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Generalization of Yang et al.'s method for fuzzy programming with piecewise linear membership functions

FUZZY SETS AND SYSTEMS 2002年第3期132卷 347-352页

作者： Lin, CC Chen, AP Kung Shan Univ Technol Dept Informat Management Tainan 710 Taiwan Natl Chiao Tung Univ Inst Informat Management Hsinchu 300 Taiwan

Li and Yu (Fuzzy Sets and Systems 101 (1999) 109) argued that the model of Yang et al. for fuzzy programming (Fuzzy Sets and Systems 41 (1991) 39) is correct only for a specific type of piecewise linear membership function and proposed their model for other type of membership functions. This study generalizes the model of Yang et al. A numerical example indicates that the model of Li and Yu is inapplicable to a fuzzy programming problem that involves more than one membership function, whereas the proposed model gives the optimal solution. (C) 2002 Elsevier Science B.V. All rights reserved.

关键词： fuzzy programming piecewise linear membership functions quasi-concave membership functions

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A novel approach for FNLP with piecewise linear membership functions

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CHEMOMETRICS AND INTELLIGENT LABORATORY SYSTEMS 2019年 191卷 88-95页

作者： Wen, Bo Gu, Wen Yang, Bo Li, Hongguang Chen, Xiaochun Beijing Univ Chem Technol Coll Informat Sci & Technol Beijing Peoples R China Beijing Univ Chem Technol Coll Chem Engn Beijing Peoples R China Changzheng Engn Co Ltd Shanghai Peoples R China

In the fuzzy nonlinear programming (FNLP) domain, piecewise linear membership functions (PLMFs) are often employed to linearize the nonlinear membership functions. However, the linearization error will reduce the accuracy of the solution, which has become an obstacle to the application of PLMFs. In this paper, we present an iterative algorithm based on geometrical means to solve the problems mentioned above. Firstly, the linearization error can be reduced by gradually modifying the programming model. Subsequently, compared with traditional methods, the linearization model is determined only by weighing the linearization degree of membership function and the accuracy of programming results, the proposed method is more directly and effectively. Furthermore, in-depth discussions are also given along with the algorithm for demonstrating the rationality. Finally, the proposed method is validated and compared with other methods. A real example is examined to demonstrate applicability of the proposed method in this paper.

关键词： Fuzzy nonlinear programming piecewise linear membership functions Error analysis Iterative algorithm

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Stability Analysis and Stabilization of Polynomial Fuzzy-Model-Based Control Systems Using piecewise linear membership functions

Stability Analysis and Stabilization of Polynomial Fuzzy-Mod...

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2010 IEEE World Congress on Computational Intelligence

作者： Lam, H. K. Narimani, Mohammad Leung, F. H. F. Kings Coll London Div Engn Dept Elect Engn Strand London WC2R 2LC England Hong Kong Polytech Univ Elect & Informat Engn Dept Kowloon Hong Kong Peoples R China

ISBN: (纸本)9781424469208

This paper presents the stability analysis of polynomial fuzzy-model-based (PFMB) control system, formed by a polynomial fuzzy model and a fuzzy controller connected in a closed loop, using sum-of-squares (SOS) approach. Unlike the published work, the PFMB control system is not required that the polynomial fuzzy controller shares the same premises membership functions as those of the polynomial fuzzy model. piecewise linear membership functions are employed to approximate the membership functions of the polynomial fuzzy model and polynomial fuzzy controller to facilitate stability analysis and controller synthesis with consideration of approximation error. The piecewise linear membership functions offer a nice property that the grades of membership are governed by a finite number of sampled points. It is worth mentioning that the piecewise linear membership functions, which are not necessarily implemented physically, are a tool to carry out the stability analysis. The nice property of the piecewise linear membership functions allows them to be brought to the SOS-based stability conditions derived based on the Lyapunov stability theory. Consequently, the proposed SOS-based stability conditions are applied to PFMB control systems with the specified piecewise linear membership functions rather than any shapes. A simulation example is given to verify the stability analysis results and demonstrate the effectiveness of the proposed approach.

