Journal articles: 'Fuzzy interval optimal control problem'

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Campos, José Renato, Edvaldo Assunção, Geraldo Nunes Silva, Weldon Alexander Lodwick, Marcelo Carvalho Minhoto Teixeira, and Gino Gustavo Maqui-Huamán. "Fuzzy interval optimal control problem." Fuzzy Sets and Systems 385 (April 2020): 169–81. http://dx.doi.org/10.1016/j.fss.2019.05.003.

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Abd El-Wahed Khalifa, Hamiden, Sultan S. Alodhaibi, and Pavan Kumar. "Solving Constrained Flow-Shop Scheduling Problem through Multistage Fuzzy Binding Approach with Fuzzy Due Dates." Advances in Fuzzy Systems 2021 (March 4, 2021): 1–8. http://dx.doi.org/10.1155/2021/6697060.

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This paper deals with constrained multistage machines flow-shop (FS) scheduling model in which processing times, job weights, and break-down machine time are characterized by fuzzy numbers that are piecewise as well as quadratic in nature. Avoiding to convert the model into its crisp, the closed interval approximation for the piecewise quadratic fuzzy numbers is incorporated. The suggested method leads a noncrossing optimal sequence to the considered problem and minimizes the total elapsed time under fuzziness. The proposed approach helps the decision maker to search for applicable solution related to real-world problems and minimizes the total fuzzy elapsed time. A numerical example is provided for the illustration of the suggested methodology.

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Lin, Jian, Qiang Zhang, and Fanyong Meng. "A Novel Algorithm for Group Decision Making Based on Continuous Optimal Aggregation Operator and Shapley Value." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 27, no. 06 (December 2019): 969–1002. http://dx.doi.org/10.1142/s0218488519500430.

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Interval linguistic preference relation is an effective tool for expressing experts’ preference in group decision making under uncertain linguistic environment. A new aggregation operator called continuous chi-square deviation based 2-tuple linguistic ordered weighted quasi-averaging (C-CDLOWQ) operator is proposed to transform the interval linguistic preference relations into precise linguistic preference relations. Some desirable properties and special cases of the C-CDLOWQ operator are analyzed in detail. To take the interactive phenomenon among experts into account, the Shapley weighting vector is presented to integrate the expected linguistic preference relations. The λ-fuzzy measure is employed to simplify the fuzzy measure on expert set. A CS-GDM algorithm is developed to group decision making with interval linguistic preference relations. The application in commercial investment problem is provided to illustrate the effectiveness of CS-GDM algorithm.

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LI, DENG-FENG, and YONG-CHUN WANG. "MATHEMATICAL PROGRAMMING APPROACH TO MULTIATTRIBUTE DECISION MAKING UNDER INTUITIONISTIC FUZZY ENVIRONMENTS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 16, no. 04 (August 2008): 557–77. http://dx.doi.org/10.1142/s0218488508005418.

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There exists little investigation on multiattribute decision making under intuitionistic fuzzy environments although both crisp and fuzzy multiattribute decision making have achieved a great progress. In this paper, multiattribute decision making problems using intuitionistic fuzzy sets are investigated and the TOPSIS is further extended to develop one new methodology for solving such problems. In this methodology, an interval fractional programming model is constructed on the basis of the relative closeness coefficient using the TOPSIS. Comprehensive evaluation of each alternative, which may be described as an intuitionistic fuzzy set or interval number, is calculated using two auxiliary mathematical programming problems derived from the interval fractional programming model proposed in this paper. Optimal degrees of membership for alternatives are calculated to determine their ranking order using the concept of likelihood based on the ranking method of interval numbers. Implementation process of the method proposed in this paper is illustrated with a numerical example.

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Castillo, Oscar, Fevrier Valdez, Cinthia Peraza, Jin Hee Yoon, and Zong Woo Geem. "High-Speed Interval Type-2 Fuzzy Systems for Dynamic Parameter Adaptation in Harmony Search for Optimal Design of Fuzzy Controllers." Mathematics 9, no. 7 (April 1, 2021): 758. http://dx.doi.org/10.3390/math9070758.

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Fuzzy systems have become a good solution to the problem of fixed parameters in metaheuristic algorithms, proving their efficiency when performing dynamic parameter adaptations using type-1 and type-2 fuzzy logic. However, the computational cost of type-2 fuzzy systems when using the continuous enhanced Karnik–Mendel (CKM) algorithm for type-reduction, when applied to control and optimization, is too high. Therefore, it is proposed to use an approximation to the CKM algorithm in the type-2 fuzzy system for adjusting the pitch adjustment rate (PArate) parameter in the original harmony search algorithm (HS). The main contribution of this article is to verify that the implementation of the proposed methodology achieves results that are equivalent to the interval type-2 fuzzy system with the CKM algorithm, but in less computing time and also allowing an efficient dynamic parameter adaptation. It is noteworthy that this method is relatively new in the area of metaheuristics algorithms so there is a current interest to work with this methodology. The proposed method was used in optimizing the antecedents and consequents for an interval type-2 fuzzy controller of direct current motor. Experimental results without noise and then with uniform random noise numbers (Gaussian noise) in the controller were obtained to verify that the implementation is efficient when compared to conventional and other existing methods.

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Khooban, Mohammad Hassan, Alireza Alfi, and Davood Nazari Maryam Abadi. "Teaching–learning-based optimal interval type-2 fuzzy PID controller design: a nonholonomic wheeled mobile robots." Robotica 31, no. 7 (April 19, 2013): 1059–71. http://dx.doi.org/10.1017/s0263574713000283.

