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Journal articles on the topic 'Fuzzy optimization'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Yari, Gholamhossein, and Mohamadtaghi Rahimi. "General solution for fuzzy portfolio optimization." International Journal of Academic Research 6, no. 6 (November 30, 2014): 220–26. http://dx.doi.org/10.7813/2075-4124.2014/6-6/a.28.

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2

Uehara, Kiyohiko, and Kaoru Hirota. "A Fast Method for Fuzzy Rules Learning with Derivative-Free Optimization by Formulating Independent Evaluations of Each Fuzzy Rule." Journal of Advanced Computational Intelligence and Intelligent Informatics 25, no. 2 (March 20, 2021): 213–25. http://dx.doi.org/10.20965/jaciii.2021.p0213.

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A method is proposed for evaluating fuzzy rules independently of each other in fuzzy rules learning. The proposed method is named α-FUZZI-ES (α-weight-based fuzzy-rule independent evaluations) in this paper. In α-FUZZI-ES, the evaluation value of a fuzzy system is divided out among the fuzzy rules by using the compatibility degrees of the learning data. By the effective use of α-FUZZI-ES, a method for fast fuzzy rules learning is proposed. This is named α-FUZZI-ES learning (α-FUZZI-ES-based fuzzy rules learning) in this paper. α-FUZZI-ES learning is especially effective when evaluation functions are not differentiable and derivative-based optimization methods cannot be applied to fuzzy rules learning. α-FUZZI-ES learning makes it possible to optimize fuzzy rules independently of each other. This property reduces the dimensionality of the search space in finding the optimum fuzzy rules. Thereby, α-FUZZI-ES learning can attain fast convergence in fuzzy rules optimization. Moreover, α-FUZZI-ES learning can be efficiently performed with hardware in parallel to optimize fuzzy rules independently of each other. Numerical results show that α-FUZZI-ES learning is superior to the exemplary conventional scheme in terms of accuracy and convergence speed when the evaluation function is non-differentiable.

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3

ISHII, Hiroaki. "Fuzzy Combinatiorial Optimization." Journal of Japan Society for Fuzzy Theory and Systems 4, no. 1 (1992): 31–40. http://dx.doi.org/10.3156/jfuzzy.4.1_31.

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4

Murat, Y. Sazi, and Shinya Kikuchi. "Fuzzy Optimization Approach." Transportation Research Record: Journal of the Transportation Research Board 2024, no. 1 (January 2007): 82–91. http://dx.doi.org/10.3141/2024-10.

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5

NASSERI, S. H. "FUZZY NONLINEAR OPTIMIZATION." Journal of Nonlinear Sciences and Applications 01, no. 04 (December 21, 2008): 230–35. http://dx.doi.org/10.22436/jnsa.001.04.05.

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6

Dey, Samir, and Tapan Kumar Roy. "Multi-objective Structural Optimization Using Fuzzy and Intuitionistic Fuzzy Optimization Technique." International Journal of Intelligent Systems and Applications 7, no. 5 (April 8, 2015): 57–65. http://dx.doi.org/10.5815/ijisa.2015.05.08.

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7

Ammar, Elsaid, and Joachim Metz. "On fuzzy convexity and parametric fuzzy optimization." Fuzzy Sets and Systems 49, no. 2 (July 1992): 135–41. http://dx.doi.org/10.1016/0165-0114(92)90319-y.

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8

Revathi, M., Dr M. Valliathal, and R. Saravanan Dr K. Rathi. "A New Hendecagonal Fuzzy Number For Optimization Problems." International Journal of Trend in Scientific Research and Development Volume-1, Issue-5 (August 31, 2017): 326–31. http://dx.doi.org/10.31142/ijtsrd2258.

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9

Chen, Cheng-Hung, and Wen-Hsien Chen. "Symbiotic Particle Swarm Optimization for Neural Fuzzy Controllers." International Journal of Machine Learning and Computing 4, no. 5 (2014): 433–36. http://dx.doi.org/10.7763/ijmlc.2014.v4.450.

