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Journal articles on the topic 'FUZZY SIMILARITY'

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Author: Grafiati

Published: 11 September 2023

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1

BEG, ISMAT, and SAMINA ASHRAF. "FUZZY SIMILARITY AND MEASURE OF SIMILARITY WITH LUKASIEWICZ IMPLICATOR." New Mathematics and Natural Computation 04, no. 02 (July 2008): 191–206. http://dx.doi.org/10.1142/s1793005708000994.

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Given a universe of discourse X. A fuzzy similarity mapping ST,Inc : F(X) × F(X) → F(X) is defined, where F(X) denotes the set of all fuzzy subsets of X. Mapping ST,Inc maps two fuzzy sets A and B to a fuzzy set ST,Inc(A,B) in X called their fuzzy set of similarity. A measure of similarity between A and B is then obtained by applying the composite of fuzzy measure and fuzzy similarity mapping on the pair (A,B). Several properties of fuzzy set of similarity and the measure of fuzzy similarity are obtained within the framework of Lukasiewicz fuzzy implicator and its respective t-norm and t-conorm. Many examples of measure of similarity are also constructed.

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2

Phong, Pham Hong, and Vu Thi Hue. "On Integration Linguistic Factors to Fuzzy Similarity Measures and Intuitionistic Fuzzy Similarity Measures." International Journal of Synthetic Emotions 10, no. 1 (January 2019): 1–37. http://dx.doi.org/10.4018/ijse.2019010101.

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The article is concerned with integrating linguistic elements into fuzzy similarity measures and intuitionistic fuzzy similarity measure. Some new concepts are proposed: a fuzzy linguistic value (FLv), a fuzzy linguistic vector (FLV), an intuitionistic fuzzy linguistic vector (ILV) and similarity measures. The proposed measures are used to build classification algorithms. As predicted theoretically, experiments show that with the same type of similarity measures, the linguistic-aggregated similarity measures produce better results in classification problems.

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3

BEG, ISMAT, and SAMINA ASHRAF. "FUZZY INCLUSION AND FUZZY SIMILARITY WITH GÖDEL FUZZY IMPLICATOR." New Mathematics and Natural Computation 05, no. 03 (November 2009): 617–33. http://dx.doi.org/10.1142/s1793005709001489.

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Fuzzy inclusion and fuzzy similarity are introduced as mappings which produce fuzzy sets constructed with the help of Gödel implicator. The properties of resulting fuzzy sets of inclusion and similarity are studied in detail. Some axiomatic characteristics for being fuzzy orders and fuzzy equivalence relations are also included.

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4

Soylu, Gültekin. "Similarity-based fuzzy limits." Fuzzy Sets and Systems 159, no. 24 (December 2008): 3380–87. http://dx.doi.org/10.1016/j.fss.2008.03.026.

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5

Calvo, Tomasa. "On fuzzy similarity relations." Fuzzy Sets and Systems 47, no. 1 (April 1992): 121–23. http://dx.doi.org/10.1016/0165-0114(92)90069-g.

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6

Liu, Xiao Jing, Wei Feng Du, and Xiao Min. "Fuzzy Attribute Reduction Based on Fuzzy Similarity." Applied Mechanics and Materials 533 (February 2014): 237–41. http://dx.doi.org/10.4028/www.scientific.net/amm.533.237.

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The measure of the significance of the attribute and attribute reduction is one of the core content of rough set theory. The classical rough set model based on equivalence relation, suitable for dealing with discrete-valued attributes. Fuzzy-rough set theory, integrating fuzzy set and rough set theory together, extending equivalence relation to fuzzy relation, can deal with fuzzy-valued attributes. By analyzing three problems of FRAR which is a fuzzy decision table attribute reduction algorithm having extensive use, this paper proposes a new reduction algorithm which has better overcome the problem, can handle larger fuzzy decision table. Experimental results show that our reduction algorithm is much quicker than the FRAR algorithm.

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7

Ovchinnikov, Sergei. "Similarity relations, fuzzy partitions, and fuzzy orderings." Fuzzy Sets and Systems 40, no. 1 (March 1991): 107–26. http://dx.doi.org/10.1016/0165-0114(91)90048-u.