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SUMMARYThis paper introduces an optimal interval type-2 fuzzy proportional–integral–derivative (PID) controller to achieve the best trajectory tracking for nonholonomic wheeled mobile robots (WMRs). In the core of the proposed method, a novel population-based optimization algorithm, called teaching–learning-based optimization (TLBO), is employed for evolving the parameters of the controller as well as the parameters of the input and output membership functions. Two PID controllers are designed for each of two wheels separately whereas each controller has two inputs and one output that are logically connected by nine rules. The controller can handle the problem of integrated kinematic and dynamic tracking in the presence of uncertainties. Simulation results demonstrate the superiority of the proposed control scheme.

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Sama, Hanumantha Rao, Vasanta Kumar Vemuri, and Venkata Siva Nageswara Hari Prasad Boppana. "Optimal Control Policy for a Two-Phase M/M/1 Unreliable Gated Queue under N-Policy with a Fuzzy Environment." Ingénierie des systèmes d information 26, no. 4 (August 31, 2021): 357–64. http://dx.doi.org/10.18280/isi.260403.

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The two-phase service models analyzed by several authors considered only the probabilistic nature of the queue parameters with fixed cost elements. But the queue parameters and cost elements will be in general are of both possibilistic and probabilistic in nature. Analyzing the performance of the queueing systems with fuzzy environment facilitates to investigate for the possibilistic interval estimates to the performance measures of a queueing system rather than point estimates. In this work, it is proposed to construct membership function of the fuzzy cost function to obtain confidence estimates for some performance measures of a controllable two-phase service single server Markovian gated queue with server startups and breakdowns under N-policy in which the queue parameters viz. arrival rate, startup rate, batch service rate, individual service rate, repair rate and cost elements are all defined as fuzzy numbers. Based on Zadeh’s extension principle and the α-cuts, a set of parametric nonlinear programming problems are developed to find the upper and lower bounds of the minimum total expected cost per unit time at the possibility level α. As the analytical solutions of the nonlinear programming problems developed for the proposed model are tedious, considering the system parameters and cost elements as trapezoidal fuzzy numbers, numerical results for the lower and upper bounds of the optimal threshold N* and the minimum total expected cost per unit time are computed using the nonlinear programming solver available in MATLAB.

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Khan, Indadul, Sova Pal, and Manas Kumar Maiti. "A Hybrid PSO-GA Algorithm for Traveling Salesman Problems in Different Environments." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 27, no. 05 (October 2019): 693–717. http://dx.doi.org/10.1142/s0218488519500314.

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In this study particle swarm optimization (PSO) is modified and hybridised with genetic algorithm (GA) using one’s output as the other's input to solve Traveling Salesman Problem(TSP). Here multiple velocity update rules are introduced to modify the PSO and at the time of the movement of a solution, one rule is selected depending on its performances using roulette wheel selection process. Each velocity update rule and the corresponding solution update rule are defined using swap sequence (SS) and swap operation (SO). K-Opt operation is applied in a regular interval of iterations for the movement of any stagnant solution. GA is applied on the final output swarm of the PSO to search the optimal path of the large size TSPs. Roulette wheel selection process, multi-point cyclic crossover and the K-opt operation for the mutation are used in the GA phase. The algorithm is tested in crisp environment using different size benchmark test problems available in the TSPLIB. In the crisp environment the algorithm gives approximately 100% success rate for the test problems up to considerably large sizes. Efficiency of the algorithm is tested with some other existing algorithms in the literature using Friedman test. Some approaches are incorporated with this algorithm for finding solutions of the TSPs in imprecise (fuzzy/rough) environment. Imprecise problems are generated from the crisp problems randomly, solved and obtained results are discussed. It is observed that the performance of the proposed algorithm is better compared to the some other algorithms in the existing literature with respect to the accuracy and the consistency for the symmetric TSPs as well as the Asymmetric TSPs.

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Campos, J. R., E. Assunção, G. N. Silva, W. A. Lodwick, and M. C. M. Teixeira. "Discrete-time interval optimal control problem." International Journal of Control 92, no. 8 (December 8, 2017): 1778–84. http://dx.doi.org/10.1080/00207179.2017.1410575.

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Ji, Linna, Fengbao Yang, and Xiaoming Guo. "Image Fusion Algorithm Selection Based on Fusion Validity Distribution Combination of Difference Features." Electronics 10, no. 15 (July 21, 2021): 1752. http://dx.doi.org/10.3390/electronics10151752.

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Aiming at addressing the problem whereby existing image fusion models cannot reflect the demand of diverse attributes (e.g., type or amplitude) of difference features on algorithms, leading to poor or invalid fusion effect, this paper puts forward the construction and combination of difference features fusion validity distribution based on intuition-possible sets to deal with the selection of algorithms with better fusion effect in dual mode infrared images. Firstly, the distances of the amplitudes of difference features between fused images and source images are calculated. The distances can be divided into three levels according to the fusion result of each algorithm, which are regarded as intuition-possible sets of fusion validity of difference features, and a novel construction method of fusion validity distribution based on intuition-possible sets is proposed. Secondly, in view of multiple amplitude intervals of each difference feature, this paper proposes a distribution combination method based on intuition-possible set ordering. Difference feature score results are aggregated by a fuzzy operator. Joint drop shadows of difference feature score results are obtained. Finally, the experimental results indicate that our proposed method can achieve optimal selection of algorithms that has relatively better effect on the fusion of difference features according to the varied feature amplitudes.

