Статті в журналах: "FUZZY INDEX"

1

Omana, Rebecca Walo. "FUZZY CONLEY INDEX AND INVARIANT FUZZY SETS." Advances in Fuzzy Sets and Systems 26, no. 2 (October 20, 2021): 175–209. http://dx.doi.org/10.17654/fs026020175.

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2

BUSTINCE, H., E. BARRENECHEA, M. PAGOLA, and F. SORIA. "WEAK FUZZY S-SUBSETHOOD MEASURES: OVERLAP INDEX." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 14, no. 05 (October 2006): 537–60. http://dx.doi.org/10.1142/s0218488506004187.

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Starting from the definitions of the weak fuzzy subsethood measure (V.R. Young, Fuzzy subsethood. Fuzzy Sets and Systems, 77 (1996) 371–384) and of strong fuzzy inclusion, (D. Dubois and H. Prade, Fuzzy Sets and Systems: Theory and Applications, New York, Academic Press, 1980) we define weak fuzzy S-subsethood measures. We analyze their axiomatization and present various constructions obtained by aggregating implication operators with special properties. We conclude by presenting the conditions under which we can construct fuzzy entropies and overlap indices from these measures.

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3

Abdolshah, Mohammad. "Measuring Loss-Based Process Capability IndexLeand Its GenerationLe′′with Fuzzy Numbers." Mathematical Problems in Engineering 2015 (2015): 1–8. http://dx.doi.org/10.1155/2015/217406.

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Loss-based process capability indices are appropriate and realistic tools in order to measure the process capability. Among them, indexLeand its generationLe′′are well-known loss-based process capability indices, whose concepts are based on the worth (the opposite concept of loss). Sometimes, in order to calculateLeandLe′′there are some uncertainties in observations, so fuzzy logic can be employed to manage the uncertainties. This paper investigates fuzzification of process capability indexL~eand its generationL~e′′. In order to find the membership function of process capability indicesL~eandL~e′′, theα-cuts of fuzzy observation were employed. Then with an example of fuzzy process capability index,L~eandL~e′′were calculated and compared. Results showed that fuzzyL~e′′was more sensitive compared withL~eand was increased while the target departs (asymmetric tolerance). This example also showed that, with departure from the target, variation of fuzzyL~e′′and consequently its fuzziness were increased.

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4

Bala, Kalla Hema, and Dr B. Srinivasa Kumar. "Index Number of Multi Fuzzy Sets." International Journal of Recent Technology and Engineering (IJRTE) 8, no. 4 (November 30, 2019): 2873–76. http://dx.doi.org/10.35940/ijrte.d2888.118419.

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Multi fuzzy set theory is an extension of fuzzy set theory. In this paper we developing the theory of Index number of multi fuzzy sets. This theory is applied to medical diagnosis system and will help doctors to select the effective symptoms and could make diagnosis of diseases concern. This theory also helps in selecting right political leaders.

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5

BUSTINCE, HUMBERTO, EDURNE BARRENECHEA, MIGUEL PAGOLA, JAVIER FERNANDEZ, CARLOS GUERRA, PEDRO COUTO, and PEDRO MELO-PINTO. "GENERALIZED ATANASSOV'S INTUITIONISTIC FUZZY INDEX: CONSTRUCTION OF ATANASSOV'S FUZZY ENTROPY FROM FUZZY IMPLICATION OPERATORS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 19, no. 01 (February 2011): 51–69. http://dx.doi.org/10.1142/s0218488511006885.

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In this paper we introduce the concept of Generalized Atanassov's Intuitionistic Fuzzy Index. We characterize it in terms of fuzzy implication operators and propose a construction method with order automorphisms. Finally, we obtain, by means of special aggregation functions applied to the generalized Atanassov's intuitionistic fuzzy index, the Atanassov's intuitionistic fuzzy entropy given by Burillo and Bustince.

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6

Shi, Xiaolong, Maryam Akhoundi, Ali Asghar Talebi, and Seyed Hossein Sadati. "Some Properties of Cubic Fuzzy Graphs with an Application." Symmetry 14, no. 12 (December 11, 2022): 2623. http://dx.doi.org/10.3390/sym14122623.

