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Journal articles on the topic 'Fuzzy Relation Equations (FREs)'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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1

QIN, FENG, and PING FANG. "A NEW KIND OF FUZZY RELATIONAL EQUATIONS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 18, no. 03 (2010): 333–42. http://dx.doi.org/10.1142/s0218488510006568.

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In this paper, a new kind of fuzzy relational equations (FREs for short) A ∘R*x = b is first introduced, and then the problem of solving solution to the FREs is discussed, where A is an m × n matrix, x and b are an n and an m dimensional column vectors, respectively. More specifically, their solvability and unique solvability are investigated, the corresponding necessary and sufficient conditions are presented, the complete solution set is obtained. It is worth noting the method to construct the complete solution set.

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2

A. Danya. "Fuzzy Smbd Mathematical Model for Marriage Divorce." Advances in Nonlinear Variational Inequalities 28, no. 7s (2025): 158–70. https://doi.org/10.52783/anvi.v28.4494.

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In this study, a deterministic SMBD model for marriage and divorce in a population is put out and qualitatively analyzed using the stability theory of differential equations. Using a next-generation matrix technique, the basic reproduction number in relation to the divorce-free equilibrium was determined. The parameters for divorce-free equilibrium is local asymptotic stability have been determined. Fuzzy analysis has been done by taking into account the heartbroken couple overcame their differences and decided to get back together and some will pass away as a result of divorcing as membership

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3

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

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4

DI NOLA, ANTONIO, WITOLD PEDRYCZ, and SALVATORE SESSA. "PROCESSING OF FUZZY NUMBERS BY FUZZY RELATION EQUATIONS." Kybernetes 15, no. 1 (1986): 43–47. http://dx.doi.org/10.1108/eb005730.

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5

Ćirić, Miroslav, Aleksandar Stamenković, Jelena Ignjatović, and Tatjana Petković. "Fuzzy relation equations and reduction of fuzzy automata." Journal of Computer and System Sciences 76, no. 7 (2010): 609–33. http://dx.doi.org/10.1016/j.jcss.2009.10.015.

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6

Di Martino, Ferdinando, and Salvatore Sessa. "Spatial Analysis and Fuzzy Relation Equations." Advances in Fuzzy Systems 2011 (2011): 1–14. http://dx.doi.org/10.1155/2011/429498.

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We implement an algorithm that uses a system of fuzzy relation equations (SFRE) with the max-min composition for solving a problem of spatial analysis. We integrate this algorithm in a Geographical Information System (GIS) tool, and the geographical area under study is divided in homogeneous subzones (with respect to the parameters involved) to which we apply our process to determine the symptoms after that an expert sets the SFRE with the values of the impact coefficients. We find that the best solutions and the related results are associated to each subzone. Among others, we define an index

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7

Dubois, Didier, and Henri Prade. "Fuzzy relation equations and causal reasoning." Fuzzy Sets and Systems 75, no. 2 (1995): 119–34. http://dx.doi.org/10.1016/0165-0114(95)00105-t.

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8

Di Nola, Antonio, Salvatore Sessa, and Witold Pedrycz. "On some finite fuzzy relation equations." Information Sciences 50, no. 1 (1990): 93–109. http://dx.doi.org/10.1016/0020-0255(90)90006-v.

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9

Guangzhi Li and Shu-Cherng Fang. "Solving interval-valued fuzzy relation equations." IEEE Transactions on Fuzzy Systems 6, no. 2 (1998): 321–24. http://dx.doi.org/10.1109/91.669033.

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10

WANG, HSIAO-FAN, and HSI-MEI HSU. "SENSITIVITY ANALYSIS OF FUZZY RELATION EQUATIONS." International Journal of General Systems 19, no. 2 (1991): 155–69. http://dx.doi.org/10.1080/03081079108935169.

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11

Ignjatović, Jelena, Miroslav Ćirić, and Vesna Simović. "Fuzzy relation equations and subsystems of fuzzy transition systems." Knowledge-Based Systems 38 (January 2013): 48–61. http://dx.doi.org/10.1016/j.knosys.2012.02.008.

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12

Tiwari, Vijay Lakshmi, and Antika Thapar. "Covering Problem for Solutions of Max-Archimedean Bipolar Fuzzy Relation Equations." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 28, no. 04 (2020): 613–34. http://dx.doi.org/10.1142/s0218488520500269.