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10

Chen, T. Y., and C. C. Shieh. "Fuzzy multiobjective topology optimization." Computers & Structures 78, no. 1-3 (November 2000): 459–66. http://dx.doi.org/10.1016/s0045-7949(00)00091-2.

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11

Medaglia, Andrés L., Shu-Cherng Fang, and Henry L. W. Nuttle. "Fuzzy controlled simulation optimization." Fuzzy Sets and Systems 127, no. 1 (April 2002): 65–84. http://dx.doi.org/10.1016/s0165-0114(01)00153-1.

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12

Pedrycz, W., and J. V. de Oliveira. "Optimization of fuzzy models." IEEE Transactions on Systems, Man and Cybernetics, Part B (Cybernetics) 26, no. 4 (1996): 627–36. http://dx.doi.org/10.1109/3477.517038.

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13

Luhandjula, M. K., and M. M. Gupta. "On fuzzy stochastic optimization." Fuzzy Sets and Systems 81, no. 1 (July 1996): 47–55. http://dx.doi.org/10.1016/0165-0114(95)00240-5.

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14

Luhandjula, M. K. "Fuzzy optimization: An appraisal." Fuzzy Sets and Systems 30, no. 3 (May 1989): 257–82. http://dx.doi.org/10.1016/0165-0114(89)90019-5.

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15

BURGIN, MARK. "FUZZY OPTIMIZATION OF REAL FUNCTIONS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 12, no. 04 (August 2004): 471–97. http://dx.doi.org/10.1142/s021848850400293x.

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The main goal of this paper is to develop such means of analysis that allows us to reflect and model vagueness and uncertainty of our knowledge, which result from imprecision of measurement and inaccuracy of computation. To achieve this goal, we use here neoclassical analysis to problems of optimization. Neoclassical analysis extends the scope and results of the classical mathematical analysis by applying fuzzy concepts to conventional mathematical objects, such as functions, sequences, and derivatives. Basing on the theory of fuzzy limits, we construct a fuzzy extension for the classical theory of differentiation in the context of computational mathematics. It is done in the second part of this paper, going after introduction. Two kinds of fuzzy derivatives of real functions are considered: weak and strong ones. In addition, we introduce and study extended fuzzy derivatives, which may take infinite values. In the third part of this paper, fuzzy derivatives are applied to a study of maxima and minima of real functions. Different conditions for maxima and minima of real functions are obtained. Some of them are the same or at least similar to the conditions for the differentiable functions, while others differ in many aspects from those for the standard differentiable functions. Many classical results are obtained as direct corollaries of propositions for fuzzy derivatives, which are proved in this paper. Such results as the Fuzzy Intermediate Value theorem, Fuzzy Fermat's theorem, Fuzzy Rolle's theorem, and Fuzzy Mean Value theorem are proved. These results provide better theoretical base for computational methods of optimization.

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16

Lodwick, Weldon A., and K. David Jamison. "Interval Methods and Fuzzy Optimization." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 05, no. 03 (June 1997): 239–49. http://dx.doi.org/10.1142/s0218488597000221.

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In this paper, we describe interval-based methods for solving constrained fuzzy optimization problems. The class of fuzzy functions we consider for the optimization problems is the set of real-valued functions where one or more parameters/coefficients are fuzzy numbers. The focus of this research is to explore some relationships between fuzzy set theory and interval analysis as it relates to optimization problems.

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17

Shirin, Shapla, and Kamrunnahar. "Application of Fuzzy Optimization Problem in Fuzzy Environment." Dhaka University Journal of Science 62, no. 2 (February 8, 2015): 119–25. http://dx.doi.org/10.3329/dujs.v62i2.21976.

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In this paper application of optimization problem has been introduced which belong to fuzzy environment. An attempt has been taken to find out a suitable option in order to obtain the optimum solutions of optimization problems in fuzzy environment. Optimum solutions of the proposed optimization problem computed by using three methods, such as Bellman-Zadehs method, Zimmermans Method, and Fuzzy Version of Simplex method, are compared to each other. In support of that the three algorithms of the above three methods have been reviewed. However, the main objective of this paper is to focus on the appropriate method and how to achieve good enough or optimum solution of linear programming using triangular fuzzy numbers with equal widths because of complex and undefined situations in our daily life. DOI: http://dx.doi.org/10.3329/dujs.v62i2.21976 Dhaka Univ. J. Sci. 62(2): 119-125, 2014 (July)

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18

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

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19

Budnitzki, Alina. "Linear optimization with fuzzy variable over fuzzy polytope." Journal of Intelligent & Fuzzy Systems 29, no. 2 (October 5, 2015): 499–507. http://dx.doi.org/10.3233/ifs-141225.