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Mustafa, Altyeb Mohammed, Zengtai Gong, and Mawia Osman. "Fuzzy Optimal Control Problem of Several Variables." Advances in Mathematical Physics 2019 (December 29, 2019): 1–12. http://dx.doi.org/10.1155/2019/2182640.

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The purpose of this paper is to establish the necessary conditions for a fuzzy optimal control problem of several variables. Also, we define fuzzy optimal control problems involving isoperimetric constraints and higher order differential equations. Then, we convert these problems to fuzzy optimal control problems of several variables in order to solve these problems using the same solution method. The main results of this paper are illustrated throughout three examples, more specifically, a discussion on the strong solutions (fuzzy solutions) of our problems.

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Plotnikov, Andrej, Tatyana Komleva, Liliya Plotnikova, and Natalia Skripnik. "Time-Optimal Control Problem for a Fuzzy Object." Modeling, Control and Information Technologies, no. 4 (October 22, 2020): 31–34. http://dx.doi.org/10.31713/mcit.2020.01.

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In this article one optimal control problem when the system behavior is described by linear fuzzy differential equations is considered. The conditions of its solvability are formulated, and the optimal time and optimal controls are obtained.

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Niftiyev, A. A., C. I. Zeynalov, and M. Poormanuchehri. "Fuzzy Optimal Control Problem with Non-linear Functional." Fuzzy Information and Engineering 3, no. 3 (September 2011): 311–20. http://dx.doi.org/10.1007/s12543-011-0085-6.

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Victoria Olegovna, O. "Interval optimal control problem in a Hilbert space." Computational Mathematics and Mathematical Physics 53, no. 4 (April 2013): 389–95. http://dx.doi.org/10.1134/s0965542513040064.

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Phu, Nguyen Dinh, and Nguyen Nhut Hung. "Minimum stability control problem and time-optimal control problem for fuzzy linear control systems." Fuzzy Sets and Systems 371 (September 2019): 1–24. http://dx.doi.org/10.1016/j.fss.2018.09.005.

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Aliev, F. A., Aghaddin Aslan Niftiyev, and C. I. Zeynalov. "Optimal synthesis problem for the fuzzy systems." Optimal Control Applications and Methods 32, no. 6 (August 31, 2010): 660–67. http://dx.doi.org/10.1002/oca.964.

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Haitao, Liu, Gong Aihong, and Hu Mingmao. "An optimal control method for fuzzy supplier switching problem." International Journal of Machine Learning and Cybernetics 6, no. 4 (July 5, 2015): 651–54. http://dx.doi.org/10.1007/s13042-015-0392-z.

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Bharati, S. K., and S. R. Singh. "Interval-Valued Intuitionistic Fuzzy Linear Programming Problem." New Mathematics and Natural Computation 16, no. 01 (March 2020): 53–71. http://dx.doi.org/10.1142/s1793005720500040.

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In many existing methods of linear programming problem (LPP), precise values of parameters have been used but parameters of LPP are imprecise and ambiguous due to incomplete information. Several approaches and theories have been developed for dealing LPP based on fuzzy set (FS), intuitionistic fuzzy set (IFS) which are characterized by membership degree, membership and non-membership degrees, respectively. It’s interesting to note that single membership and non-membership degrees do not deal properly the state of uncertainty and hesitation. Further, we face a kind of uncertainty occurs a kind of uncertainty. Interval-valued intuitionistic fuzzy sets (IV-IFS) is a perfect key for handling uncertainty and hesitation than FS and IFS. In this paper, we define an interval-valued intuitionistic fuzzy number (IV-IFN) and its expected interval and expected values. We also introduce the concept of interval-valued intuitionistic fuzzy linear programming problem (IV-IFLPP). Further, we find the solutions of IV-IFLPP and compare the obtained optimal solutions with existing methods [D. Dubey and A. Mehra, Linear programming with Triangular Intuitionistic Fuzzy Numbers, in Proc. of the 7th Conf. and of the European Society for Fuzzy Logic and Technology (EUSFLAT-LFA 2011), R. Parvathi and C. Malathi, Intuitionistic fuzzy linear optimization, Notes on Intuitionistic Fuzzy Sets 18 (2012) 48–56]. Proposed technique may be used successfully in various areas in the formulation of our country’s five year plans, these include transportation, food-grain storage, urban development, national, state and district level plans, etc., The Indian Railways may use IV-IFLPP technique for linking different railway zones in more realistic way. Agricultural research institutes may use proposed technique for crop rotation mix of cash crops, food crops and fertilizer mix. Airlines can apply IV-IFLPP in the selection of routes and allocation of aircrafts to different routes. Private and public sector oil refineries may use IV-IFLPP for blending of oil ingredients to produce finished petroleum products.

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Abd El-Wahed Khalifa, Hamiden, Pavan Kumar, and Majed G. Alharbi. "Enhancement of Capacitated Transportation Problem in Fuzzy Environment." Advances in Fuzzy Systems 2020 (October 1, 2020): 1–9. http://dx.doi.org/10.1155/2020/8893976.

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This research work aims to study a capacitated transportation problem (CTP) with penalty cost, supplies, and demands represented by hexagonal fuzzy numbers. Based on ranking function, the supplies and demands are converted to the crisp form. Through the use of the α‐level, the problem is converted into interval linear programming. To optimize the interval objective function, we define the order relations represented by policy maker’s choice between intervals. The maximization (minimization) problem considering the interval objective function is transformed to multiobjective optimization problem based on order relations introduced by the preference of policy makers between interval profits (costs). A numerical example is given for illustration and to check the validity of the suggested approach.

