm for structure learning. More notably, the FALCONART can on-line partition the input/output spaces, tune membership functions, and find proper fuzzy logic rules dynamically without any a priori knowledge or even any initial information on these. The proposed learning scheme has been successfully used to control two unstable nonlinear systems. They are the seesaw system and the inverted wedge system.

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Widiyanto, Max Teja Ajie Cipta. "Perrbandingan Validitas Fuzzy Clustering pada Fuzzy C - Means Dan Particle Swarms Optimazation (PSO) pada Pengelompokan Kelas." JISKA (Jurnal Informatika Sunan Kalijaga) 4, no. 1 (November 16, 2019): 22. http://dx.doi.org/10.14421/jiska.2019.41-03.

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Clustering adalah metode yang membagi objek data ke dalam kelompok berdasarkan informasi yang ditemukan dalam data yang menggambarkan objek dan hubungan di antara mereka. Dalam analis cluster berbasis partisi metode K-Means dan Metode Fuzzy C-Means yang merupakan metode clustering yang sering dan lazim banyak digunakan masih banyak kelemahan. Dalam beberapa tahun terakhir, Particle Swarm Optimization (PSO) telah berhasil diterapkan untuk sejumlah masalah pengelompokan dunia nyata dengan konvergensi cepat dan efektif untuk data dimensi tinggi. Pengukuran yang dilakukan untuk kualitas clustering dengan fuzzy haruslah diukur dengan validitas cluster yang tepat dan sesuai dengan kriterianya masing – masing. Pengukuran perbandingan yang sangat sesuai dengan fuzzy clustering yaitu partition coefficient (PC),classification entropy (CE),Partition Index (PI),Fukuyama Sugeno Index (FS), Xie Beni Index (XBI),Modified Partition Coefficient (MPC),Partition Coefficient and Exponential Sparation (PCAES) Index.

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ALKasasbeh, Hussein, Irina Perfilieva, Muhammad Ahmad, and Zainor Yahya. "New Approximation Methods Based on Fuzzy Transform for Solving SODEs: II." Applied System Innovation 1, no. 3 (August 23, 2018): 30. http://dx.doi.org/10.3390/asi1030030.

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In this research, three approximation methods are used in the new generalized uniform fuzzy partition to solve the system of differential equations (SODEs) based on fuzzy transform (FzT). New representations of basic functions are proposed based on the new types of a uniform fuzzy partition and a subnormal generating function. The main properties of a new uniform fuzzy partition are examined. Further, the simpler form of the fuzzy transform is given alongside some of its fundamental results. New theorems and lemmas are proved. In accordance with the three conventional numerical methods: Trapezoidal rule (one step) and Adams Moulton method (two and three step modifications), new iterative methods (NIM) based on the fuzzy transform are proposed. These new fuzzy approximation methods yield more accurate results in comparison with the above-mentioned conventional methods.

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Karayiannis, Nicolaos B. "Fuzzy Partition Entropies and Entropy Constrained Fuzzy Clustering Algorithms." Journal of Intelligent and Fuzzy Systems 5, no. 2 (1997): 103–11. http://dx.doi.org/10.3233/ifs-1997-5202.

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Chuang, Chen-Chia. "Fuzzy Weighted Support Vector Regression With a Fuzzy Partition." IEEE Transactions on Systems, Man and Cybernetics, Part B (Cybernetics) 37, no. 3 (June 2007): 630–40. http://dx.doi.org/10.1109/tsmcb.2006.889611.

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Chen, Ji Wen, Jin Sheng Zhang, Zhi Wang, and Jing Kun Wang. "Function Module Dynamic Partition for Product Innovation Design." Applied Mechanics and Materials 58-60 (June 2011): 2095–100. http://dx.doi.org/10.4028/www.scientific.net/amm.58-60.2095.

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The reasonable functional modules partition is crucial to technical solution of function in product innovation design. Technical evolution factors are not considered in current product module partition method. The correlation of customer demand and product function unit, function unit flow correlation and function technology correlation are synthesized for function module partition in product innovation design. Based on function base expression, function chain and function structure is established to provide basis of function correlation analysis. Function correlation matrix is established by combining the correlation matrix of customer demand and product function unit, the function unit flow correlation matrix and function technology correlation matrix. The dynamic cluster analysis of fuzzy equivalence matrix is used to form function module. The function module partitions are evaluated by polymerization degree and coupling degree. The presented dynamic module partition method has strong distinguishing ability.