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8

Wang, De-Gang, Yan-Ping Meng, and Hong-Xing Li. "A fuzzy similarity inference method for fuzzy reasoning." Computers & Mathematics with Applications 56, no. 10 (November 2008): 2445–54. http://dx.doi.org/10.1016/j.camwa.2008.03.054.

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9

Gora, Pawan. "Intuitionistic Fuzzy Modulus Similarity Measure." International Journal of Decision Support System Technology 15, no. 1 (January 1, 2023): 1–22. http://dx.doi.org/10.4018/ijdsst.315757.

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The concept of intuitionistic fuzzy sets (IFSs) is an expected explanation for finding the appropriate information. It originated from concept of fuzzy set (FS) theory, which extends the classical conception of a fuzzy set. This paper examines a number of widely employed similarity measures then proposes an IFSs modulus similarity measure and a weight similarity measure. Initially, the authors have discussed numerous existing similarity measures, some of which are unable to justify the axioms of being a similarity measure. Furthermore, some numerical examples are presented to compare the existing similarity measures with the proposed similarity measure. The proposed similarity measure is a practical and effective method for determining the qualitative similarity between IFSs, which do not have any paradoxical nature. In addition, the proposed similarity measure has been demonstrated practically in pattern recognition and medical diagnosis problem. Suggestions for future research comprise the conclusions of the paper.

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10

Ghosh, Debdas, and Debjani Chakraborty. "On Similarity of Fuzzy Triangles." International Journal of Fuzzy Logic Systems 3, no. 4 (October 31, 2013): 1–15. http://dx.doi.org/10.5121/ijfls.2013.3401.

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11

Georgescu, Irina. "Similarity of fuzzy choice functions." Fuzzy Sets and Systems 158, no. 12 (June 2007): 1314–26. http://dx.doi.org/10.1016/j.fss.2007.01.009.

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12

Frélicot, Carl, and Hoel Le Capitaine. "Block similarity in fuzzy tuples." Fuzzy Sets and Systems 220 (June 2013): 53–68. http://dx.doi.org/10.1016/j.fss.2012.08.012.

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13

Lee, S. H., and D. Zhang. "Dual fuzzy similarity relation equations." Computers & Mathematics with Applications 27, no. 11 (July 1994): 49–53. http://dx.doi.org/10.1016/0898-1221(94)90097-3.

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14

Belohlavek, R. "Similarity and Fuzzy Tolerance Spaces." Journal of Logic and Computation 14, no. 6 (December 1, 2004): 827–55. http://dx.doi.org/10.1093/logcom/14.6.827.

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15

Belohlavek, Radim, and Michal Krupka. "Grouping fuzzy sets by similarity." Information Sciences 179, no. 15 (July 2009): 2656–61. http://dx.doi.org/10.1016/j.ins.2009.03.020.

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16

Chaudhari, N. S., and Xiangrui Wang. "Language Structure Using Fuzzy Similarity." IEEE Transactions on Fuzzy Systems 17, no. 5 (October 2009): 1011–24. http://dx.doi.org/10.1109/tfuzz.2009.2020155.

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17

CHEN, SHYI-MING, and YONATHAN RANDYANTO. "A NOVEL SIMILARITY MEASURE BETWEEN INTUITIONISTIC FUZZY SETS AND ITS APPLICATIONS." International Journal of Pattern Recognition and Artificial Intelligence 27, no. 07 (November 2013): 1350021. http://dx.doi.org/10.1142/s0218001413500213.

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In this paper, we propose a novel similarity measure between intuitionistic fuzzy sets and apply it to deal with pattern recognition problems and medical diagnosis problems. First, we propose a new similarity measure between intuitionistic fuzzy values based on the medians of intervals, the Hausdorff distance, and the ratio of the uncertainty degrees of intuitionistic fuzzy values. We also prove some properties of the proposed similarity measure between intuitionistic fuzzy values. Then, based on the proposed similarity measure between intuitionistic fuzzy values, we propose a novel similarity measure between intuitionistic fuzzy sets. It can overcome the drawbacks of existing methods for measuring the degree of similarity between intuitionistic fuzzy sets. We also prove some properties of the proposed similarity measure between intuitionistic fuzzy sets. Finally, we apply the proposed similarity measure between intuitionistic fuzzy sets to deal with pattern recognition problems and medical diagnosis problems.