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Thanh, Ha Pham, Ho Nguyen Cat, and Lan Vu Nhu. "A METHOD BUILD FUZZY ASSOCIATE MEMORY FOR FUZZY CONTROL PROBLEMS." ASEAN Journal on Science and Technology for Development 25, no. 2 (November 22, 2017): 281–94. http://dx.doi.org/10.29037/ajstd.258.

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Building fuzzy associate memory accordance with control problems has great meaning for control methods In this paper we propose a method, that build fuzzy associate memory for control problem based on optimal trajectory of control problem, the method developed by theory hedge algebras and genetic algorithm.

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Srinivasan, A., and G. Geetharamani. "Linear Programming Problem with Interval Type 2 Fuzzy Coefficients and an Interpretation for Its Constraints." Journal of Applied Mathematics 2016 (2016): 1–11. http://dx.doi.org/10.1155/2016/8496812.

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Interval type 2 fuzzy numbers are a special kind of type 2 fuzzy numbers. These numbers can be described by triangular and trapezoidal shapes. In this paper, first, perfectly normal interval type 2 trapezoidal fuzzy numbers with their left-hand and right-hand spreads and their core have been introduced, which are normal and convex; then a new type of fuzzy arithmetic operations for perfectly normal interval type 2 trapezoidal fuzzy numbers has been proposed based on the extension principle of normal type 1 trapezoidal fuzzy numbers. Moreover, in this proposal, linear programming problems with resources and technology coefficients are perfectly normal interval type 2 fuzzy numbers. To solve this kind of fuzzy linear programming problems, a method based on the degree of satisfaction (or possibility degree) of the constraints has been introduced. In this method the fulfillment of the constraints can be measured with the help of ranking method of fuzzy numbers. Optimal solution is obtained at different degree of satisfaction by using Barnes algorithm with the help of MATLAB. Finally, the optimal solution procedure is illustrated with numerical example.

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Gurukumaresan, D., C. Duraisamy, and R. Srinivasan. "Optimal Solution of Fuzzy Transportation Problem Using Octagonal Fuzzy Numbers." Computer Systems Science and Engineering 37, no. 3 (2021): 415–21. http://dx.doi.org/10.32604/csse.2021.014130.

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Baten, Md Azizul, and Anton Abdulbasah Kamil. "Fuzzy optimal control with application to discounted profit advertising problem." Journal of Intelligent & Fuzzy Systems 23, no. 5 (2012): 187–92. http://dx.doi.org/10.3233/ifs-2012-0508.

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Li, Chunquan. "A fuzzy multi-objective linear programming with interval-typed triangular fuzzy numbers." Open Mathematics 17, no. 1 (June 27, 2019): 607–26. http://dx.doi.org/10.1515/math-2019-0048.

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Abstract A multi-objective linear programming problem (ITF-MOLP) is presented in this paper, in which coefficients of both the objective functions and constraints are interval-typed triangular fuzzy numbers. An algorithm of the ITF-MOLP is provided by introducing the cut set of interval-typed triangular fuzzy numbers and the dominance possibility criterion. In particular, for a given level, the ITF-MOLP is converted to the maximization of the sum of membership degrees of each objective in ITF-MOLP, whose membership degrees are established based on the deviation from optimal solutions of individual objectives, and the constraints are transformed to normal inequalities by utilizing the dominance possibility criterion when compared with two interval-typed triangular fuzzy numbers. Then the equivalent linear programming model is obtained which could be solved by Matlab toolbox. Finally several examples are provided to illuminate the proposed method by comparing with the existing methods and sensitive analysis demonstrates the stability of the optimal solution.

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Zhang, Lifei, and Fanyong Meng. "An Approach to Interval-Valued Hesitant Fuzzy Multiattribute Group Decision Making Based on the Generalized Shapley-Choquet Integral." Complexity 2018 (June 10, 2018): 1–19. http://dx.doi.org/10.1155/2018/3941847.

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The purpose of this paper is to develop an approach to multiattribute group decision making under interval-valued hesitant fuzzy environment. To do this, this paper defines some new operations on interval-valued hesitant fuzzy elements, which eliminate the disadvantages of the existing operations. Considering the fact that elements in a set may be interdependent, two generalized interval-valued hesitant fuzzy operators based on the generalized Shapley function and the Choquet integral are defined. Then, some models for calculating the optimal fuzzy measures on the expert set and the ordered position set are established. Because fuzzy measures are defined on the power set, it makes the problem exponentially complex. To simplify the complexity of solving a fuzzy measure, models for the optimal 2-additive measures are constructed. Finally, an investment problem is offered to show the practicality and efficiency of the new method.

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Roul, Jotindra Nath, Kalipada Maity, Samarjit Kar, and Manoranjan Maiti. "Multi-item Optimal control problem with fuzzy costs and constraints using Fuzzy variational principle." RAIRO - Operations Research 53, no. 3 (July 2019): 1061–82. http://dx.doi.org/10.1051/ro/2019022.