关键词： Lyapunov methods Lyapunov stability theory approximation error closed loop closed loop systems control system analysis control system synthesis controller synthesis fuzzy control piecewise linear membership functions piecewise linear techniques polynomial approximation polynomial fuzzy-model-based control system stabilization stability stability analysis sum-of-squares approach

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An Approach to Formulation of FNLP with Complex piecewise linear membership functions

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Chinese Journal of Chemical Engineering 2014年第4期22卷 411-417页

作者：闻博李宏光 School of Information Science and Technology Beijing University of Chemical Technology

Traditionally, extra binary variables are demanded to formulate a fuzzy nonlinear programming(FNLP) problem with piecewise linear membership functions(PLMFs). However, this kind of methodology usually suffers increasing computational burden associated with formulation and solution, particularly in the face of complex PLMFs. Motivated by these challenges, this contribution introduces a novel approach free of additional binary variables to formulate FNLP with complex PLMFs, leading to superior performance in reducing computational complexity as well as simplifying formulation. A depth discussion about the approach is conducted in this paper, along with a numerical case study to demonstrate its potential benefits.

关键词： fuzzy nonlinear programming piecewise linear membership functions modeling

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Exact analytical inversion of TSK fuzzy systems with singleton and linear consequents

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INTERNATIONAL JOURNAL OF APPROXIMATE REASONING 2014年第6期55卷 1357-1368页

作者： Ulu, Cenk Guzelkaya, Mujde Eksin, Ibrahim TUBITAK Marmara Res Ctr Energy Inst TR-41470 Kocaeli Turkey Istanbul Tech Univ Fac Elect & Elect Engn Dept Control Engn TR-34469 Istanbul Turkey

In literature, exact inversion methods for TSK fuzzy systems exist only for the systems with singleton consequents. These methods have binding limitations such as strong triangular partitioning, monotonic rule bases and/or invertibility check. These extra limitations lessen the modeling capabilities of the TSK fuzzy systems. In this study, an exact analytical inversion method for TSK fuzzy systems with singleton and linear consequents is presented. The only limitation of the proposed method is that the inversion variable should be represented by piecewise linear membership functions (PWL-MFs). In this case, the universe of discourse of the inversion variable is divided into specific regions in which only one linear piece exists for each PWL-MF at most. In the proposed method, the analytical formulation of TSK fuzzy system is expressed in terms of the inversion variable by using linear equations of PWL-MFs. Thus, the fuzzy system output in any region can be obtained by using the appropriate parameters of the linear equations of PWL-MFs defined within the related region. This expression provides a way to obtain linear and quadratic equations in terms of the inversion variable for TSK fuzzy systems with singleton and linear consequents, respectively. So, it becomes very easy to find exact inverse solutions for each region by using explicit analytical solutions for linear or quadratic equations. The proposed inversion method has been illustrated through simulation examples. (c) 2014 Elsevier Inc. All rights reserved.

关键词： TSK fuzzy systems Inversion linear consequents piecewise linear membership functions

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Application of Fuzzy Multi-Objective linear Programming Model in a Multi-Period Multi-Product Production Planning Problem

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INTERNATIONAL JOURNAL OF COMPUTATIONAL INTELLIGENCE SYSTEMS 2011年第2期4卷 228-243页

作者： Taghizadeh, Kaveh Bagherpour, Morteza Mahdavi, Iraj Mazandaran Univ Sci & Technol Dept Ind Engn Babol Sar Iran Iran Univ Sci & Technol Dept Ind Engn Tehran Iran

The Multi-Period Multi-Product (MPMP) production planning, as a well known problem in literature, attempts to match production rates of individual products with fluctuated market demand over planning horizon. This study, demonstrates how the conventional MPMP linear Programming (LP) model may fail to utilize available capacity of machines, and also a novel Multi Objective linear Programming (MOLP) model is developed to simultaneously minimize net present value of production costs and maximize machine utilization. The proposed model consists of production constraints such as available labor, inventory, maximum subcontracting levels and also forecasted demands. The proposed MOLP model is further converted to a Fuzzy Multi Objective linear Programming (FMOLP) model utilizing piecewise linear membership functions. The model, accommodates the Decision Maker (DM) with a more systematic decision making approach enabling the DM to adjust the search direction during the solving procedure to achieve the most satisfactory result.

关键词： Multi-Period Multi-Product production planning Aggregate production planning Fuzzy Multi-Objective linear Programming piecewise linear membership functions Mixed Integer linear Programming

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Application of Fuzzy Sets to Aggregate Production Planning With Multiproducts and Multitime Periods

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IEEE TRANSACTIONS ON FUZZY SYSTEMS 2011年第3期19卷 465-477页

作者： Liang, Tien-Fu Cheng, Hung-Wen Chen, Ping-Yen Shen, Kuan-Hsinung Hsiuping Inst Technol Dept Ind Engn & Management Taichung 412 Taiwan

The objective of this study is to develop a fuzzy mathematical programming method to solve aggregate production planning (APP) decision problems that involve multiproducts and multitime periods in a fuzzy environment. The fuzzy APP model that is developed here attempts to minimize total cost with respect to inventory carrying levels, available labor levels, machine capacity and warehouse space, and the constraint of available budget. The proposed APPmethod evaluates monetary interest of related operating cost categories and provides greater computational efficiency and flexibility by adopting triangular fuzzy numbers and piecewise linear membership functions to represent both imprecise data and fuzzy goals. The actual performance of an industrial company was used to demonstrate the feasibility of applying the proposed method to real-world APP decisions. The proposed method yields an efficient solution and presents overall decision-maker satisfaction with the given goal values. This paper also presents several significant management implications that are related to the practical application of the proposed method.