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The advent of fuzzy sets, and consequently fuzzy graphs, has solved many problems in ambiguous and uncertain contexts. It is interesting and necessary to study the Wiener index in a cubic fuzzy graph that employs both fuzzy membership and interval-valued fuzzy membership at the same time. In this paper, the Wiener index in a cubic fuzzy graph is introduced as a cubic fuzzy number and some related results are described. The comparison between connectivity index and Wiener index, changes in Wiener index through deleting a node or an edge, and determining the Wiener index in some specific cubic fuzzy graphs have been the other topics studied in this research. In addition, the Wiener index is determined by mentioning concepts of the saturated cubic fuzzy cycle. In this review, the Wiener index is shown as a combination of classical and interval numbers. The results indicate that when some vertices are removed, the Wiener index may change. However, this change will not be exclusively related to both values. Finally, an application of the Wiener index is presented in the study of the properties of some monomer molecules.

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7

Wang, Gui Xiang, and Guang Tao Zhou. "Ranking Fuzzy Numbers Based on the Mean and Fuzzy Degree of Fuzzy Number." Applied Mechanics and Materials 220-223 (November 2012): 2102–8. http://dx.doi.org/10.4028/www.scientific.net/amm.220-223.2102.

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In this paper, a novel approach to ranking fuzzy numbers based on the mean and the fuzzy degree of fuzzy number is proposed. In the approach, a new ranking index that is comprehensive consideration of the mean and the fuzzy degree of fuzzy number is constructed, and then the properties of the ranking index are given. Moreover, to compare the proposed approach with the existing approaches, numerical examples are given. The comparative results illustrate that the approach proposed in this paper is better and has simpler calculations.

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8

De, Sujit Kumar, and Shib Sankar Sana. "Fuzzy order quantity inventory model with fuzzy shortage quantity and fuzzy promotional index." Economic Modelling 31 (March 2013): 351–58. http://dx.doi.org/10.1016/j.econmod.2012.11.046.

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9

Wang, Zhenyuan, and Li Zhang-Westmant. "New Ranking Method For Fuzzy Numbers By Their Expansion Center." Journal of Artificial Intelligence and Soft Computing Research 4, no. 3 (July 1, 2014): 181–87. http://dx.doi.org/10.1515/jaiscr-2015-0007.

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Abstract Based on the area between the curve of the membership function of a fuzzy number and the horizontal real axis, a characteristic as a new numerical index, called the expansion center, for fuzzy numbers is proposed. An intuitive and reasonable ranking method for fuzzy numbers based on this characteristic is also established. The new ranking method is applicable for decision making and data analysis in fuzz environments. An important criterion of the goodness for ranking fuzzy numbers, the geometric intuitivity, is also introduced. It guarantees coinciding with the natural ordering of the real numbers.

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10

Gil, María Angeles, Miguel López-Díaz, and Hortensia López-García. "The fuzzy hyperbolic inequality index associated with fuzzy random variables." European Journal of Operational Research 110, no. 2 (October 1998): 377–91. http://dx.doi.org/10.1016/s0377-2217(97)00252-x.

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11

Fang, Juanyan, Irfan Nazeer, Tabasam Rashid, and Jia-Bao Liu. "Connectivity and Wiener Index of Fuzzy Incidence Graphs." Mathematical Problems in Engineering 2021 (February 3, 2021): 1–7. http://dx.doi.org/10.1155/2021/6682966.

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Connectivity is a key theory in fuzzy incidence graphs FIGs . In this paper, we introduced connectivity index CI , average connectivity index ACI , and Wiener index WI of FIGs . Three types of nodes including fuzzy incidence connectivity enhancing node FICEN , fuzzy incidence connectivity reducing node FICRN , and fuzzy incidence connectivity neutral node FICNN are also discussed in this paper. A correspondence between WI and CI of a FIG is also computed.

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12

Lu, Juanjuan, Linli Zhu, and Wei Gao. "Cyclic connectivity index of bipolar fuzzy incidence graph." Open Chemistry 20, no. 1 (January 1, 2022): 331–41. http://dx.doi.org/10.1515/chem-2022-0149.

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Abstract In the performance characterization of chemical molecular structures, several uncertain properties are often encountered, and fuzzy theory is precisely the tool to characterize these uncertainties. When molecular structures are described by molecular graphs, the corresponding fuzzy graph theory is used to characterize the uncertainty of atoms and atomic bonds. In this study, there is introduced cyclic connectivity index and its average version for bipolar fuzzy incidence graph (BFIG), and several theoretical results are obtained in the light of graph theory and fuzzy theory. Finally, the given new fuzzy index is applied to the testing of anti-aging-related drugs yields average uncertainty data for the corresponding molecular structures.