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An imperfect multi-item production system is considered against time dependent demands for a finite time horizon. Here production is defective. Following [Khouja and Mehrez J. Oper. Res. Soc. 45 (1994) 1405–1417], unit production cost depends on production, raw-material and maintenance costs. Produced items have same fixed life-time. Warehouse capacity is limited and used as a constraint. Available space, production, stock and different costs are assumed as crisp or imprecise. With the above considerations, crisp and fuzzy constrained optimal control problems are formulated for the minimization of total cost consisting of raw-material, production and holding costs. These models are solved using conventional and fuzzy variational principles with equality constraint condition and no-stock as end conditions. For the first time, the inequality space constraint is converted into an equality constraint introducing a pseudo state variable following Bang Bang control. [Roul et al., J. Intell. Fuzzy Syst. 32 (2017) 565–577], as stock is mainly controlled by production, for the control problems production is taken as the control variable and stock as state variable. The reduced optimal control problem is solved by generalised reduced gradient method using Lingo-11.0. The models are illustrated numerically. For the fuzzy model, optimum results are obtained as fuzzy numbers expressed by their membership functions. From fuzzy results, crisp results are derived using α-cuts.

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Mcbeth, Douglas W., and Ananda P. N. Weerasinghe. "Finite-time optimal control of a process leaving an interval." Journal of Applied Probability 33, no. 3 (September 1996): 714–28. http://dx.doi.org/10.2307/3215353.

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Consider the optimal control problem of leaving an interval (– a, a) in a limited playing time. In the discrete-time problem, a is a positive integer and the player's position is given by a simple random walk on the integers with initial position x. At each time instant, the player chooses a coin from a control set where the probability of returning heads depends on the current position and the remaining amount of playing time, and the player is betting a unit value on the toss of the coin: heads returning +1 and tails − 1. We discuss the optimal strategy for this discrete-time game. In the continuous-time problem the player chooses infinitesimal mean and infinitesimal variance parameters from a control set which may depend upon the player's position. The problem is to find optimal mean and variance parameters that maximize the probability of leaving the interval [— a, a] within a finite time T > 0.

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Mcbeth, Douglas W., and Ananda P. N. Weerasinghe. "Finite-time optimal control of a process leaving an interval." Journal of Applied Probability 33, no. 03 (September 1996): 714–28. http://dx.doi.org/10.1017/s0021900200100154.

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Consider the optimal control problem of leaving an interval (– a, a) in a limited playing time. In the discrete-time problem, a is a positive integer and the player's position is given by a simple random walk on the integers with initial position x. At each time instant, the player chooses a coin from a control set where the probability of returning heads depends on the current position and the remaining amount of playing time, and the player is betting a unit value on the toss of the coin: heads returning +1 and tails − 1. We discuss the optimal strategy for this discrete-time game. In the continuous-time problem the player chooses infinitesimal mean and infinitesimal variance parameters from a control set which may depend upon the player's position. The problem is to find optimal mean and variance parameters that maximize the probability of leaving the interval [— a, a] within a finite time T > 0.

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Gardashova, Latafat A. "Application of DEO Method to Solving Fuzzy Multiobjective Optimal Control Problem." Applied Computational Intelligence and Soft Computing 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/971894.

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In the present paper a problem of optimal control for a single-product dynamical macroeconomic model is considered. In this model gross domestic product is divided into productive consumption, gross investment, and nonproductive consumption. The model is described by a fuzzy differential equation (FDE) to take into account imprecision inherent in the dynamics that may be naturally conditioned by influence of various external factors, unforeseen contingencies of future, and so forth. The considered problems are characterized by four criteria and by several important aspects. On one hand, the problem is complicated by the presence of fuzzy uncertainty as a result of a natural imprecision inherent in information about dynamics of real-world systems. On the other hand, the number of the criteria is not small and most of them are integral criteria. Due to the above mentioned aspects, solving the considered problem by using convolution of criteria into one criterion would lead to loss of information and also would be counterintuitive and complex. We applied DEO (differential evolution optimization) method to solve the considered problem.

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Witayakiattilerd, Wichai. "Nonlinear Fuzzy Differential Equation with Time Delay and Optimal Control Problem." Abstract and Applied Analysis 2015 (2015): 1–14. http://dx.doi.org/10.1155/2015/659072.

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The existence and uniqueness of a mild solution to nonlinear fuzzy differential equation constrained by initial value were proven. Initial value constraint was then replaced by delay function constraint and the existence of a solution to this type of problem was also proven. Furthermore, the existence of a solution to optimal control problem of the latter type of equation was proven.

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Mandal, Nirmal. "Fuzzy economic order quantity model with ranking fuzzy number cost parameters." Yugoslav Journal of Operations Research 22, no. 2 (2012): 247–64. http://dx.doi.org/10.2298/yjor110727014m.

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In this paper, a multi-objective economic order quantity model with shortages and demand dependent unit cost under storage space constraint is formulated. In real life situation, the objective and constraint goals and cost parameters are not precisely defined. These are defined in fuzzy environment. The cost parameters are represented here as triangular shaped fuzzy numbers with different types of left and right branch membership functions. The fuzzy numbers are then expressed as ranking fuzzy numbers with best approximation interval. Geometric programming approach is applied to derive the optimal decisions in closed form. The inventory problem without shortages is discussed as a special case of the original problem. A numerical illustration is given to support the problem.

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Rapoport, Edgar Ya, and Nikoly G. Rogachev. "Fuzzy optimization of feedback control at induction heating." Vestnik of Samara State Technical University. Technical Sciences Series 29, no. 2 (August 30, 2021): 61–75. http://dx.doi.org/10.14498/tech.2021.4.

