Showing papers on "Fuzzy logic published in 2009"

On fuzzy soft sets

Abstract: We further contribute to the properties of fuzzy soft sets as defined and studied in the work of Maji et al. (2001), Roy and Maji (2007), and Yang et al. (2007) and support them with examples and counterexamples. We improve Proposition 3.3 by Maji et al., (2001). Finally we define arbitrary fuzzy soft union and fuzzy soft intersection and prove DeMorgan Inclusions and DeMorgan Laws in Fuzzy Soft Set Theory.

Weapon selection using the AHP and TOPSIS methods under fuzzy environment

Abstract: The weapon selection problem is a strategic issue and has a significant impact on the efficiency of defense systems. On the other hand, selecting the optimal weapon among many alternatives is a multi-criteria decision-making (MCDM) problem. This paper develops an evaluation model based on the analytic hierarchy process (AHP) and the technique for order performance by similarity to ideal solution (TOPSIS), to help the actors in defence industries for the selection of optimal weapon in a fuzzy environment where the vagueness and subjectivity are handled with linguistic values parameterized by triangular fuzzy numbers. The AHP is used to analyze the structure of the weapon selection problem and to determine weights of the criteria, and fuzzy TOPSIS method is used to obtain final ranking. A real world application is conducted to illustrate the utilization of the model for the weapon selection problem. The application could be interpreted as demonstrating the effectiveness and feasibility of the proposed model.

Risk evaluation in failure mode and effects analysis using fuzzy weighted geometric mean

Abstract: Failure mode and effects analysis (FMEA) has been extensively used for examining potential failures in products, processes, designs and services. An important issue of FMEA is the determination of risk priorities of the failure modes that have been identified. The traditional FMEA determines the risk priorities of failure modes using the so-called risk priority numbers (RPNs), which require the risk factors like the occurrence (O), severity (S) and detection (D) of each failure mode to be precisely evaluated. This may not be realistic in real applications. In this paper we treat the risk factors O, S and D as fuzzy variables and evaluate them using fuzzy linguistic terms and fuzzy ratings. As a result, fuzzy risk priority numbers (FRPNs) are proposed for prioritization of failure modes. The FRPNs are defined as fuzzy weighted geometric means of the fuzzy ratings for O, S and D, and can be computed using alpha-level sets and linear programming models. For ranking purpose, the FRPNs are defuzzified using centroid defuzzification method, in which a new centroid defuzzification formula based on alpha-level sets is derived. A numerical example is provided to illustrate the potential applications of the proposed fuzzy FMEA and the detailed computational process of the FRPNs.

New Approaches to Fuzzy-Rough Feature Selection

Abstract: There has been great interest in developing methodologies that are capable of dealing with imprecision and uncertainty. The large amount of research currently being carried out in fuzzy and rough sets is representative of this. Many deep relationships have been established, and recent studies have concluded as to the complementary nature of the two methodologies. Therefore, it is desirable to extend and hybridize the underlying concepts to deal with additional aspects of data imperfection. Such developments offer a high degree of flexibility and provide robust solutions and advanced tools for data analysis. Fuzzy-rough set-based feature (FS) selection has been shown to be highly useful at reducing data dimensionality but possesses several problems that render it ineffective for large datasets. This paper proposes three new approaches to fuzzy-rough FS-based on fuzzy similarity relations. In particular, a fuzzy extension to crisp discernibility matrices is proposed and utilized. Initial experimentation shows that the methods greatly reduce dimensionality while preserving classification accuracy.

Fuzzy hierarchical TOPSIS for supplier selection

Abstract: This study simplifies the complicated metric distance method [L.S. Chen, C.H. Cheng, Selecting IS personnel using ranking fuzzy number by metric distance method, Eur. J. Operational Res. 160 (3) 2005 803-820], and proposes an algorithm to modify Chen's Fuzzy TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) [C.T. Chen, Extensions of the TOPSIS for group decision-making under fuzzy environment, Fuzzy Sets Syst., 114 (2000) 1-9]. From experimental verification, Chen directly assigned the fuzzy numbers [email protected]? and [email protected]? as fuzzy positive ideal solution (PIS) and negative ideal solution (NIS). Chen's method sometimes violates the basic concepts of traditional TOPSIS. This study thus proposes fuzzy hierarchical TOPSIS, which not only is well suited for evaluating fuzziness and uncertainty problems, but also can provide more objective and accurate criterion weights, while simultaneously avoiding the problem of Chen's Fuzzy TOPSIS. For application and verification, this study presents a numerical example and build a practical supplier selection problem to verify our proposed method and compare it with other methods.