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This paper discusses the resolution of max-Archimedean bipolar fuzzy relation equations. In the literature, many methods have been proposed based on 0-1 integer programming problem or reduction methods for the optimization with bipolar fuzzy relation equations. A new concept based on the idea of covering and the notions of leading, non-leading variables are introduced in the present paper for finding the solutions of max-Archimedean bipolar fuzzy relation equations. It is shown that the problem of finding the complete solution set of the system of max-Archimedean bipolar fuzzy relation equatio

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13

Kim, Yong Chan. "Fuzzy relation equations in pseudo BL-algebras." International Journal of Fuzzy Logic and Intelligent Systems 13, no. 3 (2013): 208–14. http://dx.doi.org/10.5391/ijfis.2013.13.3.208.

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14

Luoh, Leh, Wen-June Wang, and Yi-Ke Liaw. "New algorithms for solving fuzzy relation equations." Mathematics and Computers in Simulation 59, no. 4 (2002): 329–33. http://dx.doi.org/10.1016/s0378-4754(01)00387-1.

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15

Drewniak, Józef, and Zofia Matusiewicz. "Properties of $$\text{max-}*$$ fuzzy relation equations." Soft Computing 14, no. 10 (2009): 1037–41. http://dx.doi.org/10.1007/s00500-009-0481-6.

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16

Fernández, M. J., and P. Gil. "Some specific types of fuzzy relation equations." Information Sciences 164, no. 1-4 (2004): 189–95. http://dx.doi.org/10.1016/j.ins.2003.05.007.

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17

PERFILIEVA, IRINA, and ALEXANDER TONIS. "COMPATIBILITY OF SYSTEMS OF FUZZY RELATION EQUATIONS." International Journal of General Systems 29, no. 4 (2000): 511–28. http://dx.doi.org/10.1080/03081070008960959.

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18

Xu, Xueyan. "Resolution of Fuzzy Relation Equations with Constraints." Fuzzy Information and Engineering 15, no. 3 (2023): 220–32. http://dx.doi.org/10.26599/fie.2023.9270017.

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19

KOŁODZIEJCZYK, WALDEMAR. "ON TRANSITIVE SOLUTIONS OF $-FUZZY RELATION EQUATIONS DESCRIBING FUZZY SYSTEMS." International Journal of General Systems 17, no. 2-3 (1990): 277–88. http://dx.doi.org/10.1080/03081079008935111.

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20

Stamou, G. B., and S. G. Tzafestas. "Fuzzy relation equations and fuzzy inference systems: an inside approach." IEEE Transactions on Systems, Man and Cybernetics, Part B (Cybernetics) 29, no. 6 (1999): 694–702. http://dx.doi.org/10.1109/3477.809025.

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21

Dı´az, Juan Carlos, and Jesús Medina. "Solving systems of fuzzy relation equations by fuzzy property-oriented concepts." Information Sciences 222 (February 2013): 405–12. http://dx.doi.org/10.1016/j.ins.2012.08.017.

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22

Hayao, Miyagi, Fan Yiping, and Yamashita Katsumi. "Solution of Fuzzy Relation Equations Using Composite Operators." IEEJ Transactions on Electronics, Information and Systems 121, no. 4 (2001): 756–61. http://dx.doi.org/10.1541/ieejeiss1987.121.4_756.

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23

Gr. Voskoglou, Michael. "Application of Fuzzy Relation Equations to Student Assessment." American Journal of Applied Mathematics and Statistics 6, no. 2 (2018): 67–71. http://dx.doi.org/10.12691/ajams-6-2-5.

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24

Wang, Hsiao-Fan, and Yu-Chee Chang. "Resolution of composite interval-valued fuzzy relation equations." Fuzzy Sets and Systems 44, no. 2 (1991): 227–40. http://dx.doi.org/10.1016/0165-0114(91)90006-c.

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25

Neundorf, Dörte, and Rolf Böhm. "Solvability criteria for systems of fuzzy relation equations." Fuzzy Sets and Systems 80, no. 3 (1996): 345–52. http://dx.doi.org/10.1016/0165-0114(95)00204-9.

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26

Perfilieva, Irina, and Siegfried Gottwald‡. "Solvability and approximate solvability of fuzzy relation equations*." International Journal of General Systems 32, no. 4 (2003): 361–72. http://dx.doi.org/10.1080/0308107031000135035.

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27

Shieh, Bih-Sheue. "Infinite fuzzy relation equations with continuous t-norms." Information Sciences 178, no. 8 (2008): 1961–67. http://dx.doi.org/10.1016/j.ins.2007.12.006.

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28

Di Martino, Ferdinando, and Salvatore Sessa. "Comparison between images via bilinear fuzzy relation equations." Journal of Ambient Intelligence and Humanized Computing 9, no. 5 (2017): 1517–25. http://dx.doi.org/10.1007/s12652-017-0576-3.