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18

Zhou, Jing Li, Xue Jun Nie, Lei Hua Qin, and Jian Feng Zhu. "Document Clustering Based on Fuzzy Similarity." Applied Mechanics and Materials 29-32 (August 2010): 2620–26. http://dx.doi.org/10.4028/www.scientific.net/amm.29-32.2620.

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This paper proposes a novel fuzzy similarity measure based on the relationships between terms and categories. A term-category matrix is presented to represent such relationships and each element in the matrix denotes a membership degree that a term belongs to a category, which is computed using term frequency inverse document frequency and fuzzy relationships between documents and categories. Fuzzy similarity takes into account the situation that one document belongs to multiple categories and is computed using fuzzy operators. The experimental results show that the proposed fuzzy similarity surpasses other common similarity measures not only in the reliable derivation of document clustering results, but also in document clustering accuracies.

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19

Zheng, Gao. "A Similarity Measure between Fuzzy Sets." Applied Mechanics and Materials 229-231 (November 2012): 2663–66. http://dx.doi.org/10.4028/www.scientific.net/amm.229-231.2663.

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The similarity measure is one of the most useful fuzzy measures in fuzzy logic theory. In this paper, we propose a new similarity measure between fuzzy sets. As a preparation, we first choose an axiomatic definition for the similarity measure. Then, according to the chosen axiomatic definition, we propose a new computation formula. Finally, we give two examples to validate its performance. The results show that the new similarity measure is rational for fuzzy sets.

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20

.., M., V. Kamalakannan, S. M. Chithra, and Broumi Said. "Pseudo Similarity of Neutrosophic Fuzzy matrices." International Journal of Neutrosophic Science 20, no. 4 (2023): 191–96. http://dx.doi.org/10.54216/ijns.200415.

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In this paper, first we shall define Pseudo Similarity for Neutrosophic Fuzzy Matrices and prove that Pseudo Similarity relation on pair of Neutrosophic Fuzzy Matrices. Also, we derive some relation between Pseudo Similarity and Idempotent matrices. Finally, we give in varies inverse of Neutrosophic Fuzzy Matrices.

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21

Liu, Peide, Muhammad Munir, Tahir Mahmood, and Kifayat Ullah. "Some Similarity Measures for Interval-Valued Picture Fuzzy Sets and Their Applications in Decision Making." Information 10, no. 12 (November 25, 2019): 369. http://dx.doi.org/10.3390/info10120369.

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Similarity measures, distance measures and entropy measures are some common tools considered to be applied to some interesting real-life phenomena including pattern recognition, decision making, medical diagnosis and clustering. Further, interval-valued picture fuzzy sets (IVPFSs) are effective and useful to describe the fuzzy information. Therefore, this manuscript aims to develop some similarity measures for IVPFSs due to the significance of describing the membership grades of picture fuzzy set in terms of intervals. Several types cosine similarity measures, cotangent similarity measures, set-theoretic and grey similarity measures, four types of dice similarity measures and generalized dice similarity measures are developed. All the developed similarity measures are validated, and their properties are demonstrated. Two well-known problems, including mineral field recognition problems and multi-attribute decision making problems, are solved using the newly developed similarity measures. The superiorities of developed similarity measures over the similarity measures of picture fuzzy sets, interval-valued intuitionistic fuzzy sets and intuitionistic fuzzy sets are demonstrated through a comparison and numerical examples.

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22

Song, Yafei, Xiaodan Wang, Lei Lei, and Aijun Xue. "A New Similarity Measure between Intuitionistic Fuzzy Sets and Its Application to Pattern Recognition." Abstract and Applied Analysis 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/384241.