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Chen, Yan Hui, and De Jian Zhou. "Min-Max Partition Method of Product Modularization Based on Fuzzy Clustering." Advanced Materials Research 308-310 (August 2011): 273–79. http://dx.doi.org/10.4028/www.scientific.net/amr.308-310.273.

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This paper presents a new method of product module partition based on the fuzzy clustering analysis. This method demonstrates the relevant definitions and calculation methods of the initial partition, min-max partition, submodule relevancy and module aggregation etc., and establishes the incidence matrix to respectively carry out the initial partition for the products and calculation of min-max partition according to various incidence relations between parts and components. Taking the submodule as computing unit in each module set, this paper carries out the fuzzy cluster analysis to obtain the module partition results of the products, and finally demonstrates the rationality and effectiveness of this method by taking the example of the working units of the wheel loaders.

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Yin, Kedong, Benshuo Yang, and Xue Jin. "Grey Fuzzy Multiple Attribute Group Decision-Making Methods Based on Interval Grey Triangular Fuzzy Numbers Partitioned Bonferroni Mean." Symmetry 12, no. 4 (April 15, 2020): 628. http://dx.doi.org/10.3390/sym12040628.

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Considering the characteristics such as fuzziness and greyness in real decision-making, the interval grey triangular fuzzy number is easy to express fuzzy and grey information simultaneously. And the partition Bonferroni mean (PBM) operator has the ability to calculate the interrelationship among the attributes. In this study, we combine the PBM operator into the interval grey triangular fuzzy numbers to increase the applicable scope of PBM operators. First of all, we introduced the definition, properties, expectation, and distance of the interval grey triangular fuzzy numbers, and then we proposed the interval grey triangular fuzzy numbers partitioned Bonferroni mean (IGTFPBM) and the interval grey triangular fuzzy numbers weighted partitioned Bonferroni mean (IGTFWPBM), the adjusting of parameters in the operator can bring symmetry effect to the evaluation results. After that, a novel method based on IGTFWPBM is developed for solving the grey fuzzy multiple attribute group decision-making (GFMAGDM) problems. Finally, we give an example to expound the practicability and superiority of this method.

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Surono, Sugiyarto, Khang Wen Goh, Choo Wou Onn, Afif Nurraihan, Nauval Satriani Siregar, A. Borumand Saeid, and Tommy Tanu Wijaya. "Optimization of Markov Weighted Fuzzy Time Series Forecasting Using Genetic Algorithm (GA) and Particle Swarm Optimization (PSO)." Emerging Science Journal 6, no. 6 (September 20, 2022): 1375–93. http://dx.doi.org/10.28991/esj-2022-06-06-010.

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The Markov Weighted Fuzzy Time Series (MWFTS) is a method for making predictions based on developing a fuzzy time series (FTS) algorithm. The MWTS has overcome certain limitations of FTS, such as repetition of fuzzy logic relationships and weight considerations of fuzzy logic relationships. The main challenge of the MWFTS method is the absence of standardized rules for determining partition intervals. This study compares the MWFTS model to the partition methods Genetic Algorithm-Fuzzy K-Medoids clustering (GA-FKM) and Fuzzy K-Medoids clustering-Particle Swarm Optimization (FKM-PSO) to solve the problem of determining the partition interval and develop an algorithm. Optimal partition optimization. The GA optimization algorithm’s performance on GA-FKM depends on optimizing the clustering of FKM to obtain the most significant partition interval. Implementing the PSO optimization algorithm on FKM-PSO involves maximizing the interval length following the FKM procedure. The proposed method was applied to Anand Vihar, India’s air quality data. The MWFTS method combined with the GA-FKM partitioning method reduced the mean absolute square error (MAPE) from 17.440 to 16.85%. While the results of forecasting using the MWFTS method in conjunction with the FKM-PSO partition method were able to reduce the MAPE percentage from 9.78% to 7.58%, the MAPE percentage was still 9.78%. Initially, the root mean square error (RMSE) score for the GA-FKM partitioning technique was 48,179 to 47,01. After applying the FKM-PSO method, the initial RMSE score of 30,638 was reduced to 24,863. Doi: 10.28991/ESJ-2022-06-06-010 Full Text: PDF

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Kembaren, Ricky Crist Geoversam Imantara, Opim Salim Sitompul, and Sawaluddin Sawaluddin. "Analysis Clustering Using Normalized Cross Correlation In Fuzzy C-Means Clustering Algorithm." Sinkron 7, no. 4 (October 3, 2022): 2262–71. http://dx.doi.org/10.33395/sinkron.v7i4.11666.