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20

Umamaheswari, P., and K. Ganesan. "Fuzzy Unconstrained Optimization Problems with Triangular Fuzzy Numbers." IOP Conference Series: Materials Science and Engineering 912 (September 12, 2020): 062048. http://dx.doi.org/10.1088/1757-899x/912/6/062048.

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21

Bernal, Emer, Oscar Castillo, José Soria, and Fevrier Valdez. "Optimization of Fuzzy Controller Using Galactic Swarm Optimization with Type-2 Fuzzy Dynamic Parameter Adjustment." Axioms 8, no. 1 (February 25, 2019): 26. http://dx.doi.org/10.3390/axioms8010026.

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Galactic swarm optimization (GSO) is a recently created metaheuristic which is inspired by the motion of galaxies and stars in the universe. This algorithm gives us the possibility of finding the global optimum with greater precision since it uses multiple exploration and exploitation cycles. In this paper we present a modification to galactic swarm optimization using type-1 (T1) and interval type-2 (IT2) fuzzy systems for the dynamic adjustment of the c3 and c4 parameters in the algorithm. In addition, the modification is used for the optimization of the fuzzy controller of an autonomous mobile robot. First, the galactic swarm optimization is tested for fuzzy controller optimization. Second, the GSO algorithm with the dynamic adjustment of parameters using T1 fuzzy systems is used for the optimization of the fuzzy controller of an autonomous mobile robot. Finally, the GSO algorithm with the dynamic adjustment of parameters using the IT2 fuzzy systems is applied to the optimization of the fuzzy controller. In the proposed approaches, perturbation (noise) was added to the plant in order to find out if our approach behaves well under perturbation to the autonomous mobile robot plant; additionally, we consider our ability to compare the results obtained with the approaches when no perturbation is considered.

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22

Zou, Tingting. "Extended Duality in Fuzzy Optimization Problems." Mathematical Problems in Engineering 2015 (2015): 1–11. http://dx.doi.org/10.1155/2015/826752.

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Duality theorem is an attractive approach for solving fuzzy optimization problems. However, the duality gap is generally nonzero for nonconvex problems. So far, most of the studies focus on continuous variables in fuzzy optimization problems. And, in real problems and models, fuzzy optimization problems also involve discrete and mixed variables. To address the above problems, we improve the extended duality theory by adding fuzzy objective functions. In this paper, we first define continuous fuzzy nonlinear programming problems, discrete fuzzy nonlinear programming problems, and mixed fuzzy nonlinear programming problems and then provide the extended dual problems, respectively. Finally we prove the weak and strong extended duality theorems, and the results show no duality gap between the original problem and extended dual problem.

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23

MIRANDA, PEDRO, and MICHEL GRABISCH. "OPTIMIZATION ISSUES FOR FUZZY MEASURES." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 07, no. 06 (December 1999): 545–60. http://dx.doi.org/10.1142/s0218488599000477.

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In this paper, we address the problem of identification of fuzzy measures through different representations, namely the Möbius, the Shapley and the Banzhaf interaction representations. In the first part of the paper, we recall the main results concerning these representations, and give a simple algorithm to compute them. Then we determine the bounds of the Möbius and the interaction representations for fuzzy measures. Lastly, the identification of fuzzy measures by minimizing a quadratic error criterion is addressed. We give expressions of the quadratic program for all the considered representations, and study the uniqueness of the solution.

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24

Wei, Jing-xuan, and Yu-ping Wang. "Fuzzy Particle Swarm Optimization for Constrained Optimization Problems." Journal of Electronics & Information Technology 30, no. 5 (March 15, 2011): 1218–21. http://dx.doi.org/10.3724/sp.j.1146.2007.00689.