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As a generation of ordinary fuzzy set, the concept of intuitionistic fuzzy set (IFS), characterized both by a membership degree and by a nonmembership degree, is a more flexible way to cope with the uncertainty. Similarity measures of intuitionistic fuzzy sets are used to indicate the similarity degree between intuitionistic fuzzy sets. Although many similarity measures for intuitionistic fuzzy sets have been proposed in previous studies, some of those cannot satisfy the axioms of similarity or provide counterintuitive cases. In this paper, a new similarity measure and weighted similarity measure between IFSs are proposed. It proves that the proposed similarity measures satisfy the properties of the axiomatic definition for similarity measures. Comparison between the previous similarity measures and the proposed similarity measure indicates that the proposed similarity measure does not provide any counterintuitive cases. Moreover, it is demonstrated that the proposed similarity measure is capable of discriminating difference between patterns.

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23

Boora, Rozy, and Vijay Prakash Tomar. "Two Trigonometric Intuitionistic Fuzzy Similarity Measures." International Journal of Decision Support System Technology 14, no. 1 (January 2022): 1–23. http://dx.doi.org/10.4018/ijdsst.286694.

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Intuitionistic Fuzzy Sets(1986) invented by Atanassov(Atanassov, 1986) has gained the wide popularity among various researchers because of its applications in various fields such as image processing, edge detection, medical diagnosis, pattern recognition etc. One of the significant tool by which the decision can be made is Intuitionistic Fuzzy Similarity Measure. In this communication, the authors have introduced two new Intuitionistic fuzzy similarity measures based on the trigonometric functions and its validity is proved. The proposed similarity measure is applied to medical diagnosis and pattern recognition.

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24

K., SELVAKUMARI. "Similarity Measure in Dengue Diagnosis Problem Using Intuitionistic Fuzzy Set." Journal of Research on the Lepidoptera 51, no. 2 (April 20, 2020): 73–79. http://dx.doi.org/10.36872/lepi/v51i2/301079.

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25

Kundu, Sukhamay. "Similarity relations, fuzzy linear orders, and fuzzy partial orders." Fuzzy Sets and Systems 109, no. 3 (February 2000): 419–28. http://dx.doi.org/10.1016/s0165-0114(97)00370-9.

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26

BHUTANI, KIRAN R., and JOHN N. MORDESON. "SIMILARITY RELATIONS, VAGUE GROUPS, AND FUZZY SUBGROUPS." New Mathematics and Natural Computation 02, no. 03 (November 2006): 195–208. http://dx.doi.org/10.1142/s1793005706000488.

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We define vague groups in terms of similarity relations rather than fuzzy equalities. This yields a bijection between the set of all right-invariant similarity relations on a group and the set of all fuzzy subgroups of the group. Under this bijection, right-invariant and left-invariant similarity relations correspond to normal fuzzy subgroups. We show how this bijection allows for the transfer of results between vague groups and fuzzy subgroups. In particular, certain numerical invariants that characterize fuzzy subgroups of an Abelian group can be used to characterize vague groups.

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27

Shahari, Nor Azni, and Khairulanwar Rasmani. "Job satisfaction evaluation based on fuzzy conjoint method with continuous fuzzy sets." Indonesian Journal of Electrical Engineering and Computer Science 19, no. 1 (July 1, 2020): 363. http://dx.doi.org/10.11591/ijeecs.v19.i1.pp363-370.

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<span lang="EN-GB">Fuzzy conjoint method (FCM) is one of the available methods suggested for job satisfaction evaluation. The main feature of job satisfaction evaluation is the use of rating of agreement to indicate employee feelings and beliefs about their job. Currently the linguistic terms used for rating of agreement in FCM are represented in the form of discrete fuzzy sets. This paper investigates the potential use of continuous fuzzy sets to represent linguistic terms used in the FCM process. To investigate the consistency of the decision outcomes produced by the proposed approach, four different types of fuzzy similarity measures were used: similarity based on Matching Function, similarity based on Euclidean Distance, similarity based on Set-Theoretic and similarity based on vector. These classification outcomes are also compared with classification drawn on the basis of statistical inference. The finding of this study shows that both discrete fuzzy sets and continuous fuzzy sets produce consistent results regardless of whether the fuzzy similarity measure was used. Hence, the inclusion of other methods in FCM is particularly very useful for calculating the closeness coefficients and specifically addresses the shortcoming in FCM for job satisfaction evaluation. </span>

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28

Zhang, Xixiang, Weimin Ma, and Liping Chen. "New Similarity of Triangular Fuzzy Number and Its Application." Scientific World Journal 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/215047.