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Abstract: Fuzzy C-Means Clustering (FCM) has been widely known as a technique for performing data clustering, such as image segmentation. This study will conduct a trial using the Normalized Cross Correlation method on the Fuzzy C-Means Clustering algorithm in determining the value of the initial fuzzy pseudo-partition matrix which was previously carried out by a random process. Clustering technique is a process of grouping data which is included in unsupervised learning. Data mining generally has two techniques in performing clustering, namely: hierarchical clustering and partitional clustering. The FCM algorithm has a working principle in grouping data by adding up the level of similarity between pairs of data groups. The method applied to measure the similarity of the data based on the correlation value is the Normalized Cross Correlation (NCC). The methodology in this research is the steps taken to measure clustering performance by adding the Normalized Cross Correlation (NCC) method in determining the initial fuzzy pseudo-partition matrix in the Fuzzy C-Means Clustering (FCM) algorithm. the results of data clustering using the Normalized Cross Correlation (NCC) method on the Fuzzy C-Means Clustering (FCM) algorithm gave better results than the ordinary Fuzzy C-Means Clustering (FCM) algorithm. The increase that occurs in the proposed method is 4.27% for the Accuracy, 4.73% for the rand index and 8.26% for the F-measure..

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Dujet, Christiane, and Hamza Si Kaddour. "Separating Power of a Fuzzy Set and Decreasing Rearrangement." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 06, no. 06 (December 1998): 577–85. http://dx.doi.org/10.1142/s0218488598000446.

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Let E be a set and f a characteristic property of E. The problem is that often elements of E have the property f with some degree and then we must find some process to make a "good partition" of E. In 1980, Dujet introduced the notion of separating power of a fuzzy set which gives, in many cases, a "good partition" called max-separating partition. In this paper, we discuss some ways to give a "good partition". This is achieved by the use of the decreasing rearrangement of a function. We prove that the measure of separation of a function is invariant through the corresponding decreasing rearrangement function and moreover it is possible to recover the initial max-separating partition by a knowledge of the max-separating partition of the decreasing rearrangement by an algorithmic way.

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Yu, Hai Yan. "An Image Adaptive Watermarking Algorithm Based on Ridgelet Transform and Two-Dimensional Fuzzy Partition." Advanced Materials Research 301-303 (July 2011): 1299–304. http://dx.doi.org/10.4028/www.scientific.net/amr.301-303.1299.

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An image adaptive watermarking algorithm based on ridgelet transform and two- dimensional(2-D) fuzzy partition classification is proposed. In order to obtain a sparse representation of straight edge singularity, the image is first partitioned into small pieces and the ridgelet transform is applied for each piece. After analyzing texture distribution in ridgelet coefficients of each piece, two feature vectors are selected to make up for the ‘wrap around’ effect for FRIT on representation of the image texture. Then the image is classifed into frat regions and texture regions by applying 2-D fuzzy partition classification algorithm with the two feature vectors prepocessed. An watermark sequence is embedded into texture regions with the embedding strength adaptively adjusted by ridgelet coefficients based on the feature of luminance masking and texture masking. Experimental results prove robustness and transparency of the proposed watermarking scheme.

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Shiono, Yasunori, Tadaaki Kirishima, Yoshinori Ueda, and Kensei Tsuchida. "Drawing Algorithm for Fuzzy Graphs Using the Partition Tree." Journal of Advanced Computational Intelligence and Intelligent Informatics 16, no. 5 (July 20, 2012): 641–52. http://dx.doi.org/10.20965/jaciii.2012.p0641.