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13

Nishanthini, Radhakrishnan, Ramasamy Jeyabalan, Samipillai Balasundar, and Gurunathan Kumar. "Consecutive z-index vertex magic labeling graphs." Journal of Intelligent & Fuzzy Systems 41, no. 1 (August 11, 2021): 219–30. http://dx.doi.org/10.3233/jifs-201489.

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The conception of magic labeling in fuzzy graphs elongates to fuzzy vertex magic labeling together with consecutive non-integer values in (0, 1] and the graph’s repercussion is named as fuzzy consecutive vertex magic labeling graphs (FCVM) along with the z-index. In this manuscript, we give some properties associated with FCVM labeling along with z-index as well as the presence of FCVM labeling with z-index in trees and some generalizations. Moreover, we examine the FCVM labeling along with z-index of both regular and irregular graphs. Finally, in real-time applications, we bestow an instance for fuzzy consecutive vertex magic labeling graphs.

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14

Garai, Arindam, and Tapan Kumar Roy. "Intuitionistic fuzzy optimization: Usage of hesitation index." INTERNATIONAL JOURNAL OF COMPUTERS & TECHNOLOGY 10, no. 4 (August 15, 2013): 1489–95. http://dx.doi.org/10.24297/ijct.v10i4.3248.

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This paper presents the concept of usage of hesitation index in optimization problem under uncertainty. Our technique is an extension of idea of intuitionistic fuzzy optimization technique, proposed by Plamen P. Angelov in 1997, which is widely considered as a successful intuitionistic fuzzy optimization tool by researchers all over the world. It is well known that the advantages of the intuitionistic fuzzy optimization problems are twofold: firstly, they give the richest apparatus for formulation of optimization problems and on the other hand, the solution of intuitionistic fuzzy optimization problems can satisfy the objective(s) with bigger degree of satisfaction than the analogous fuzzy optimization problem and the crisp one. Angelovâ€™s approach is an application of the intuitionistic fuzzy (IF) set concept to optimization problems. In his approach, the degree of acceptance is maximized while the degree of rejection is minimized. In our approach, not only the degree of acceptance is maximized and the degree of rejection is minimized but also the degree of hesitation is minimized. For the sake simplicity alone, the same problem, as studied by Angelov, is considered. Varied importance (and hence weights) to each of the degree of acceptance and the degree of rejection and the degree of hesitation have been given. Tables with these results are formulated and compared among.

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15

Hedar, Abdel-Rahman, Alaa Abdel-Hakim, and Youseef Alotaibi. "Normalised fuzzy index for research ranking." Behaviour & Information Technology 37, no. 10-11 (June 6, 2018): 1083–96. http://dx.doi.org/10.1080/0144929x.2018.1482370.

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16

Lee, Hong Tau. "Cpk index estimation using fuzzy numbers." European Journal of Operational Research 129, no. 3 (March 2001): 683–88. http://dx.doi.org/10.1016/s0377-2217(99)00438-5.

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17

Choobineh, F., and Huishen Li. "An index for ordering fuzzy numbers." Fuzzy Sets and Systems 54, no. 3 (March 1993): 287–94. http://dx.doi.org/10.1016/0165-0114(93)90374-q.

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18

Kwon, S. H. "Cluster validity index for fuzzy clustering." Electronics Letters 34, no. 22 (1998): 2176. http://dx.doi.org/10.1049/el:19981523.

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19

Machias, A. V., and G. D. Skikos. "Fuzzy risk index of wind sites." IEEE Transactions on Energy Conversion 7, no. 4 (1992): 638–43. http://dx.doi.org/10.1109/60.182645.

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20

Kalathian, Shriram, Sujatha Ramalingam, Sundareswaran Raman, and Narasimman Srinivasan. "Some topological indices in fuzzy graphs." Journal of Intelligent & Fuzzy Systems 39, no. 5 (November 19, 2020): 6033–46. http://dx.doi.org/10.3233/jifs-189077.