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The similarity of triangular fuzzy numbers is an important metric for application of it. There exist several approaches to measure similarity of triangular fuzzy numbers. However, some of them are opt to be large. To make the similarity well distributed, a new method SIAM (Shape’s Indifferent Area and Midpoint) to measure triangular fuzzy number is put forward, which takes the shape’s indifferent area and midpoint of two triangular fuzzy numbers into consideration. Comparison with other similarity measurements shows the effectiveness of the proposed method. Then, it is applied to collaborative filtering recommendation to measure users’ similarity. A collaborative filtering case is used to illustrate users’ similarity based on cloud model and triangular fuzzy number; the result indicates that users’ similarity based on triangular fuzzy number can obtain better discrimination. Finally, a simulated collaborative filtering recommendation system is developed which uses cloud model and triangular fuzzy number to express users’ comprehensive evaluation on items, and result shows that the accuracy of collaborative filtering recommendation based on triangular fuzzy number is higher.

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29

Batyrshin, Ildar Z., and Edit Tóth-Laufer. "Bipolar Dissimilarity and Similarity Correlations of Numbers." Mathematics 10, no. 5 (March 2, 2022): 797. http://dx.doi.org/10.3390/math10050797.

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Many papers on fuzzy risk analysis calculate the similarity between fuzzy numbers. Usually, they use symmetric and reflexive similarity measures between parameters of fuzzy sets or “centers of gravity” of generalized fuzzy numbers represented by real numbers. This paper studies bipolar similarity functions (fuzzy relations) defined on a domain with involutive (negation) operation. The bipolarity property reflects a structure of the domain with involutive operation, and bipolar similarity functions are more suitable for calculating a similarity between elements of such domain. On the set of real numbers, similarity measures should take into account symmetry between positive and negative numbers given by involutive negation of numbers. Another reason to consider bipolar similarity functions is that these functions define measures of correlation (association) between elements of the domain. The paper gives a short introduction to the theory of correlation functions defined on sets with an involutive operation. It shows that the dissimilarity function generating Pearson’s correlation coefficient is bipolar. Further, it proposes new normalized similarity and dissimilarity functions on the set of real numbers. It shows that non-bipolar similarity functions have drawbacks in comparison with bipolar similarity functions. For this reason, bipolar similarity measures can be recommended for use in fuzzy risk analysis. Finally, the correlation functions between numbers corresponding to bipolar similarity functions are proposed.

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30

Tang, Hui-Chin, and Kuan-Sheng Cheng. "Counterintuitive Test Problems for Transformed Fuzzy Number-Based Similarity Measures between Intuitionistic Fuzzy Sets." Symmetry 11, no. 5 (May 2, 2019): 612. http://dx.doi.org/10.3390/sym11050612.

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This paper analyzes the counterintuitive behaviors of transformed fuzzy number (FN)- based similarity measures between intuitionistic fuzzy sets (IFSs). Among these transformed FN-based similarity measures, Chen and Chang’s similarity measure (2015) is a novel one. An algorithm of computing Chen and Chang’s similarity measure is proposed. We analyze the counterintuitive behaviors of Chen and Chang’s similarity measure for seven general test problems and four test problems with three inclusive IFSs. The results indicate that there are six counterintuitive test problems for Chen and Chang’s similarity measure.

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31

Lee, Sang-Hyuk, Wook-Je Park, and Dong-yean Jung. "Similarity measure design and similarity computation for discrete fuzzy data." Journal of Central South University 18, no. 5 (October 2011): 1602–8. http://dx.doi.org/10.1007/s11771-011-0878-0.