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Fuzzy graphs have been used frequently and effectively as a method for sociogram analysis. A fuzzy graph has the fundamental characteristic of being able to express a variety of relationships between nodes. The drawing of fuzzy graphs has been studied in computer-aided analysis systems with human interfaces and methods using genetic algorithms. However, computer-aided analysis systems with human interfaces do not provide for automatic drawing, while methods using genetic algorithms have the defect of requiring too much execution time for finding a locally optimum solution. To overcome these defects, we propose an algorithm for drawing intelligible and comprehensive fuzzy graphs using a partition tree. This method automatically draws the fuzzy graphwith nodes arranged on the intersections of a latticed space. Since nodes are optimally arranged on the latticed intersections and put together at a nearby position in accordance with the transition of clusters according to cluster levels in the partition tree, drawing the algorithm makes fuzzy relations easier to understand through fuzzy graph representation. Moreover, fuzzy graphs can be drawn faster than by conventional methods. This paper describes the algorithm and its verification by introducing a system implementing the method for displaying fuzzy graphs. Moreover, we have carried out a case study in which a questionnaire has been administered to students, allowing us to analyze human relations quantitatively using a method based on fuzzy theory. Human relations are represented as fuzzy graphs by our algorithm and analyzed using the fuzzy graph.

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Park, Keon-Jun, Wei Huang, C. Yu, and Yong K. Kim. "Nonlinear Characteristics of Fuzzy Scatter Partition-Based Fuzzy Inference System." International journal of advanced smart convergence 2, no. 1 (May 31, 2013): 12–17. http://dx.doi.org/10.7236/ijasc.2013.2.1.012.

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Park, Keon-Jun, and Yong-Kab Kim. "Nonlinear Characteristics of Fuzzy Scatter Partition-Based Fuzzy Inference System." International Journal of Software Engineering and Its Applications 7, no. 5 (September 30, 2013): 77–86. http://dx.doi.org/10.14257/ijseia.2013.7.5.08.

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Joo, Y. H., H. S. Hwang, K. B. Kim, and K. B. Woo. "Fuzzy system modeling by fuzzy partition and GA hybrid schemes." Fuzzy Sets and Systems 86, no. 3 (March 1997): 279–88. http://dx.doi.org/10.1016/s0165-0114(95)00414-9.

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Liu, Wei-Yi. "An Effective Partition Method of the Fuzzy Inheritance Hierarchies on the basis of the Semantic Proximity." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 06, no. 05 (October 1998): 503–13. http://dx.doi.org/10.1142/s0218488598000380.

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In this paper, based on the concept of the semantic proximity, a partition method of fuzzy inheritance hierarchies has been given. It is shown that this method is reasonable and effective. Particularly, for a problem with fuzzy concepts, such as systematic botany and zoology, this partition method has especial advantages.

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Castiblanco, Fabian, Camilo Franco, J. Tinguaro Rodríguez, and Javier Montero. "Evaluation of the quality and relevance of a fuzzy partition." Journal of Intelligent & Fuzzy Systems 39, no. 3 (October 7, 2020): 4211–26. http://dx.doi.org/10.3233/jifs-200286.

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This paper proposes a couple of criteria for evaluating the quality and relevance of a fuzzy partition. These criteria are established from a fuzzy classification system and its recursive De Morgan triplet. We propose a comparison process between the classes of a fuzzy partition, based on a translation invariant similarity relation. Therefore a classification process is carried out with the equivalence relations determined by the similarity relation. Such a relation is built on the commutative group structure formed by the elements of the fuzzy classification system. Our approach is illustrated through an example on image analysis by the fuzzy c-means algorithm.

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Yin, Zhen, Qi Gao, and Xue Ji. "A New Service Module Partition Approach for Product Service System Based on Fuzzy Graph and Dempster-Shafer Theory of Evidence." Mathematical Problems in Engineering 2018 (June 27, 2018): 1–14. http://dx.doi.org/10.1155/2018/8346859.

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Due to the personalized and diverse service needs, service scheme configuration should be more quick and flexible in the process of product service system (PSS) scheme design. Service modularization can effectively improve the service configuration efficiency and modules’ reusability. However, compared with the modularity of tangible products, the partition of service modules in the practical context is still a problem to be discussed. In this paper, a service partition approach for PSS based on the fuzzy graph and Dempster-Shafer theory of evidence is presented. Firstly, service activities correlation analysis is carried out, according to which the fuzzy graph is drawn. By setting different thresholds, the fuzzy graph is cut, and different partition results are obtained. Secondly, the evaluation indexes of customization, generalization, and technological evolution are proposed and used as evidence sources of the Dempster-Shafer theory of evidence. Through the synthesis of the evidence sources, the optimal partition scheme is got. Finally, to verify the method, a case study is illustrated through the NC machine tools module partition. And results show that the proposed method can provide specific ideas and concrete guidance of the service module partition.