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The problem of multi-criteria fuzzy-optimal feedback control of an induction heater as an object of technological thermophysics with distributed parameters is considered. A general formulation of the fuzzy optimization problem is given, including requirements for the final and intermediate states and taking into account the fuzziness of competing quality criteria. When solving the problem, interconnected electromagnetic and thermal models of the induction heating process were used. The secondary source method was used to simulate electromagnetic processes, and the differential-difference method was used to simulate thermal conductivity. The numerical method for solving the problem is based on the presentation of the control algorithm in the form of an a priori non-fixed and variable system of rules determined during the heating process. The obtained results of numerical modeling confirm the effectiveness of the proposed fuzzy-optimal method for determining the positional control of objects with distributed parameters.

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Ren, Aihong. "A Novel Method for Solving the Fully Fuzzy Bilevel Linear Programming Problem." Mathematical Problems in Engineering 2015 (2015): 1–11. http://dx.doi.org/10.1155/2015/280380.

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We address a fully fuzzy bilevel linear programming problem in which all the coefficients and variables of both objective functions and constraints are expressed as fuzzy numbers. This paper is to develop a new method to deal with the fully fuzzy bilevel linear programming problem by applying interval programming method. To this end, we first discretize membership grade of fuzzy coefficients and fuzzy decision variables of the problem into a finite number ofα-level sets. By usingα-level sets of fuzzy numbers, the fully fuzzy bilevel linear programming problem is transformed into an interval bilevel linear programming problem for eachα-level set. The main idea to solve the obtained interval bilevel linear programming problem is to convert the problem into two deterministic subproblems which correspond to the lower and upper bounds of the upper level objective function. Based on theKth-best algorithm, the two subproblems can be solved sequentially. Based on a series ofα-level sets, we introduce a linear piecewise trapezoidal fuzzy number to approximate the optimal value of the upper level objective function of the fully fuzzy bilevel linear programming problem. Finally, a numerical example is provided to demonstrate the feasibility of the proposed approach.

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Zhao, Yu Chi, and Jing Liu. "The Application of Fuzzy Control in Computer Control." Advanced Materials Research 756-759 (September 2013): 349–53. http://dx.doi.org/10.4028/www.scientific.net/amr.756-759.349.

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Fuzzy control theory is a computer numerical control theory based on fuzzy set theory, fuzzy language variable and fuzzy logic reasoning. It is widely used for it doesnt require exact mathematical model of controlled object in system design, so that fuzzy control has an advantage in researching high nonlinear system like inverted pendulum. However, rule explosion problem is unavoidable when we use fuzzy control theory to solve some multivariable system control problems such as inverted pendulum. This paper presents the application of the optimal control theory to reduce the input variable dimensions and the rules of the fuzzy controller through designing a fusion function, solving rule explosion problem successfully. The paper also discusses the control effect influenced by quantification factors, promoting performance quality of the fuzzy controller by setting threshold value to make quantification factors automatic regulation.

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T.Allawi, Ziyad, and Turki Y. Abdalla. "An Optimized Interval Type-2 Fuzzy Logic Control Scheme based on Optimal Defuzzification." International Journal of Computer Applications 95, no. 13 (June 18, 2014): 26–31. http://dx.doi.org/10.5120/16655-6633.

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Dimitrov, Valery P., Lyudmila V. Borisova, Inna N. Nurutdinova, Viktor I. Pakhomov, and V. P. Maksimov. "The problem of choice of optimal technological decisions on harvester control." MATEC Web of Conferences 226 (2018): 04023. http://dx.doi.org/10.1051/matecconf/201822604023.

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The paper considers the problem of determining optimal technological decisions on a harvester control which includes the choice of the harvester adjustable parameters at presetting and also their updating in the process of operation. To solve this problem, an information system of decision making support based on fuzzy expert knowledge is used. The expedience of this approach is stipulated by the data fuzziness about the factors of the environment in which the harvester is operating and also by complex and system of uncertain interrelations among external factors, adjustable parameters and harvesting quality indices. For the case of harvesting grain crops an expert knowledge base has been made which makes it possible to formalize empirical knowledge about the dependencies of the harvester adjustable parameters on the environment factors such as crop yield, stand of grain humidity, stand of grain dockage rough straw. The most essential adjustable parameters have been considered: speed of the harvester motion, rotational speed of a threshing drum and rotor speed of a separator fan. Fuzzy logic inference has been performed with the help of Fuzzy Logic Toolbox application package (Matlab). The examples of technological decisions of the harvester preliminary adjustment at different environmental conditions have been presented, accurate values of the adjustable parameters were calculated by the «barycentre» method.

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GRIGORIEVA, ELLINA V., EVGENII N. KHAILOV, NATALIA V. BONDARENKO, and ANDREI KOROBEINIKOV. "MODELING AND OPTIMAL CONTROL FOR ANTIRETROVIRAL THERAPY." Journal of Biological Systems 22, no. 02 (June 2014): 199–217. http://dx.doi.org/10.1142/s0218339014400026.

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We consider a three-dimensional nonlinear control model based on the Wodarz HIV model. The model phase variables are populations of the uninfected and infected target cells and the concentration of an antiretroviral drug. The drug intake rate is assumed to be a bounded control function. An optimal control problem of minimizing the cumulative infection level (the infected cells population) on a given time interval is stated and solved, and the types of the optimal control for different model parameters are found by analytical methods. We thereby reduce the two-point boundary value problem (TPBVP) for the Pontryagin maximum principle to a problem of the finite-dimensional optimization. Numerical results are presented to illustrate the optimal solution.