A fuzzy MCDM approach for evaluating banking performance based on Balanced Scorecard

Abstract: The paper proposed a Fuzzy Multiple Criteria Decision Making (FMCDM) approach for banking performance evaluation. Drawing on the four perspectives of a Balanced Scorecard (BSC), this research first summarized the evaluation indexes synthesized from the literature relating to banking performance. Then, for screening these indexes, 23 indexes fit for banking performance evaluation were selected through expert questionnaires. Furthermore, the relative weights of the chosen evaluation indexes were calculated by Fuzzy Analytic Hierarchy Process (FAHP). And the three MCDM analytical tools of SAW, TOPSIS, and VIKOR were respectively adopted to rank the banking performance and improve the gaps with three banks as an empirical example. The analysis results highlight the critical aspects of evaluation criteria as well as the gaps to improve banking performance for achieving aspired/desired level. It shows that the proposed FMCDM evaluation model of banking performance using the BSC framework can be a useful and effective assessment tool.

Combination of interval-valued fuzzy set and soft set

Abstract: The soft set theory, proposed by Molodtsov, can be used as a general mathematical tool for dealing with uncertainty. By combining the interval-valued fuzzy set and soft set models, the purpose of this paper is to introduce the concept of the interval-valued fuzzy soft set. The complement, ''AND'' and ''OR'' operations are defined on the interval-valued fuzzy soft sets. The DeMorgan's, associative and distribution laws of the interval-valued fuzzy soft sets are then proved. Finally, a decision problem is analyzed by the interval-valued fuzzy soft set. Some numerical examples are employed to substantiate the conceptual arguments.

A Sum-of-Squares Approach to Modeling and Control of Nonlinear Dynamical Systems With Polynomial Fuzzy Systems

Abstract: This paper presents a sum of squares (SOS) approach for modeling and control of nonlinear dynamical systems using polynomial fuzzy systems. The proposed SOS-based framework provides a number of innovations and improvements over the existing linear matrix inequality (LMI)-based approaches to Takagi-Sugeno (T-S) fuzzy modeling and control. First, we propose a polynomial fuzzy modeling and control framework that is more general and effective than the well-known T--S fuzzy modeling and control. Secondly, we obtain stability and stabilizability conditions of the polynomial fuzzy systems based on polynomial Lyapunov functions that contain quadratic Lyapunov functions as a special case. Hence, the stability and stabilizability conditions presented in this paper are more general and relaxed than those of the existing LMI-based approaches to T-S fuzzy modeling and control. Moreover, the derived stability and stabilizability conditions are represented in terms of SOS and can be numerically (partially symbolically) solved via the recently developed SOSTOOLS. To illustrate the validity and applicability of the proposed approach, a number of analysis and design examples are provided. The first example shows that the SOS approach renders more relaxed stability results than those of both the LMI-based approaches and a polynomial system approach. The second example presents an extensive application of the SOS approach in comparison with a piecewise Lyapunov function approach. The last example is a design exercise that demonstrates the viability of the SOS-based approach to synthesizing a stabilizing controller.

Long term supplier selection using a combined fuzzy MCDM approach: A case study for a telecommunication company

Abstract: With the globalization and the emergence of the extended enterprise of interdependent organizations, there has been a steady increase in the outsourcing of parts and services. This has led firms to give more importance to the purchasing function and its associated decisions. Since these decisions require a long term investment for the telecommunication industry especially and affect the strategic positioning of the companies in the sector, the selection of the proper supplier is one of the most important problems. Supplier selection is a multi-criteria problem which includes both tangible and intangible factors. This paper develops a supplier evaluation approach based on the analytic network process (ANP) and the technique for order performance by similarity to ideal solution (TOPSIS) methods to help a telecommunication company in the GSM sector in Turkey under the fuzzy environment where the vagueness and subjectivity are handled with linguistic terms parameterized by triangular fuzzy numbers. Contrary to conventional Fuzzy ANP (FANP) methodology in the literature, we use triangular fuzzy numbers in all pairwise comparison matrices in the FANP. Hence, criteria weights are calculated as the triangular fuzzy numbers and then these fuzzy criteria weights are inserted to the fuzzy TOPSIS methodology to rank the alternatives. This approach is demonstrated with a real world case study involving six main evaluation criteria that the company has determined to choose the most appropriate supplier. The study was followed by the sensitivity analyses of the results.