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29

Alcalde, Cristina, Ana Burusco, Juan Carlos Díaz-Moreno, and Jesús Medina. "Fuzzy Concept Lattices and Fuzzy Relation Equations in the Retrieval Processing of Images and Signals." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 25, Suppl. 1 (2017): 99–120. http://dx.doi.org/10.1142/s0218488517400050.

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This paper considers the introduced relations between fuzzy property-oriented concept lattices and fuzzy relation equations, on the one hand, and mathematical morphology, on the other hand, in the retrieval processing of images and signals. In the first part, it studies how the original images and signals can be retrieved using fuzzy property-oriented concept lattices and fuzzy relation equations. In the second one we analyze two of the most important tools in fuzzy mathematical morphology from the point of view of the fuzzy property-oriented concepts and the aforementioned study. Both parts a

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30

Ge, Aidong, Zhen Chang, and Jun-e. Feng. "Solving interval type-2 fuzzy relation equations via semi-tensor product of interval matrices." Mathematical Modelling and Control 3, no. 4 (2023): 331–44. http://dx.doi.org/10.3934/mmc.2023027.

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<abstract><p>This paper mainly studied the problem of solving interval type-2 fuzzy relation equations $ \widetilde A \circ \widetilde X = \widetilde B $. First, to solve the interval type-2 fuzzy relation equations, we extend the semi-tensor product of matrices to interval matrices and give its specific definition. Second, the interval type-2 fuzzy relation equation was divided into two parts: primary fuzzy matrix equation $ {\widetilde A_\mu } \circ {\widetilde X_\mu }{\rm{ = }}{\widetilde B_\mu} $ and secondary fuzzy matrix equation $ {\widetilde A_f} \circ {\widetilde X_f} = {\

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31

Di Nola, A., W. Pedrycz, S. Sessa, and E. Sanchez. "Fuzzy relation equations theory as a basis of fuzzy modelling: An overview." Fuzzy Sets and Systems 40, no. 3 (1991): 415–29. http://dx.doi.org/10.1016/0165-0114(91)90170-u.

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32

Ignjatovic, Jelena, and Miroslav Ciric. "Weakly linear systems of fuzzy relation inequalities and their applications: A brief survey." Filomat 26, no. 2 (2012): 207–41. http://dx.doi.org/10.2298/fil1202207i.

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Weakly linear systems of fuzzy relation inequalities and equations have recently emerged from research in the theory of fuzzy automata. From the general aspect of the theory of fuzzy relation equations and inequalities homogeneous and heterogeneousweakly linear systems have been discussed in two recent papers. Here we give a brief overview of the main results from these two papers, as well as from a series of papers on applications of weakly linear systems in the state reduction of fuzzy automata, the study of simulation, bisimulation and equivalence of fuzzy automata, and in the social networ

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33

LOIA, VINCENZO, WITOLD PEDRYCZ, and SALVATORE SESSA. "FUZZY RELATION CALCULUS IN THE COMPRESSION AND DECOMPRESSION OF FUZZY RELATIONS." International Journal of Image and Graphics 02, no. 04 (2002): 617–31. http://dx.doi.org/10.1142/s0219467802000871.

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We firstly review some fundamentals of fuzzy relation calculus and, by recalling some known results, we improve the mathematical contents of our previous papers by using the properties of a triangular norm over [0,1]. We make wide use of the theory of fuzzy relation equations for getting lossy compression and decompression of images interpreted as two-argument fuzzy matrices.The same scope is achieved by decomposing a fuzzy matrix using the concept of Schein rank. We illustrate two algorithms with a few examples.

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34

Fang, Shu-Cherng, and Guangzhi Li. "Solving fuzzy relation equations with a linear objective function." Fuzzy Sets and Systems 103, no. 1 (1999): 107–13. http://dx.doi.org/10.1016/s0165-0114(97)00184-x.

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35

Loetamonphong, Jiranut, and Shu-Cherng Fang. "Optimization of fuzzy relation equations with max-product composition." Fuzzy Sets and Systems 118, no. 3 (2001): 509–17. http://dx.doi.org/10.1016/s0165-0114(98)00417-5.

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36

Wang, Hsiao-Fan. "Numerical analysis on fuzzy relation equations with various operators." Fuzzy Sets and Systems 53, no. 2 (1993): 155–66. http://dx.doi.org/10.1016/0165-0114(93)90169-i.

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37

Adamopoulos, G. I., and C. P. Pappis. "Some results on the resolution of fuzzy relation equations." Fuzzy Sets and Systems 60, no. 1 (1993): 83–88. http://dx.doi.org/10.1016/0165-0114(93)90292-p.

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38

Ames, W. F. "Fuzzy relation equations and their applications to knowledge engineering." Mathematics and Computers in Simulation 31, no. 6 (1990): 595. http://dx.doi.org/10.1016/0378-4754(90)90068-t.