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32

Dewi, Meira Parma, and Nurtami Soedarsono. "The Similarity Measurement of Human DNA Profile Using Fuzzy Similarity." Eksakta : Berkala Ilmiah Bidang MIPA 21, no. 1 (April 30, 2020): 46–53. http://dx.doi.org/10.24036/eksakta/vol21-iss1/216.

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This research investigated the similarity of human DNA profile using fuzzy similarity measure. The similarity measurement of DNA profile had been done by measuring the similarity between query’s DNA profile and its biological family such as father, mother, brother, sister, grandmother and grandfather. The similarity measurement had been done to the short tandem repeat (STR) alleles in sixteen loci. The result of the experiment showed that each simulation gave matching result. This research is useful for Indonesian National Police (POLRI) in identifying process of disaster victim, terrorism victim and other criminal conduct.

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33

Tiwari, Pratiksha. "Generalized Entropy and Similarity Measure for Interval-Valued Intuitionistic Fuzzy Sets With Application in Decision Making." International Journal of Fuzzy System Applications 10, no. 1 (January 2021): 64–93. http://dx.doi.org/10.4018/ijfsa.2021010104.

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Interval-valued intuitionistic fuzzy environment is appropriate for most of the practical scenarios involving uncertainty, vagueness, and insufficient information. Entropy, similarity, distance, inclusion, and cross entropy measures are a few methods used for measuring uncertainty and classifying fuzzy sets and its generalizations. Entropy of a fuzzy set describes fuzziness degree of the set and similarity measure measures similarity between two fuzzy or members of its extended family. This paper presents generalized entropy and similarity measures for interval-valued intuitionistic fuzzy sets. Further, the proposed similarity measure is compared with some existing measure of similarity with the help of an illustrative example, and a method is used to define optimal point using the existing information. Finally, entropy and similarity measures are used to identify best alternatives to solve multi-attribute decision making.

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34

Guo, Wenping, Lvqing Bi, Bo Hu, and Songsong Dai. "Cosine Similarity Measure of Complex Fuzzy Sets and Robustness of Complex Fuzzy Connectives." Mathematical Problems in Engineering 2020 (July 22, 2020): 1–9. http://dx.doi.org/10.1155/2020/6716819.

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Complex fuzzy set (CFS), as a generalization of fuzzy set (FS), is characterized by complex-valued membership degrees. By considering the complex-valued membership degree as a vector in the complex unit disk, we introduce the cosine similarity measures between CFSs. Then, we investigate some invariance properties of the cosine similarity measure. Finally, the cosine similarity measure is applied to measure the robustness of complex fuzzy connectives and complex fuzzy inference.

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35

Kehagias, A., and M. Konstantinidou. "L-fuzzy valued inclusion measure, L-fuzzy similarity and L-fuzzy distance." Fuzzy Sets and Systems 136, no. 3 (June 2003): 313–32. http://dx.doi.org/10.1016/s0165-0114(02)00407-4.

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36

HUNG, WEN-LIANG, and MIIN-SHEN YANG. "SIMILARITY MEASURES BETWEEN TYPE-2 FUZZY SETS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 12, no. 06 (December 2004): 827–41. http://dx.doi.org/10.1142/s0218488504003235.

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In this paper, we give similarity measures between type-2 fuzzy sets and provide the axiom definition and properties of these measures. For practical use, we show how to compute the similarities between Gaussian type-2 fuzzy sets. Yang and Shih's [22] algorithm, a clustering method based on fuzzy relations by beginning with a similarity matrix, is applied to these Gaussian type-2 fuzzy sets by beginning with these similarities. The clustering results are reasonable consisting of a hierarchical tree according to different levels.

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37

HWANG, CHAO-MING, MIIN-SHEN YANG, and WEN-LIANG HUNG. "ON SIMILARITY, INCLUSION MEASURE AND ENTROPY BETWEEN TYPE-2 FUZZY SETS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 20, no. 03 (May 17, 2012): 433–49. http://dx.doi.org/10.1142/s0218488512500225.