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Simanihuruk, Tiarma, H. Hartono, Dahlan Abdullah, Cut Ita Erliana, Darmawan Napitupulu, Erianto Ongko, Robbi Rahim, Sukiman ., and Ansari Saleh Ahmar. "Hesitant Fuzzy Linguistic Term Sets with Fuzzy Grid Partition in Determining the Best Lecturer." International Journal of Engineering & Technology 7, no. 2.3 (March 8, 2018): 59. http://dx.doi.org/10.14419/ijet.v7i2.3.12322.

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Decision-making on conditions that involve many alternatives, many criteria, and many judgments is a difficult thing to do. The difficulty is coupled with assessors who sometimes make decisions in hesitant, unclear, and inconsistent circumstances and each person can provide different judgments. One of the methods that can be used is Hesitant Fuzzy Linguistic Term Sets which is the development of Fuzzy Sets that can make decisions by using Hesitant Fuzzy Sets. Hesitant linguistic term has been introduced for capturing the human way of reasoning using linguistic expressions involving different levels of precision. The integration of Hesitant Fuzzy Linguistic Term Sets with Fuzzy Grid Partition will enhance the ability in the decision making process. This research will discuss the use of Hesitant Fuzzy Linguistic Term Sets method and Fuzzy Grid Partition for best lecturers determination.

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WIJAYANTI, WIDYA, IZZATI RAHMI HG, and FERRA YANUAR. "PENGGUNAAN METODE FUZZY C-MEANS UNTUK PENGELOMPOKAN PROVINSI DI INDONESIA BERDASARKAN INDIKATOR KESEHATAN LINGKUNGAN." Jurnal Matematika UNAND 10, no. 1 (January 12, 2021): 129. http://dx.doi.org/10.25077/jmu.10.1.129-136.2021.

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Analisis Klaster (cluster analisis) memiliki tujuan untuk mengelompokkan objek-objek berdasarkan karakteristik yang dimiliki. Pengelompokan dengan analisis klaster dibagi menjadi dua metode yaitu metode berhirarki dan metode tak berhirarki. Salah satu metode tak berhirarki adalah Metode Fuzzy C-Means. Metode Fuzzy C-Means merupakan suatu metode yang mempertimbangkan derajat keanggotaan dan himpunan fuzzy sebagai dasar pembobotan. Untuk jumlah klaster optimum didapatkan dengan menggunakan kriteria indeks validitas Partition Entropy Index (PE). Pada penelitian ini Metode Fuzzy C-Means digunakan untuk mengelompokan provinsi-provinsi yang ada di Indonesia berdasarkan indikator kesehatan lingkungan. Indikator kesehatan lingkungan yang digunakan adalah STBM, tatanan kawasan sehat, air minum layak rumah tangga, TTU yang memenuhi syarat kesehatan, TPM yang memenuhi syarat kesehatan, sanitasi layak rumah tangga dan rumah tangga layak huni. Jumlah klaster optimum diperoleh sebanyak 2 klaster yang memiliki nilai partition entropy 0,4633829. Klaster 1 terdiri dari 22 provinsi dan klaster 2 terdiri dari 12 provinsi.Kata Kunci: Fuzzy C-Means, Indikator Kesehatan Lingkungan, Partition Entropy Index

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Guitiérrez, Nicolás Enrique Salgado, Sergio Andrés Valencia Ramírez, and José Soriano Méndez. "An approach to Fuzzy clustering of the iris petals by using Ac-means Analysis." International Journal on Soft Computing 12, no. 4 (November 30, 2021): 1–20. http://dx.doi.org/10.5121/ijsc.2021.12401.

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This paper proposes a definition of a fuzzy partition element based on the homomorphism between type-1 fuzzy sets and the three-valued Kleene algebra. A new clustering method based on the C-means algorithm, using the defined partition, is presented in this paper, which will be validated with the traditional iris clustering problem by measuring its petals.

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Rezaee, Alireza. "Partition Fuzzy Median Filter for Image Restoration." Fuzzy Information and Engineering 13, no. 2 (April 3, 2021): 199–210. http://dx.doi.org/10.1080/16168658.2021.1921377.

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Journal articles on the topic 'Fuzzy partition'

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