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Zarei, Hassan, Ali Vahidian Kamyad, and Sohrab Effati. "Multiobjective Optimal Control of HIV Dynamics." Mathematical Problems in Engineering 2010 (2010): 1–29. http://dx.doi.org/10.1155/2010/568315.

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Various aspects of the interaction of HIV with the human immune system can be modeled by a system of ordinary differential equations. This model is utilized, and a multiobjective optimal control problem (MOOCP) is proposed to maximize the CD4+ T cells population and minimize both the viral load and drug costs. The weighted sum method is used, and continuous Pareto optimal solutions are derived by solving the corresponding optimality system. Moreover, a model predictive control (MPC) strategy is applied, with the final goal of implementing Pareto optimal structured treatment interruptions (STI) protocol. In particular, by using a fuzzy approach, the MOOCP is converted to a single-objective optimization problem to derive a Pareto optimal solution which among other Pareto optimal solutions has the best satisfaction performance. Then, by using an embedding method, the problem is transferred into a modified problem in an appropriate space in which the existence of solution is guaranteed by compactness of the space. The metamorphosed problem is approximated by a linear programming (LP) model, and a piecewise constant solution which shows the desired combinations of reverse transcriptase inhibitor (RTI) and protease inhibitor (PI) drug efficacies is achieved.

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Mullier, Olivier, Julien Alexandre dit Sandretto, and Alexandre Chapoutot. "Optimal Switching Instants for the Control of Hybrid Systems." Acta Cybernetica 24, no. 3 (March 18, 2020): 449–65. http://dx.doi.org/10.14232/actacyb.24.3.2020.10.

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The problem of determining optimal switching instants for the control of hybrid systems under reachability constraints is considered. This optimization problem is cast into an interval global optimization problem with differential constraints, where validated simulation techniques and dynamic time meshing are used for its solution. The approach is applied on two examples, one being the well-known example of the Goddard's problem where a rocket has to reach a given altitude while consuming the smallest amount of fuel.

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Zarei, Hassan, Ali Vahidian Kamyad, and Ali Akbar Heydari. "Fuzzy Modeling and Control of HIV Infection." Computational and Mathematical Methods in Medicine 2012 (2012): 1–17. http://dx.doi.org/10.1155/2012/893474.

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The present study proposes a fuzzy mathematical model of HIV infection consisting of a linear fuzzy differential equations (FDEs) system describing the ambiguous immune cells level and the viral load which are due to the intrinsic fuzziness of the immune system's strength in HIV-infected patients. The immune cells in question are considered CD4+ T-cells and cytotoxic T-lymphocytes (CTLs). The dynamic behavior of the immune cells level and the viral load within the three groups of patients with weak, moderate, and strong immune systems are analyzed and compared. Moreover, the approximate explicit solutions of the proposed model are derived using a fitting-based method. In particular, a fuzzy control function indicating the drug dosage is incorporated into the proposed model and a fuzzy optimal control problem (FOCP) minimizing both the viral load and the drug costs is constructed. An optimality condition is achieved as a fuzzy boundary value problem (FBVP). In addition, the optimal fuzzy control function is completely characterized and a numerical solution for the optimality system is computed.

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Roul, J. N., K. Maity, S. Kar, and M. Maiti. "Optimal control problem for an imperfect production process using fuzzy variational principle." Journal of Intelligent & Fuzzy Systems 32, no. 1 (January 13, 2017): 565–77. http://dx.doi.org/10.3233/jifs-152503.

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ZHANG, HUAGUANG, ZHILIANG WANG, and DERONG LIU. "CHAOTIFYING FUZZY HYPERBOLIC MODEL USING ADAPTIVE INVERSE OPTIMAL CONTROL APPROACH." International Journal of Bifurcation and Chaos 14, no. 10 (October 2004): 3505–17. http://dx.doi.org/10.1142/s0218127404011442.

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In this paper, the problem of chaotifying the continuous-time fuzzy hyperbolic model (FHM) is studied. By tracking the dynamics of a chaotic system, a controller based on inverse optimal control and adaptive parameter tuning methods is designed to chaotify the FHM. Simulation results show that for any initial value the FHM can track a chaotic system asymptotically.

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Dmitruk, A. V., and N. V. Kuz'kina. "Existence Theorem in the Optimal Control Problem on an Infinite Time Interval." Mathematical Notes 78, no. 3-4 (September 2005): 466–80. http://dx.doi.org/10.1007/s11006-005-0147-3.

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Tan, Chunqiao, Benjiang Ma, Desheng Dash Wu, and Xiaohong Chen. "Multi-Criteria Decision Making Methods Based on Interval-Valued Intuitionistic Fuzzy Sets." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 22, no. 03 (June 2014): 469–88. http://dx.doi.org/10.1142/s0218488514500238.

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Fuzziness is inherent in decision data and decision making process. In this paper, interval-valued intuitionistic fuzzy set is used to capture fuzziness in multi-criteria decision making problems. The purpose of this paper is to develop a new method for solving multi-criteria decision making problem in interval-valued intuitionistic fuzzy environments. First, we introduce and discuss the concept of interval-valued intuitionistic fuzzy point operators. Using the interval-valued intuitionistic fuzzy point operators, we can reduce the degree of uncertainty of the elements in a universe corresponding to an interval-valued intuitionistic fuzzy set. Then, we define an evaluation function for the decision-making problem to measure the degrees to which alternatives satisfy and do not satisfy the decision-maker's requirement. Furthermore, a series of new score functions are defined for multi-criteria decision making problem based on the interval-valued intuitionistic fuzzy point operators and the evaluation function and their effectiveness and advantage are illustrated by examples.