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In this paper, new similarity, inclusion measure and entropy between type-2 fuzzy sets corresponding to grades of memberships are proposed. We also create the relationships among these measures between type-2 fuzzy sets. Several examples are used to present the calculation of these similarity, inclusion measure and entropy between type-2 fuzzy sets. The comparison results show that the proposed similarity measure presents better than those of Hung and Yang (2004) and Yang and Lin (2009). Moreover, measuring the similarity between type-2 fuzzy sets is important in clustering. We also use the proposed similarity measure as a clustering method for type-2 fuzzy sets.

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38

Intan, Rolly, and Masao Mukaidono. "Approximate Data Querying in Fuzzy Relational Database." Journal of Advanced Computational Intelligence and Intelligent Informatics 6, no. 1 (February 20, 2002): 33–40. http://dx.doi.org/10.20965/jaciii.2002.p0033.

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Fuzzy relational database was proposed for dealing with imprecise data or fuzzy information in a relational database. In order to provide a more realistic relation in representing similarity between two imprecise data, we need to weaken fuzzy similarity relation to be weak fuzzy similarity relation in which fuzzy conditional probability relation (FCPR, for short) is regarded as a concrete example of the weak fuzzy similarity relation. In this paper, application of approximate data querying is discussed induced by FCPR in the presence of the fuzzy relational database. Application of approximate data querying in order to provide fuzzy query relation is presented into two frameworks, namely dependent inputs and independent inputs. Finally, related to join operator, approximate join of two or more fuzzy query relations is given for the purpose of extending query system.

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39

Zuo, Xin, Lijun Wang, and Yuanlong Yue. "A New Similarity Measure of Generalized Trapezoidal Fuzzy Numbers and Its Application on Rotor Fault Diagnosis." Mathematical Problems in Engineering 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/824706.

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Fault diagnosis technology plays a vital role in the variety of critical engineering applications. Fuzzy approach is widely employed to cope with decision-making problems because it is in the simplest and most used form. This paper proposed a new similarity measure of generalized trapezoidal fuzzy numbers used for fault diagnosis. The presented similarity measure combines concepts of the geometric distance, the center of gravity point, the perimeter, and the area of the generalized trapezoidal fuzzy numbers for calculating the degree of similarity between generalized trapezoidal fuzzy numbers. This method is proposed to deal with both standardized and nonstandardized generalized trapezoidal fuzzy numbers. Some properties of the proposed similarity measure have been proved, and 12 sets of generalized fuzzy numbers have been used to compare the calculation results of the proposed similarity measures with the existing similarity measures. Comparison results indicate that the proposed similarity measure can overcome the drawbacks of existing similarity measures. Finally, a fault diagnosis experiment is carried out in laboratory based on multifunctional flexible rotor experiment bench. Experimental results demonstrate that the proposed similarity measure is more effective than other methods in terms of rotor fault diagnosis.

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40

Mohamad, Daud, Noorlisa Sara Adlene Ramlan, and Sharifah Aniza Sayed Ahmad. "An improvised similarity measure for generalized fuzzy numbers." Bulletin of Electrical Engineering and Informatics 8, no. 4 (December 1, 2019): 1232–38. http://dx.doi.org/10.11591/eei.v8i4.1629.

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Similarity measure between two fuzzy sets is an important tool for comparing various characteristics of the fuzzy sets. It is a preferred approach as compared to distance methods as the defuzzification process in obtaining the distance between fuzzy sets will incur loss of information. Many similarity measures have been introduced but most of them are not capable to discriminate certain type of fuzzy numbers. In this paper, an improvised similarity measure for generalized fuzzy numbers that incorporate several essential features is proposed. The features under consideration are geometric mean averaging, Hausdorff distance, distance between elements, distance between center of gravity and the Jaccard index. The new similarity measure is validated using some benchmark sample sets. The proposed similarity measure is found to be consistent with other existing methods with an advantage of able to solve some discriminant problems that other methods cannot. Analysis of the advantages of the improvised similarity measure is presented and discussed. The proposed similarity measure can be incorporated in decision making procedure with fuzzy environment for ranking purposes.