A new approach for ranking of trapezoidal fuzzy numbers

Abstract: Ranking fuzzy numbers plays an very important role in linguistic decision making and some other fuzzy application systems. Several strategies have been proposed for ranking of fuzzy numbers. Each of these techniques have been shown to produce non-intuitive results in certain cases. In this paper, we will introduce a new approach for ranking of trapezoidal fuzzy numbers based on the left and the right spreads at some @a-levels of trapezoidal fuzzy numbers. The calculation of the proposed method is far simpler and easier. Finally, some comparative examples are used to illustrate the advantage of the proposed method.

A Combined Backstepping and Small-Gain Approach to Robust Adaptive Fuzzy Output Feedback Control

Abstract: In this paper, an adaptive fuzzy output feedback control approach is proposed for single-input-single-output nonlinear systems without the measurements of the states. The nonlinear systems addressed in this paper are assumed to possess unmodeled dynamics in the presence of unstructured uncertainties and dynamic disturbances, where the unstructured uncertainties are not linearly parameterized, and no prior knowledge of their bounds are available. Fuzzy logic systems are used to approximate the unstructured uncertainties, and a state observer is developed to estimate the unmeasured states. By combining the backstepping technique with the small-gain approach, a stable adaptive fuzzy output feedback control method is proposed. It is shown that by applying the proposed adaptive fuzzy control approach, the closed-loop systems are semiglobally uniformly ultimately bounded. The effectiveness of the proposed approach is illustrated from simulation results.

FURIA: an algorithm for unordered fuzzy rule induction

Abstract: This paper introduces a novel fuzzy rule-based classification method called FURIA, which is short for Fuzzy Unordered Rule Induction Algorithm. FURIA extends the well-known RIPPER algorithm, a state-of-the-art rule learner, while preserving its advantages, such as simple and comprehensible rule sets. In addition, it includes a number of modifications and extensions. In particular, FURIA learns fuzzy rules instead of conventional rules and unordered rule sets instead of rule lists. Moreover, to deal with uncovered examples, it makes use of an efficient rule stretching method. Experimental results show that FURIA significantly outperforms the original RIPPER, as well as other classifiers such as C4.5, in terms of classification accuracy.

Path planning for autonomous mobile robot navigation with ant colony optimization and fuzzy cost function evaluation

Abstract: In the Motion Planning research field, heuristic methods have demonstrated to outperform classical approaches gaining popularity in the last 35 years. Several ideas have been proposed to overcome the complex nature of this NP-Complete problem. Ant Colony Optimization algorithms are heuristic methods that have been successfully used to deal with this kind of problems. This paper presents a novel proposal to solve the problem of path planning for mobile robots based on Simple Ant Colony Optimization Meta-Heuristic (SACO-MH). The new method was named SACOdm, where d stands for distance and m for memory. In SACOdm, the decision making process is influenced by the existing distance between the source and target nodes; moreover the ants can remember the visited nodes. The new added features give a speed up around 10 in many cases. The selection of the optimal path relies in the criterion of a Fuzzy Inference System, which is adjusted using a Simple Tuning Algorithm. The path planner application has two operating modes, one is for virtual environments, and the second one works with a real mobile robot using wireless communication. Both operating modes are global planners for plain terrain and support static and dynamic obstacle avoidance.

A fuzzy AHP approach to personnel selection problem

Abstract: Due to the increasing competition of globalization and fast technological improvements, world markets demand companies to have quality and professional human resources. This can only be achieved by employing potentially adequate personnel. In this paper, we proposed a personnel selection system based on Fuzzy Analytic Hierarchy Process (FAHP). The FAHP is applied to evaluate the best adequate personnel dealing with the rating of both qualitative and quantitative criteria. The result obtained by FAHP is compared with results produced by Yager's weighted goals method. In addition to above-mentioned methods, a practical computer-based decision support system is introduced to provide more information and help manager make better decisions under fuzzy circumstances.

Multicriteria fuzzy decision-making method based on a novel accuracy function under interval-valued intuitionistic fuzzy environment

Abstract: The interval-valued intuitionistic fuzzy weighted arithmetic average operator, the interval-valued intuitionistic fuzzy weighted geometric average operator, and an accuracy function of interval-valued intuitionistic fuzzy value are introduced in this paper. A novel accuracy function for interval-valued intuitionistic fuzzy sets (IVIFSs) is proposed by taking into account the unknown degree (hesitancy degree) of IVIFSs to overcome the situation of difficult decision of existing accuracy functions to the alternatives in some cases. To identify the best alternative in multicriteria decision-making problems, a multicriteria fuzzy decision-making method is established in which criterion values for alternatives are IVIFSs. We utilize the interval-valued intuitionistic fuzzy weighted aggregation operators to aggregate the interval-valued intuitionistic fuzzy information corresponding to each alternative, and then rank the alternatives and select the most desirable one(s) according to the accuracy degree of the aggregated the interval-valued intuitionistic fuzzy information corresponding to the new accuracy function. Finally, an illustrative example is given to verify the developed approach.