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A fuzzy graph is one of the versatile application tools in the field of mathematics, which allows the user to easily describe the fuzzy relation between any objects. The nature of fuzziness is favorable for any environment, which supports to predict the problem and solving it. Fuzzy graphs are beneficial to give more precision and flexibility to the system as compared to the classical model (i.e.,) crisp theory. A topological index is a numerical quantity for the structural graph of the molecule and it can be represented through Graph theory. Moreover, its application not only in the field of chemistry can also be applied in areas including computer science, networking, etc. A lot of topological indices are available in chemical-graph theory and H. Wiener proposed the first index to estimate the boiling point of alkanes called ‘Wiener index’. Many topological indices exist only in the crisp but it’s new to the fuzzy graph environment. The main aim of this paper is to define the topological indices in fuzzy graphs. Here, indices defined in fuzzy graphs are Modified Wiener index, Hyper Wiener index, Schultz index, Gutman index, Zagreb indices, Harmonic index, and Randić index with illustrations. Bounds for some of the indices are proved. The algorithms for distance matrix and MWI are shown. Finally, the application of these indices is discussed.

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21

Ali, Abdualmtalab, Usama Heneash, Amgad Hussein, and Mohamed Eskebi. "Predicting Pavement Condition Index Using Fuzzy Logic Technique." Infrastructures 7, no. 7 (July 2, 2022): 91. http://dx.doi.org/10.3390/infrastructures7070091.

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The fuzzy logic technique is one of the effective approaches for evaluating flexible and rigid pavement distress. The process of classifying pavement distress is usually performed by visual inspection of the pavement surface or using data collected by automated distress measurement equipment. Fuzzy mathematics provides a convenient tool for incorporating subjective analysis, uncertainty in pavement condition index, and maintenance-needs assessment, and can greatly improve consistency and reduce subjectivity in this process. This paper aims to develop a fuzzy logic-based system of pavement condition index and maintenance-needs evaluation for a pavement road network by utilizing pavement distress data from the U.S. and Canada. Considering rutting, fatigue cracking, block cracking, longitudinal cracking, transverse cracking, potholes, patching, bleeding, and raveling as input variables, the variables were fuzzified into fuzzy subsets. The fuzzy subsets of the variables were considered to have triangular membership functions. The relationships between nine pavement distress parameters and PCI were represented by a set of fuzzy rules. The fuzzy rules relating input variables to the output variable of sediment discharge were laid out in the IF–THEN format. The commonly used weighted average method was employed for the defuzzification procedure. The coefficient of determination (R2), root mean squared error (RMSE), and mean absolute error (MAE) were used as the performance indicator metrics to evaluate the performance of analytical models.

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22

Nivendhaa, R. K., and R. Parvathi. "Intuitionistic fuzzy index matrix representation of color images." Notes on Intuitionistic Fuzzy Sets 26, no. 4 (December 2020): 64–70. http://dx.doi.org/10.7546/nifs.2020.26.4.64-70.

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It is usual in image processing that binary (black & white) and gray images are represented by crisp sets and fuzzy sets respectively. In this paper, an attempt has been made to represent a color image (RGB) using intuitionistic fuzzy index matrices. The objective of this representation is to apply mathematical operators on intuitionistic fuzzy index matrices in processing RGB images.

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23

Xu, Senqi, and Xinggao Liu. "Melt index prediction by fuzzy functions with dynamic fuzzy neural networks." Neurocomputing 142 (October 2014): 291–98. http://dx.doi.org/10.1016/j.neucom.2014.03.056.

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24

Mufti, Zeeshan Saleem, Eiman Fatima, Rukhshanda Anjum, Fairouz Tchier, Qin Xin, and Md Moyazzem Hossain. "Computing First and Second Fuzzy Zagreb Indices of Linear and Multiacyclic Hydrocarbons." Journal of Function Spaces 2022 (March 22, 2022): 1–8. http://dx.doi.org/10.1155/2022/6281592.

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Fuzzy graph theory was invented by Rosenfeld. It is the extension of the work of L.A. Zadeh on fuzzy sets. Rosenfeld extracted the fuzzy-related concepts using the graph theoretic concepts. Topological indices for crisp theory have already been discussed in the literature but these days, topological index-related fuzzy graphs are much popular. Fuzzy graphs are being used as an application in different fields of sciences such as broadcast, communications, producing, social network, man-made reasoning, data hypothesis, and neural systems. In this paper, we have computed some fuzzy topological indices such as first and second Zagreb indices, Randic index, and harmonic index of fuzzy chemical graph named phenylene.

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25

Du, Baoku, Wei Xiong, and Hongwang Du. "AG600 Amphibious Aircraft Selection Model Based on Improved Fuzzy Evaluation Algorithm." Computational Intelligence and Neuroscience 2022 (May 20, 2022): 1–6. http://dx.doi.org/10.1155/2022/2358264.