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25

Zhu, Qiang, and Per-Åke Larson. "A Fuzzy Query Optimization Approach for Multidatabase Systems." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 05, no. 06 (December 1997): 701–22. http://dx.doi.org/10.1142/s0218488597000518.

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A crucial challenge for global query optimization in a multidatabase system (MDBS) is that some local optimization information, such as local cost parameters, may not be accurately known at the global level because of local autonomy. Traditional query optimization techniques using a crisp cost model may not be suitable for an MDBS because precise information is required. In this paper we present a new approach that performs global query optimization using a fuzzy cost model that allows fuzzy information. We suggest methods for establishing a fuzzy cost model and introduce a fuzzy optimization criterion that can be used with a fuzzy cost model. We discuss the relationship between the fuzzy optimization approach and the traditional (crisp) optimization approach and show that the former has a better chance to find a good execution strategy for a query in an MDBS environment, but its complexity may grow exponentially compared with the complexity of the later. To reduce the complexity, we suggest to use so-called k-approximate fuzzy values to approximate all fuzzy values during fuzzy query optimization. It is proven that the improved fuzzy approach has the same order of complexity as the crisp approach.

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26

Luhandjula, Monga K. "On Fuzzy Random-Valued Optimization." American Journal of Operations Research 01, no. 04 (2011): 259–67. http://dx.doi.org/10.4236/ajor.2011.14030.

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27

Wang Yingfen. "Fuzzy Optimization Method in Classification." Journal of Convergence Information Technology 6, no. 6 (June 30, 2011): 231–34. http://dx.doi.org/10.4156/jcit.vol6.issue6.23.

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28

Sarosa, M., A. S. Ahmad, B. Riyanto, and A. S. Noer. "Optimization of Neuro-Fuzzy System." ITB Journal of Information and Communication Technology 1, no. 1 (2007): 56–69. http://dx.doi.org/10.5614/itbj.ict.2007.1.1.5.

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29

E., M., and A. Salama. "Optimization Model By Fuzzy Environment." International Conference on Mathematics and Engineering Physics 4, no. 4 (May 1, 2008): 1–13. http://dx.doi.org/10.21608/icmep.2008.29890.

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30

Kikuchi, Shinya, Nopadon Kronprasert, and Said M. Easa. "Aggregate Blending Using Fuzzy Optimization." Journal of Construction Engineering and Management 138, no. 12 (December 2012): 1411–20. http://dx.doi.org/10.1061/(asce)co.1943-7862.0000557.

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31

Ramík, Jaroslav. "Extension principle in fuzzy optimization." Fuzzy Sets and Systems 19, no. 1 (May 1986): 29–35. http://dx.doi.org/10.1016/s0165-0114(86)80075-6.

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32

Fu Guoyao. "Optimization methods for fuzzy clustering." Fuzzy Sets and Systems 93, no. 3 (February 1998): 301–9. http://dx.doi.org/10.1016/s0165-0114(96)00227-8.

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33

ČERNÝ, MARTIN. "FUZZY APPROACH TO VECTOR OPTIMIZATION." International Journal of General Systems 20, no. 1 (December 1991): 23–29. http://dx.doi.org/10.1080/03081079108945010.

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34

Gobi, A. F., and W. Pedrycz. "Fuzzy modelling through logic optimization." International Journal of Approximate Reasoning 45, no. 3 (August 2007): 488–510. http://dx.doi.org/10.1016/j.ijar.2006.06.026.

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35

Luhandjula, M. K. "Fuzzy optimization: Milestones and perspectives." Fuzzy Sets and Systems 274 (September 2015): 4–11. http://dx.doi.org/10.1016/j.fss.2014.01.004.

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36

Yi-Cherng, Yeh, and Hsu Deh-Shiu. "Structural optimization with fuzzy parameters." Computers & Structures 37, no. 6 (January 1990): 917–24. http://dx.doi.org/10.1016/0045-7949(90)90005-m.