Artificial neural network-polar coordinated fuzzy controller based maximum power point tracking control under partially shaded conditions

Abstract: The one of main causes of reducing energy yield of photovoltaic systems is partially shaded conditions. Although the conventional maximum power point tracking (MPPT) control algorithms operate well under uniform insolation, they do not operate well in non-uniform insolation. The non-uniform conditions cause multiple local maximum power points on the power-voltage curve. The conventional MPPT methods cannot distinguish between the global and local peaks. Since the global maximum power point (MPP) may change within a large voltage window and also its position depends on shading patterns, it is very difficult to recognise the global operating point under partially shaded conditions. In this paper, a novel MPPT system is proposed for partially shaded PV array using artificial neural network (ANN) and fuzzy logic with polar information controller. The ANN with three layer feed-forward is trained once for several partially shaded conditions to determine the global MPP voltage. The fuzzy logic with polar information controller uses the global MPP voltage as a reference voltage to generate the required control signal for the power converter. Another objective of this study is to determine the estimated maximum power and energy generation of PV system through the same ANN structure. The effectiveness of the proposed method is demonstrated under the experimental real-time simulation technique based dSPACE real-time interface system for different interconnected PV arrays such as series-parallel, bridge link and total cross tied configurations.

Extension of fuzzy TOPSIS method based on interval-valued fuzzy sets

Abstract: Decision making is one of the most complex administrative processes in management. In circumstances where the members of the decision making team are uncertain in determining and defining the decision making criteria, fuzzy theory provides a proper tool to encounter with such uncertainties. However, if decision makers cannot reach an agreement on the method of defining linguistic variables based on the fuzzy sets, the interval-valued fuzzy set theory can provide a more accurate modeling. In this paper the interval-valued fuzzy TOPSIS method is presented aiming at solving MCDM problems in which the weights of criteria are unequal, using interval-valued fuzzy sets concepts.

Online Sequential Fuzzy Extreme Learning Machine for Function Approximation and Classification Problems

Abstract: In this correspondence, an online sequential fuzzy extreme learning machine (OS-fuzzy-ELM) has been developed for function approximation and classification problems. The equivalence of a Takagi-Sugeno-Kang (TSK) fuzzy inference system (FIS) to a generalized single hidden-layer feedforward network is shown first, which is then used to develop the OS-fuzzy-ELM algorithm. This results in a FIS that can handle any bounded nonconstant piecewise continuous membership function. Furthermore, the learning in OS-fuzzy-ELM can be done with the input data coming in a one-by-one mode or a chunk-by-chunk (a block of data) mode with fixed or varying chunk size. In OS-fuzzy-ELM, all the antecedent parameters of membership functions are randomly assigned first, and then, the corresponding consequent parameters are determined analytically. Performance comparisons of OS-fuzzy-ELM with other existing algorithms are presented using real-world benchmark problems in the areas of nonlinear system identification, regression, and classification. The results show that the proposed OS-fuzzy-ELM produces similar or better accuracies with at least an order-of-magnitude reduction in the training time.

SOFMLS: Online Self-Organizing Fuzzy Modified Least-Squares Network

Abstract: In this paper, an online self-organizing fuzzy modified least-square (SOFMLS) network is proposed. The algorithm has the ability to reorganize the model and adapt itself to a changing environment where both the structure and learning parameters are performed simultaneously. The network generates a new rule if the smallest distance between the new data and all the existing rules (the winner rule) is more than a prespecified radius. The major contributions of this paper are as follows: 1) A new network is proposed, in which unidimensional membership functions are used, and only two parameters for each rule are employed, thus reducing the number of parameters. The network avoids the singularity produced by the widths in the antecedent part for online learning; 2) a new pruning algorithm based on the density is proposed, where the density is the number of times each rule is used in the algorithm. The rule that has the smallest density (the looser rule) in a selected number of iterations is pruned if the value of its density is smaller than a prespecified threshold; and 3) the stability of the proposed algorithm is proven, and the bound for the average of the identification error is found. The condition that led the algorithm to avoid the local minimum is found, and it is proven that the parameter error is bounded by the initial parameter error. Three simulations give the effectiveness of the suggested algorithm.