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Aiming at the selection research gap of AG600 amphibious aircraft for salvage of life at sea, the selection index system of AG600 has been established, and an interval intuitionistic fuzzy selection decision model based on fuzzy entropy and score function is constructed. An evaluation index system with 8 indexes was determined based on the rules of the applicability, safety, and accessibility by questionnaire and statistical analysis. Different from the traditional method of determining the fuzzy number of each index solely by experts’ scoring, this paper establishes a 5-grade fuzzy evaluation grade and index membership function, and the interval intuitionistic fuzzy number of the index is determined by combining subjective and objective methods. Fuzzy entropy and score function are used to calculate the weights of each index and AG600 selection score for different accidents, so as to obtain the matching degree of AG600 selection in marine life accidents more scientifically and reasonably. Finally, the effectiveness of the proposed model is demonstrated by a practical case.

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26

Gong, Shu, and Gang Hua. "Topological indices of bipolar fuzzy incidence graph." Open Chemistry 19, no. 1 (January 1, 2021): 894–903. http://dx.doi.org/10.1515/chem-2021-0082.

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Abstract The topological index of graph has a wide range of applications in theoretical chemistry, network design, data transmission, etc. In fuzzy graph settings, these topological indices have completely different definitions and connotations. In this work, we define new Wiener index and connectivity index for bipolar fuzzy incidence graphs, and obtain the characteristics of these indices by means of the definition of fuzzy membership functions. Furthermore, the interrelationship between Wiener index and connectivity index is considered.

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27

Hariyadi, Firma, Herry Sujaini, and Anggi Srimurdianti Sukamto. "Pengklasteran Mahasiswa UNTAN Berdasarkan IPK Menggunakan Metode Fuzzy C-Means." Jurnal Sistem dan Teknologi Informasi (Justin) 8, no. 2 (April 29, 2020): 170. http://dx.doi.org/10.26418/justin.v8i2.36506.

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Clustering merupakan salah satu metode data mining. Clustering berguna untuk mengelompokkan data (objek) yang didasarkan pada informasi yang ditemukan dalam dua data yang menggambarkan objek tersebut dan hubungan diantaranya. Mahasiswa dituntut untuk aktif dalam proses belajar mengajar melalui media yang ada. Keberhasilan mahasiswa dalam bidang akademik ditandai dengan prestasi akademik yang dicapai, ditunjukkan melalui indek prestasi (IP) maupun indek prestasi kumulatif (IPK). Jumlah data yang banyak ini membuka peluang untuk menghasilkan informasi yang berguna untuk pihak universitas, fakultas dan prodi. Penelitian ini bertujuan untuk menghasilkan aplikasi pengklasteran mahasiswa berdasarkan nilai IPK dan nilai IPS dengan menerapkan metode fuzzy c-means. Fuzzy C-means menerapkan pengelompokan fuzzy, dimana setiap data dapat menjadi anggota dari beberapa cluster dengan derajat keanggotaan yang berbeda-beda pada setiap cluster. Metode Partition Coeffiecient Index (PCI) merupakan proses pengujian validasi fuzzy clustering dengan menghitung koefisien partisi atau PC sebagai evaluasi nilai derajat keanggotaan, tanpa memandang vector (data) yang biasa mengandung informasi. Berdasarkan hasil pengujian dengan perhitungan metode Partition Coeffiecient Index (PCI) yang telah dilakukan, diketahui bahwa perbedaan hasil evaluasi dapat terjadi antara cluster. Perbedaan hasil evaluasi Partition Coeffiecient Index (PCI) disebabkan oleh jumlah cluster. Hasil dari pengujian Partition Coeffiecient Index (PCI), dapat diketahui bahwa banyaknya cluster menentukan nilai evaluasi cluster. Semakin tinggi nilai kualitas evaluasi cluster, maka akan semakin baik pula tingkat kemiripan suatu cluster.

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28

Sun, Yong Jian. "A Study of the Assessment on Air Quality on Fuzzy Comprehensive Index." Applied Mechanics and Materials 602-605 (August 2014): 3522–25. http://dx.doi.org/10.4028/www.scientific.net/amm.602-605.3522.