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39

Perfilieva, Irina. "Finitary solvability conditions for systems of fuzzy relation equations." Information Sciences 234 (June 2013): 29–43. http://dx.doi.org/10.1016/j.ins.2011.04.035.

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40

Di Martino, Ferdinando, and Salvatore Sessa. "Fragile watermarking tamper detection via bilinear fuzzy relation equations." Journal of Ambient Intelligence and Humanized Computing 10, no. 5 (2018): 2041–61. http://dx.doi.org/10.1007/s12652-018-0806-3.

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41

Di Nola, Antonio, Witold Pedrycz, and Salvatore Sessa. "Fuzzy relation equations with equality and difference composition operators." Fuzzy Sets and Systems 25, no. 2 (1988): 205–15. http://dx.doi.org/10.1016/0165-0114(88)90188-1.

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42

Zhou, Xue-Gang. "Qudratic Programming with Max-Min Fuzzy Relation Equations Constraint." Fuzzy Information and Engineering 16, no. 4 (2024): 300–313. https://doi.org/10.26599/fie.2024.9270047.

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43

Gr. Voskoglou, Michael. "Use of Fuzzy Relation Equations for Evaluating Mathematical Modelling Skills." Oriental Journal of Physical Sciences 3, no. 2 (2018): 102–7. http://dx.doi.org/10.13005/ojps03.02.05.

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In the present paper a new assessment approach is developed involving the use of fuzzy relation equations, which are associated with the composition of binary fuzzy relations, for evaluating student mathematical modelling skills. A classroom application and other examples are also presented illustrating our results, and useful conclusions are obtained.

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44

Perfilieva, Irina. "Fuzzy function as an approximate solution to a system of fuzzy relation equations." Fuzzy Sets and Systems 147, no. 3 (2004): 363–83. http://dx.doi.org/10.1016/j.fss.2003.12.007.

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45

Kshama Pandey, Pranjali Sharma, Shailesh Dhar Diwan. "Intuitionistic Fuzzy Fixed Point Theory: Relation-Theoretic Approaches and Applications." Journal of Information Systems Engineering and Management 10, no. 16s (2025): 32–51. https://doi.org/10.52783/jisem.v10i16s.2558.

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This paper explores the concept of intuitionistic fuzzy R-φ- contractive mappings and establishes key results regarding the existence and uniqueness of fixed points in non-Archimedean intuitionistic fuzzy metric spaces. To illustrate the applicability of these findings, several examples are provided. Additionally, the main results are utilized to demonstrate the existence and uniqueness of solutions for Caputo fractional differential equations within the framework of intuitionistic fuzzy metric spaces.

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46

Sophiya A. "An Application on Fuzzy Relation Using in Difficult Problem Solved." Advances in Nonlinear Variational Inequalities 27, no. 2 (2024): 333–41. http://dx.doi.org/10.52783/anvi.v27.970.

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As a basic concept in fuzzy theory, fuzzy relations are used in a variety of fields, such as fuzzy clustering, uncertainty reasoning, and fuzzy control. When fuzzy relations are applied in practise, it might be difficult to estimate and compare them. This method was therefore applied in this study to tackle a challenging issue. It turns out that a combination of this strategy and the three prior expanded ones can have a beneficial effect on the actual issue. Finally, using fuzzy quantifiers, we give a theoretical investigation into the capacity to solve systems of fuzzy relation equations. As

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47

MIYAGI, Hayao, Hayako FUKUMURA, and Katsumi YAMASHITA. "Solution of Fuzzy Relation Equations Using the Rule of Exclusion." Journal of Japan Society for Fuzzy Theory and Systems 10, no. 1 (1998): 168–75. http://dx.doi.org/10.3156/jfuzzy.10.1_168.

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48

Lobo, David, Jesús Medina, Timo Camillo Merkl, and Reinhard Pichler. "Minimal solutions of fuzzy relation equations via maximal independent elements." Information Sciences 690 (February 2025): 121558. http://dx.doi.org/10.1016/j.ins.2024.121558.

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49

Chen, L., and P. P. Wang. "Fuzzy relation equations (I): the general and specialized solving algorithms." Soft Computing - A Fusion of Foundations, Methodologies and Applications 6, no. 6 (2002): 428–35. http://dx.doi.org/10.1007/s00500-001-0157-3.

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50

Di Martino, F., and S. Sessa. "Digital watermarking in coding/decoding processes with fuzzy relation equations." Soft Computing 10, no. 3 (2005): 238–43. http://dx.doi.org/10.1007/s00500-005-0477-9.

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