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37

Marano, Giuseppe Carlo, and Giuseppe Quaranta. "Fuzzy-based robust structural optimization." International Journal of Solids and Structures 45, no. 11-12 (June 2008): 3544–57. http://dx.doi.org/10.1016/j.ijsolstr.2008.02.016.

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38

Hanebeck, Uwe D., and Günther K. Schmidt. "Genetic optimization of fuzzy networks." Fuzzy Sets and Systems 79, no. 1 (April 1996): 59–68. http://dx.doi.org/10.1016/0165-0114(95)00291-x.

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39

Robati, Amir, Gholam Abbas Barani, Hossein Nezam Abadi Pour, Mohammad Javad Fadaee, and Javad Rahimi Pour Anaraki. "Balanced fuzzy particle swarm optimization." Applied Mathematical Modelling 36, no. 5 (May 2012): 2169–77. http://dx.doi.org/10.1016/j.apm.2011.08.006.

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40

Tan, Sie-Keng, and Pei-Zhuang Wang. "A Characterization of Optimal Fuzzy Sets in Fuzzy Optimization." Journal of Intelligent and Fuzzy Systems 1, no. 4 (1993): 313–17. http://dx.doi.org/10.3233/ifs-1993-1406.

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41

Lodwick, Weldon A., and K. David Jamison. "A Constraint Fuzzy Interval Analysis approach to fuzzy optimization." Information Sciences 426 (February 2018): 38–49. http://dx.doi.org/10.1016/j.ins.2017.10.026.

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42

k, Kalaiarasi, Sumathi M, and Mary Henrietta H. "Optimization of Fuzzy Inventory EOQ Model Using Kuhn-Tucker Method." Journal of Advanced Research in Dynamical and Control Systems 11, no. 0009-SPECIAL ISSUE (September 25, 2019): 595–99. http://dx.doi.org/10.5373/jardcs/v11/20192610.

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43

Jaleesha, B. K., and Dr S. Shenbaga Ezhil. "Interval Valued Fuzzy Sets in Decision Making and Optimization Models." Journal of Advanced Research in Dynamical and Control Systems 11, no. 10-SPECIAL ISSUE (October 31, 2019): 1290–97. http://dx.doi.org/10.5373/jardcs/v11sp10/20192974.

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44

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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45

Sheibani, Kaveh. "Fuzzy Greedy Search." International Journal of Applied Management Sciences and Engineering 4, no. 2 (July 2017): 1–12. http://dx.doi.org/10.4018/ijamse.2017070101.

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This paper presents mathematics of the so-called fuzzy greedy evaluation concept which can be integrated into approaches for hard combinatorial optimization problems. The proposed method evaluates objects in a way that combines fuzzy reasoning with a greedy mechanism, thereby exploiting a fuzzy solution space using greedy methods. Given that the greedy algorithms are computationally inexpensive compared to other more sophisticated methods for combinatorial optimization; this shows practical significance of using the proposed approach. The effectiveness and efficiency of the proposed method are demonstrated on permutation flow-shop scheduling as one of the most widely studied hard combinatorial optimization problems in the area of operational research and management science.

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46

Buckley, James J., Thomas Feuring, and Yoichi Hayashi. "Solving Fuzzy Problems in Operations Research." Journal of Advanced Computational Intelligence and Intelligent Informatics 3, no. 3 (June 20, 1999): 171–76. http://dx.doi.org/10.20965/jaciii.1999.p0171.

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Fuzzy optimization problems to which traditional methods - calculus and crisp algorithms - are not directly applicable have not been completely solved. We used evolutionary algorithms to produce good approximate solutions to fuzzy optimization problems including fully fuzzified linear programming, nonlinear fuzzy regression, neural net training, and fuzzy hierarchical analysis. We applied our evolutionary algorithm package to generating good approximate solutions to fuzzy optimization problems in operations research including the fuzzy shortest route problem and the fuzzy min-cost capacitated flow problem.

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47

Li, Chen, Gong Zeng-tai, and Duan Gang. "Genetic Algorithm Optimization for Determining Fuzzy Measures from Fuzzy Data." Journal of Applied Mathematics 2013 (2013): 1–11. http://dx.doi.org/10.1155/2013/542153.