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This paper discusses the assessment problem on air quality. It will firstly make analysis on part irrationality of existing AQI and then introduces into concept of fuzzy mathematics on this basis. It makes index assessment on regional air quality according to 6 index values of selected air quality. Firstly, it will use fuzzy mathematics as basis to establish model of fuzzy comprehensive index and adopt weighting method of excess multiple considering each index to determine the weight, secondly it uses membership function of half-step trapezoidal method to determine its membership grade and makes compound operation to obtain fuzzy comprehensive assessment matrix, finally it makes fuzzy vector uniformization to get the new air quality index as well as uses national standard as reference limits to divide it into 6 grades and comprehensively makes index assessment on air quality.

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29

Qiu, Wangren, Ping Zhang, and Yanhong Wang. "Fuzzy Time Series Forecasting Model Based on Automatic Clustering Techniques and Generalized Fuzzy Logical Relationship." Mathematical Problems in Engineering 2015 (2015): 1–8. http://dx.doi.org/10.1155/2015/962597.

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In view of techniques for constructing high-order fuzzy time series models, there are three types which are based on advanced algorithms, computational method, and grouping the fuzzy logical relationships. The last type of models is easy to be understood by the decision maker who does not know anything about fuzzy set theory or advanced algorithms. To deal with forecasting problems, this paper presented novel high-order fuzz time series models denoted as GTS(M, N)based on generalized fuzzy logical relationships and automatic clustering. This paper issued the concept of generalized fuzzy logical relationship and an operation for combining the generalized relationships. Then, the procedure of the proposed model was implemented on forecasting enrollment data at the University of Alabama. To show the considerable outperforming results, the proposed approach was also applied to forecasting the Shanghai Stock Exchange Composite Index. Finally, the effects of parametersMandN, the number of order, and concerned principal fuzzy logical relationships, on the forecasting results were also discussed.

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30

Nadweh, Rama Asad. "On The Fuzzy Semi Sub-Modules of Fuzzy Modules." Galoitica: Journal of Mathematical Structures and Applications 5, no. 1 (2023): 45–48. http://dx.doi.org/10.54216/gjmsa.050104.

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In this paper, we introduce the concept of fuzzy semi-essential (large) submodule, and we study a necessary and sufficient condition for a fuzzy submodule of a fuzzy module to be a fuzzy semi-essential (large) submodule, also fuzzy images and fuzzy inverse-images of generalized fuzzy semi-essential (large) submodule are studied. Index Terms

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31

Jiang, Huiqin, and Yongsheng Rao. "Connectivity Index in Vague Graphs with Application in Construction." Discrete Dynamics in Nature and Society 2022 (February 15, 2022): 1–15. http://dx.doi.org/10.1155/2022/9082693.

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The vague graph (VG), which has recently gained a place in the family of fuzzy graph (FG), has shown good capabilities in the face of problems that cannot be expressed by fuzzy graphs and interval-valued fuzzy graphs. Connectivity index (CI) in graphs is a fundamental issue in fuzzy graph theory that has wide applications in the real world. The previous definitions’ limitations in the connectivity of fuzzy graphs directed us to offer new classifications in vague graph. Hence, in this paper, we investigate connectivity index, average connectivity index, and Randic index in vague graphs with several examples. Also, one of the motives of this research is to introduce some special types of vertices such as vague connectivity enhancing vertex, vague connectivity reducing vertex, and vague connectivity neutral vertex with their properties. Finally, an application of connectivity index in the selected town for building hospital is presented.

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32

Islam, Sk Rabiul, and Madhumangal Pal. "Hyper-Wiener index for fuzzy graph and its application in share market." Journal of Intelligent & Fuzzy Systems 41, no. 1 (August 11, 2021): 2073–83. http://dx.doi.org/10.3233/jifs-210736.

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Topological indices have an important role in molecular chemistry, network theory, spectral graph theory and several physical worlds. Most of the topological indices are defined in a crisp graph. As fuzzy graphs are more generalization of crisp graphs, those indices have more application in fuzzy graphs also. In this article, we introduced the fuzzy hyper-Wiener index (FHWI) and studied this index for various fuzzy graphs like path, cycle, star, etc and provided some interesting bounds of FHWI for that fuzzy graph. A lower bound of FHWI is established for n-vertex connected fuzzy graph depending on strength of a strong edges. A relation between FHWI of a tree and its maximum spanning tree is established and this index is calculated for the saturated cycle. Also, at the end of the article, an application in the share market of this index is presented.

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33

Nguyen, Thanh-Lam. "Methods in Ranking Fuzzy Numbers: A Unified Index and Comparative Reviews." Complexity 2017 (2017): 1–13. http://dx.doi.org/10.1155/2017/3083745.