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Bai, Xuejie, Feng Zhang, and Yankui Liu. "Modeling fuzzy data envelopment analysis under robust input and output data." RAIRO - Operations Research 52, no. 2 (April 2018): 619–43. http://dx.doi.org/10.1051/ro/2017038.

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This paper offers a fuzzy optimization framework for data envelopment analysis (DEA) to evaluate the relative efficiency of decision making units (DMUs) with parametric interval-valued fuzzy variable-based inputs and outputs. The parametric interval-valued fuzzy variable-based inputs and outputs is employed to capture the uncertainty of data on the basis of professional judgements or empirical estimations. The DEA problem is formulated as fuzzy expectation model with credibility constraints. When the inputs and outputs are mutually independent parametric interval-valued triangular fuzzy variables, we investigate the parametric equivalent representations of expectation objective function and chance constraints. In order to find the optimal solution of our DEA model, a domain decomposition method is proposed. Finally, the numerical example on the sustainable supplier evaluation and selection problem is provided to demonstrate the efficiency of the proposed DEA model and domain decomposition method.

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Deng, Liubao, and Yuanguo Zhu. "An uncertain optimal control model with n jumps and application." Computer Science and Information Systems 9, no. 4 (2012): 1453–68. http://dx.doi.org/10.2298/csis120225049d.

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Optimal control theory is an important branch of modern control theory which has been widely applied in various sciences. Uncertain optimal control is a theory dealing with optimal control problems which are based a new uncertainty theory and differs from the stochastic optimal control based on probability theory and fuzzy optimal control based on fuzzy set theory or credibility theory. As the further work of the uncertain optimal control with jump in the one-dimensional case and multidimensional linear-quadratic (LQ) uncertain optimal control problem with jump which has a quadratic objective function for a linear uncertain control system with jump, a general uncertain optimal control problem with n jumps in the multi-dimensional cases is considered in this paper. The principle of optimality is presented and the equation of optimality is obtained about multidimensional uncertain optimal control with n jumps. Finally, as an application, an optimal control problem in R&D (Research and Development) fiscal subsidy policy is discussed and the optimal control decisions are obtained.

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Abdillah, Muhammad, Teguh Aryo Nugroho, and Nita Indriani Pertiwi. "Multi-Objective Interval Type 2 Fuzzy Sine Cosine Algorithm for Solving Optimal Power Flow Problem." International Review of Electrical Engineering (IREE) 16, no. 2 (April 30, 2021): 118. http://dx.doi.org/10.15866/iree.v16i2.18188.

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Fisher, M. E., J. L. Noakes, and K. L. Teo. "A minimum trapping time problem in optimal control theory." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 32, no. 1 (July 1990): 100–114. http://dx.doi.org/10.1017/s0334270000008237.

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AbstractIn this paper we consider a natural extension of the minimum time problem in optimal control theory which we refer to as the minimum trapping time problem. The minimum trapping time problem requires a fixed time interval [0, T], where T is finite. The aim is to determine a control for which the system trajectory not only reaches a specified target in minimum time but also remains trapped within the target until time T. Our aim is to devise a computational procedure for solving the minimum trapping time problem. The computational procedure we adopt uses control parametrisation in which the class of controls is approximated by a class of piecewise constant functions. The problem we are solving is therefore an approximation to the original minimum trapping time problem. Some properties for the approximate problem are then established. These lead to an extremely efficient iterative procedure for calculating the minimum trapping time.

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Sun, Hao, Ye-Hwa Chen, Han Zhao, and Shengchao Zhen. "Optimal design for robust control parameter for active roll control system: a fuzzy approach." Journal of Vibration and Control 24, no. 19 (September 13, 2017): 4575–91. http://dx.doi.org/10.1177/1077546317730710.

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In this paper, we investigate the dynamical model of an active roll control system (ARCS) which can impose an anti-roll moment quickly by active actuators to prevent a vehicle rolling when the vehicle generates the roll tendency and effectively enhances the vehicle dynamic performance without sacrificing ride comfort. In the dynamic model of the ARCS, we consider the sprung mass of the vehicle which is (possibly) time-varying and the initial conditions are the uncertain parameters which are described by fuzzy set theory. A new optimal robust control which is deterministic and is not the usual if–then rules-based control is proposed. The desired controlled system performance is twofold: one deterministic, which includes uniform boundedness and uniform ultimate boundedness, and one fuzzy, which enhances the cost consideration. We then formulate an optimal design problem associated with the control as a constrained optimization problem. The resulting control design is systematic and is able to guarantee the deterministic performance and minimize the average fuzzy performance. Numerical simulations show that the control design renders the ARCS practically stable and achieves constraints following maneuvering.

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Li, Hongyi, Jiahui Wang, Ligang Wu, Hak-Keung Lam, and Yabin Gao. "Optimal Guaranteed Cost Sliding-Mode Control of Interval Type-2 Fuzzy Time-Delay Systems." IEEE Transactions on Fuzzy Systems 26, no. 1 (February 2018): 246–57. http://dx.doi.org/10.1109/tfuzz.2017.2648855.

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Journal articles on the topic 'Fuzzy interval optimal control problem'

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