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41

Rezaei, Hassan, Masashi Emoto, and Masao Mukaidono. "New Similarity Measure Between Two Fuzzy Sets." Journal of Advanced Computational Intelligence and Intelligent Informatics 10, no. 6 (November 20, 2006): 946–53. http://dx.doi.org/10.20965/jaciii.2006.p0946.

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We propose a new similarity measure between two fuzzy sets based on their relative sigma count and extend it to define two other measures, one a similarity measure between elements in fuzzy sets and the second a similarity measure between fuzzy sets in which all elements in the universe of discourse are weighted. We compare our proposal to several previous measures proposed in [1-6].

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42

Ali, Md Yasin. "SOME TRIGONOMETRIC SIMILARITY MEASURES OF COMPLEX FUZZY SETS WITH APPLICATION." Ural Mathematical Journal 9, no. 1 (July 27, 2023): 18. http://dx.doi.org/10.15826/umj.2023.1.002.

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Similarity measures of fuzzy sets are applied to compare the closeness among fuzzy sets. These measures have numerous applications in pattern recognition, image processing, texture synthesis, medical diagnosis, etc. However, in many cases of pattern recognition, digital image processing, signal processing, and so forth, the similarity measures of the fuzzy sets are not appropriate due to the presence of dual information of an object, such as amplitude term and phase term. In these cases, similarity measures of complex fuzzy sets are the most suitable for measuring proximity between objects with two-dimensional information. In the present paper, we propose some trigonometric similarity measures of the complex fuzzy sets involving similarity measures based on the sine, tangent, cosine, and cotangent functions. Furthermore, in many situations in real life, the weight of an attribute plays an important role in making the right decisions using similarity measures. So in this paper, we also consider the weighted trigonometric similarity measures of the complex fuzzy sets, namely, the weighted similarity measures based on the sine, tangent, cosine, and cotangent functions. Some properties of the similarity measures and the weighted similarity measures are discussed. We also apply our proposed methods to the pattern recognition problem and compare them with existing methods to show the validity and effectiveness of our proposed methods.

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Hisamatsu, Tamotsu, Yoshitake Sugiyama, Satoshi Kubota, and Masaji Koshioka. "Fuzzy Clustering Based on Similarity Matrix." Engei Gakkai zasshi 70, no. 2 (2001): 264–66. http://dx.doi.org/10.2503/jjshs.70.264.

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LU, Yan-li, Ying-jie LEI, and Zhao-yuan LI. "Construction of intuitionistic fuzzy similarity relation." Journal of Computer Applications 28, no. 2 (February 20, 2008): 311–14. http://dx.doi.org/10.3724/sp.j.1087.2008.00311.

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Jacob, Rogi, and Sunny Kuriakose A. "Near sets through fuzzy similarity relation." Applied Mathematical Sciences 8 (2014): 2035–40. http://dx.doi.org/10.12988/ams.2014.42104.

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Luo, Minxia, and Ruirui Zhao. "Fuzzy reasoning algorithms based on similarity." Journal of Intelligent & Fuzzy Systems 34, no. 1 (January 12, 2018): 213–19. http://dx.doi.org/10.3233/jifs-171140.

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Liang, Zhizhen, and Pengfei Shi. "Similarity measures on intuitionistic fuzzy sets." Pattern Recognition Letters 24, no. 15 (November 2003): 2687–93. http://dx.doi.org/10.1016/s0167-8655(03)00111-9.

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Tolias, Yannis A., Stavros M. Panas, and Lefteri H. Tsoukalas. "Generalized fuzzy indices for similarity matching." Fuzzy Sets and Systems 120, no. 2 (June 2001): 255–70. http://dx.doi.org/10.1016/s0165-0114(99)00114-1.

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Gu, Tao, and Bernard Dubuisson. "Similarity of classes and fuzzy clustering." Fuzzy Sets and Systems 34, no. 2 (January 1990): 213–21. http://dx.doi.org/10.1016/0165-0114(90)90160-8.

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