关键词： Aggregate production planning (APP) fuzzy mathematical programming fuzzy sets piecewise linear membership functions triangular fuzzy numbers

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A PLMF-Based Decomposition-Coordination Algorithm for Fuzzy linear Programming in Industrial Applications

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ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING 2014年第10期39卷 7467-7474页

作者： Wen, Bo Li, Hongguang Beijing Univ Chem Technol Sch Informat Sci & Technol Beijing 100029 Peoples R China

To formulate fuzzy linear programming, Gaussian membership functions rather than triangular or trapezoidal ones are usually recognized as more reasonable descriptions for fuzziness. However, the strong nonlinearity of Gaussian membership functions is readily to cause increasing difficulties in achieving optimum solutions accordingly. Motivated by this challenge, we introduce a novel piecewise linear membership function-based decomposition-coordination algorithm, which can initially decompose a fuzzy linear programming problem with Gaussian membership functions into several crisp linear programming models and then coordinate solutions of the sub-models to eventually achieve an overall optimum one. In this paper, detailed algorithmic procedures are presented along with corresponding theoretical analysis. In addition, an application of production planning programming in a workshop of an oil refinery is provided to demonstrate the effectiveness of the proposed methodology.

关键词： Fuzzy linear programming Decomposition-coordination piecewise linear membership functions KKT conditions

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A New Approach to an Exact Inversion of TSK Fuzzy Systems

A New Approach to an Exact Inversion of TSK Fuzzy Systems

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International Conference on Technological Advances in Electrical, Electronics and Computer Engineering (TAEECE)

作者： Ulu, Cenk Guzelkaya, Mujde Eksin, Ibrahim TUBTTAK Mannara Res Ctr Energy Inst Gebze Kocaeli Turkey Tech Univ Istanbul Dept Control Engn Maslak 34469 Istanbul Turkey

ISBN: (纸本)9781467356138;9781467356121

In this study, a new approach to an exact analytical inversion of Takagi-Sugeno-Kang (TSK) fuzzy systems with singleton consequents is presented. Here, the inversion variable is represented by piecewise linear membership functions (PWL-MFs). In this case, the universe of discourse of the inversion variable is divided into specific regions in which only one linear piece exists for each PWL-MF at most. In the proposed approach, linear equations of PWL-MFs which determine membership degrees are directly used in the analytical formulation of TSK fuzzy system. This provides us to express the fuzzy system output in a unique linear form in terms of the inversion variable for any region where only the parameters of the appropriate linear equations of PWL-MFs are embedded. Thus, finding the inverse solutions for any region is transformed to solve the linear equations which is relatively easy. The proposed method has been tested on an illustrative example.

关键词： TSK fuzzy systems fuzzy model inversion piecewise linear membership functions singleton consequents

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Diagnosis from Bayesian Networks with Fuzzy Parameters - A Case in Supply Chains

Diagnosis from Bayesian Networks with Fuzzy Parameters - A C...

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5th International Conference on Grid and Pervasive Computing

作者： Kao, Han-Ying Huang, Chia-Hui Hsu, Chu-Ling Huang, Chiao-Ling Natl Dong Hwa Univ Inst Networking & Multimedia Technol 1 Sec 2 Da Hsueh Rd Shoufeng 97401 Hualien Taiwan Kainan Univ Dept Management Informat Taoyuan 33857 Taiwan Natl Dong Hwa Univ Lib Hualien 97401 Taiwan

ISBN: (纸本)9783642130663

Bayesian networks have been widely used as knowledge models in business, engineering, biomedicine, and so on. When a network is learned with incomplete knowledge, the numerical model based on probability theory needs to be extended. This study presents a robust approach for diagnosis from Bayesian networks with fuzzy parameters. A simulation algorithm is designed to answer the queries from the models. The formulation of piecewise linear possibility distribution functions maintain the scalability in exact approaches.

关键词： Bayesian networks fuzzy parameters diagnosis piecewise linear membership functions simulation

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