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Fuzzy set theory, extensively applied in abundant disciplines, has been recognized as a plausible tool in dealing with uncertain and vague information due to its prowess in mathematically manipulating the knowledge of imprecision. In fuzzy-data comparisons, exploring the general ranking measure that is capable of consistently differentiating the magnitude of fuzzy numbers has widely captivated academics’ attention. To date, numerous indices have been established; however, counterintuition, less discrimination, and/or inconsistency on their fuzzy-number rating outcomes have prohibited their comprehensive implementation. To ameliorate their manifested ranking weaknesses, this paper proposes a unified index that multiplies weighted-mean and weighted-area discriminatory components of a fuzzy number, respectively, called centroid value and attitude-incorporated left-and-right area. From theoretical proof of consistency property and comparative studies for triangular, triangular-and-trapezoidal mixed, and nonlinear fuzzy numbers, the unified index demonstrates conspicuous ranking gains in terms of intuition support, consistency, reliability, and computational simplicity capability. More importantly, the unified index possesses the consistency property for ranking fuzzy numbers and their images as well as for symmetric fuzzy numbers with an identical altitude which is a rather critical property for accurate matching and/or retrieval of information in the field of computer vision and image pattern recognition.

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34

Lu, Juanjuan, Linli Zhu, and Wei Gao. "Remarks on bipolar cubic fuzzy graphs and its chemical applications." International Journal of Mathematics and Computer in Engineering 1, no. 1 (March 28, 2023): 1–10. http://dx.doi.org/10.2478/ijmce-2023-0001.

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Abstract In theoretical chemistry, fuzzy molecular graphs can be used to model chemical molecular structures with uncertainty information, where the vertex membership function and edge membership function describe the uncertainty of atoms and chemical bonds respectively. This paper studies chemical topological index of bipolar cubic fuzzy graphs. The new concepts and theorems are given in terms of graph theory and fuzzy set theory approaches and several theoretical conclusions on bipolar Wiener index of bipolar cubic fuzzy graphs are determined. Furthermore, we apply it in chemical science and calculate the bipolar Wiener index of dimethyltryptamine and hallucinogen which are modelled by bipolar cubic fuzzy graphs.

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35

Cai, De Hua, Xi Yang, Rui Chuang Wang, Cheng Zhi Ma, Jin Cheng, and Xiao Long Zhang. "Power Transformers Health Index Calculation Method Based on Cloud Model and Fuzzy Evidential Reasoning." Advanced Materials Research 1070-1072 (December 2014): 1021–28. http://dx.doi.org/10.4028/www.scientific.net/amr.1070-1072.1021.

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Transformers health index calculation method based on cloud model and fuzzy evidential reasoning is proposed. According to the multi-level and multifactor of evaluation index information of power transformers, a layered evaluation index model is established. In order to deal with the ambiguity and uncertainty information of evaluation index, a normal cloud model is introduced, inferred the fuzzy degree of belief in the health state of evaluation index. Then use the fuzzy evidential reasoning method merge information of evaluation Index, inferred the degree of belief in the health state-level of transformer, calculated the health index of transformer. The results of an example analysis test its rationality and effectiveness.

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36

Martino, Ferdinando Di, and Salvatore Sessa. "A New Validity Index Based on Fuzzy Energy and Fuzzy Entropy Measures in Fuzzy Clustering Problems." Entropy 22, no. 11 (October 23, 2020): 1200. http://dx.doi.org/10.3390/e22111200.

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Two well-known drawbacks in fuzzy clustering are the requirement of assigning in advance the number of clusters and random initialization of cluster centers. The quality of the final fuzzy clusters depends heavily on the initial choice of the number of clusters and the initialization of the clusters, then, it is necessary to apply a validity index to measure the compactness and the separability of the final clusters and run the clustering algorithm several times. We propose a new fuzzy C-means algorithm in which a validity index based on the concepts of maximum fuzzy energy and minimum fuzzy entropy is applied to initialize the cluster centers and to find the optimal number of clusters and initial cluster centers in order to obtain a good clustering quality, without increasing time consumption. We test our algorithm on UCI (University of California at Irvine) machine learning classification datasets comparing the results with the ones obtained by using well-known validity indices and variations of fuzzy C-means by using optimization algorithms in the initialization phase. The comparison results show that our algorithm represents an optimal trade-off between the quality of clustering and the time consumption.