The potential of Fuzzy Cognitive Maps for semi-quantitative scenario development, with an example from Brazil

Abstract: The main drawback of the Story-and-Simulation approach is the weak link between qualitative and quantitative scenarios. A semi-quantitative tool, Fuzzy Cognitive Mapping, is introduced as a possible improvement. An example from the Brazilian Amazon shows that by including an integrated set of factors and feedbacks, Fuzzy Cognitive Maps can capture (future) dynamics of deforestation. The example substantiates the tool's capacity to improve the consistency of narrative storylines and the diversity of quantitative models. The tool is designed, however, to be simple and therefore has important drawbacks. Future improvements should be made in the light of applications within a larger toolbox of scenario methods.

Fuzzy Filter Design for ItÔ Stochastic Systems With Application to Sensor Fault Detection

Abstract: The paper deals with the robust fault detection problem for Takagi-Sugeno (T-S) fuzzy Ito stochastic systems. Our aim is to develop a robust fault detection approach to the T-S fuzzy systems with Brownian motion. By using a general observer-based fault detection filter as a residual generator, the robust fault detection is formulated as a filtering problem. Attention is focused on the design of both the fuzzy-rule-independent and the fuzzy-rule-dependent fault detection filters guaranteeing a prescribed noise attenuation level in an Hinfin sense. Sufficient conditions are proposed to guarantee the mean-square asymptotic stability with an Hinfin performance for the fault detection system. The corresponding solvability conditions for the desired fuzzy-rule-independent and fuzzy-rule-dependent fault detection filters are also established. Finally, a numerical example is provided to illustrate the effectiveness of the proposed theory.

Evaluation of DSP-Based PID and Fuzzy Controllers for DC–DC Converters

Abstract: In this paper, digital proportional-integral-derivative (PID)-type and fuzzy-type controllers are compared for application to the buck and boost dc-dc converters. Comparison between the two controllers is made with regard to design methodology, implementation issues, and experimentally measured performance. Design of fuzzy controllers is based on heuristic knowledge of converter behavior, and tuning requires some expertise to minimize unproductive trial and error. The design of PID control is based on the frequency response of the dc-dc converter. Implementation of linear controllers on a digital signal processor is straightforward, but realization of fuzzy controllers increases computational burden and memory requirements. For the boost converter, the performance of the fuzzy controller was superior in some respects to that of the PID controllers. The fuzzy controller was able to achieve faster transient response in most tests, had a more stable steady-state response, and was more robust under some operating conditions. In the case of the buck converter, the fuzzy controller and PID controller yielded comparable performances.

$\alpha$ -Plane Representation for Type-2 Fuzzy Sets: Theory and Applications

Abstract: This paper 1) reviews the alpha-plane representation of a type-2 fuzzy set (T2 FS), which is a representation that is comparable to the alpha-cut representation of a type-1 FS (T1 FS) and is useful for both theoretical and computational studies of and for T2 FSs; 2) proves that set theoretic operations for T2 FSs can be computed using very simple alpha-plane computations that are the set theoretic operations for interval T2 (IT2) FSs; 3) reviews how the centroid of a T2 FS can be computed using alpha-plane computations that are also very simple because they can be performed using existing Karnik Mendel algorithms that are applied to each alpha-plane; 4) shows how many theoretically based geometrical properties can be obtained about the centroid, even before the centroid is computed; 5) provides examples that show that the mean value (defuzzified value) of the centroid can often be approximated by using the centroids of only 0 and 1 alpha -planes of a T2 FS; 6) examines a triangle quasi-T2 fuzzy logic system (Q-T2 FLS) whose secondary membership functions are triangles and for which all calculations use existing T1 or IT2 FS mathematics, and hence, they may be a good next step in the hierarchy of FLSs, from T1 to IT2 to T2; and 7) compares T1, IT2, and triangle Q-T2 FLSs to forecast noise-corrupted measurements of a chaotic Mackey-Glass time series.

Robust Stability for Uncertain Delayed Fuzzy Hopfield Neural Networks With Markovian Jumping Parameters

Abstract: This paper is concerned with the problem of the robust stability of nonlinear delayed Hopfield neural networks (HNNs) with Markovian jumping parameters by Takagi-Sugeno (T-S) fuzzy model. The nonlinear delayed HNNs are first established as a modified T-S fuzzy model in which the consequent parts are composed of a set of Markovian jumping HNNs with interval delays. Time delays here are assumed to be time-varying and belong to the given intervals. Based on Lyapunov-Krasovskii stability theory and linear matrix inequality approach, stability conditions are proposed in terms of the upper and lower bounds of the delays. Finally, numerical examples are used to illustrate the effectiveness of the proposed method.