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Fuzzy measures and fuzzy integrals have been successfully used in many real applications. How to determine fuzzy measures is a very difficult problem in these applications. Though there have existed some methodologies for solving this problem, such as genetic algorithms, gradient descent algorithms, neural networks, and particle swarm algorithm, it is hard to say which one is more appropriate and more feasible. Each method has its advantages. Most of the existed works can only deal with the data consisting of classic numbers which may arise limitations in practical applications. It is not reasonable to assume that all data are real data before we elicit them from practical data. Sometimes, fuzzy data may exist, such as in pharmacological, financial and sociological applications. Thus, we make an attempt to determine a more generalized type of general fuzzy measures from fuzzy data by means of genetic algorithms and Choquet integrals. In this paper, we make the first effort to define theσ-λrules. Furthermore we define and characterize the Choquet integrals of interval-valued functions and fuzzy-number-valued functions based onσ-λrules. In addition, we design a special genetic algorithm to determine a type of general fuzzy measures from fuzzy data.

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48

Zhang, Jing. "Multidisciplinary Fuzzy Optimization Design of Planar Linkage Mechanism." Advanced Materials Research 211-212 (February 2011): 1016–20. http://dx.doi.org/10.4028/www.scientific.net/amr.211-212.1016.

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Based on the fuzzy theory and an idea of multidisciplinary design optimization, a fuzzy optimization model of multidisciplinary design is established. Fuzzy constraints are changed by a fuzzy comprehensive evaluation and an amplification-coefficient method. Using collaborative optimization and genetic algorithms, the multidisciplinary fuzzy optimum of planar linkage mechanism is achieved and a four-bar mechanism is given as an example. Two disciplines are involved in the design optimization of mechanism, i.e., kinematics and control. The numerical results indicate that the optimized mechanism not only satisfies the mechanism and control constraints, but also synthesizes approximate optimum value, and lays a foundation for the solution of more complex mechanical system.

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49

Bakievna Khuzyatova, Lyalya, and Lenar Ajratovich Galiullin. "Optimization of parameters of neuro-fuzzy model." Indonesian Journal of Electrical Engineering and Computer Science 19, no. 1 (July 1, 2020): 229. http://dx.doi.org/10.11591/ijeecs.v19.i1.pp229-232.

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<p>The need for increasing the efficiency of the neuron-fuzzy model in the formation of knowledge bases is being updated. The task is to develop methods and algorithms for presetting and optimizing the parameters of a fuzzy neural network. To solve difficult formalized tasks, it is necessary to develop decision support systems - expert systems based on a knowledge base. ES developers are constantly faced with the problems of “extraction” and formalization of knowledge, as well as the search for new ways to obtain it. To do this, use the extraction, acquisition and formation of knowledge. Currently, the formation of knowledge bases is relevant for the creation of hybrid technologies - fuzzy neural networks that combine the advantages of neural network models and fuzzy systems. The analysis of the efficiency of the fuzzy neural network carried out in the work showed that the quality of training of the NN largely depends on the choice of the number of fuzzy granules for input drugs. In addition, to use fuzzy information formalized by the mathematical apparatus of fuzzy logic, procedures are required for selecting optimal forms and presetting the parameters of the corresponding membership functions (MF).</p>

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50

LIU, YIAN-KUI, and JINWU GAO. "THE INDEPENDENCE OF FUZZY VARIABLES WITH APPLICATIONS TO FUZZY RANDOM OPTIMIZATION." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 15, supp02 (April 2007): 1–20. http://dx.doi.org/10.1142/s021848850700456x.

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This paper presents the independence of fuzzy variables as well as its applications in fuzzy random optimization. First, the independence of fuzzy variables is defined based on the concept of marginal possibility distribution function, and a discussion about the relationship between the independent fuzzy variables and the noninteractive (unrelated) fuzzy variables is included. Second, we discuss some properties of the independent fuzzy variables, and establish the necessary and sufficient conditions for the independent fuzzy variables. Third, we propose the independence of fuzzy events, and deal with its fundamental properties. Finally, we apply the properties of the independent fuzzy variables to a class of fuzzy random programming problems to study their convexity.

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