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37

Atanassov, Krassimir, Peter Vassilev, and Olympia Roeva. "Level Operators over Intuitionistic Fuzzy Index Matrices." Mathematics 9, no. 4 (February 11, 2021): 366. http://dx.doi.org/10.3390/math9040366.

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The index matrix (IM) is an extension of the ordinary matrix with indexed rows and columns. Over IMs’ standard matrix operations are defined and a lot of other ones that do not exist in the standard case. Intuitionistic fuzzy IMs (IFIMs) are modification of the IMs, when their elements are intuitionistic fuzzy pairs (IFPs). Extended IFIMs are IFIMs whose indices of the rows and columns are evaluated by IFPs. Different operations, relations and operators over IFIMs, and some specific ones, are defined for EIFIMs. In the paper, twelve new level operators are defined for EIFIMs and in the partial case, over IFIMs. The proposed level operators fall into two groups: operators that change the values of the EIFIM elements and operators that change the IFPs associated to the indices of the rows and columns. The basic properties of the operators are studied.

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38

Georgescu, Irina. "Arrow Index of a Fuzzy Choice Function." Fundamenta Informaticae 99, no. 3 (2010): 245–61. http://dx.doi.org/10.3233/fi-2010-248.

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39

El Mousalami, Haytham H. "Fuzzy logic for preconstruction project planning index." MOJ Civil Engineering 5, no. 1 (2019): 5–19. http://dx.doi.org/10.15406/mojce.2019.05.00143.

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40

Kang, Man-Ki, and Young-Rye Park. "Fuzzy Binomial Proportion Test by Agreement Index." Journal of Korean Institute of Intelligent Systems 19, no. 1 (February 25, 2009): 19–24. http://dx.doi.org/10.5391/jkiis.2009.19.1.019.

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41

Kale, Serdar. "Fuzzy Intellectual Capital Index for Construction Firms." Journal of Construction Engineering and Management 135, no. 6 (June 2009): 508–17. http://dx.doi.org/10.1061/(asce)co.1943-7862.0000014.

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42

Gildeh, B. S., and S. Asghari. "Inertial capability index based on fuzzy data." International Journal of Metrology and Quality Engineering 2, no. 1 (2011): 45–49. http://dx.doi.org/10.1051/ijmqe/2011008.

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43

Dahda, S. S., D. Andesta, and A. S. Wicaksono. "Measuring leanness index using fuzzy logic approach." Journal of Physics: Conference Series 1469 (February 2020): 012040. http://dx.doi.org/10.1088/1742-6596/1469/1/012040.

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44

Wu, Kuo-Lung, and Miin-Shen Yang. "A cluster validity index for fuzzy clustering." Pattern Recognition Letters 26, no. 9 (July 2005): 1275–91. http://dx.doi.org/10.1016/j.patrec.2004.11.022.

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45

Tsai, Chang-Chun, and Cheng-Che Chen. "Measuring process capability index Cpkwith fuzzy data." Journal of Information and Optimization Sciences 27, no. 3 (September 2006): 733–46. http://dx.doi.org/10.1080/02522667.2006.10699722.

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46

Pal, Sankar K., Jayanta Basak, and Rajat K. De. "Fuzzy feature evaluation index and connectionist realization." Information Sciences 105, no. 1-4 (March 1998): 173–88. http://dx.doi.org/10.1016/s0020-0255(97)10023-8.

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47

Pakhira, Malay K., Sanghamitra Bandyopadhyay, and Ujjwal Maulik. "Validity index for crisp and fuzzy clusters." Pattern Recognition 37, no. 3 (March 2004): 487–501. http://dx.doi.org/10.1016/j.patcog.2003.06.005.

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48

Grekousis, George, and Yorgos N. Fotis. "A fuzzy index for detecting spatiotemporal outliers." GeoInformatica 16, no. 3 (October 12, 2011): 597–619. http://dx.doi.org/10.1007/s10707-011-0145-4.

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49

Boutros, Tony, and Ming Liang. "Mechanical fault detection using fuzzy index fusion." International Journal of Machine Tools and Manufacture 47, no. 11 (September 2007): 1702–14. http://dx.doi.org/10.1016/j.ijmachtools.2007.01.001.

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50

Rezaee, Babak. "A cluster validity index for fuzzy clustering." Fuzzy Sets and Systems 161, no. 23 (December 2010): 3014–25. http://dx.doi.org/10.1016/j.fss.2010.07.005.

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