Showing papers on "Fuzzy associative matrix published in 2017"
TL;DR: It is shown how to introduce the concepts of fuzzy learning into DL to overcome the shortcomings of fixed representation and the fuzzy dDL paradigm greatly outperforms other nonfuzzy and shallow learning approaches on these tasks.
Abstract: Deep learning (DL) is an emerging and powerful paradigm that allows large-scale task-driven feature learning from big data. However, typical DL is a fully deterministic model that sheds no light on data uncertainty reductions. In this paper, we show how to introduce the concepts of fuzzy learning into DL to overcome the shortcomings of fixed representation. The bulk of the proposed fuzzy system is a hierarchical deep neural network that derives information from both fuzzy and neural representations. Then, the knowledge learnt from these two respective views are fused altogether forming the final data representation to be classified. The effectiveness of the model is verified on three practical tasks of image categorization, high-frequency financial data prediction and brain MRI segmentation that all contain high level of uncertainties in the raw data. The fuzzy dDL paradigm greatly outperforms other nonfuzzy and shallow learning approaches on these tasks.
268 citations
TL;DR: A novel fuzzy inference system on picture fuzzy set called picture inference system (PIS), adapted for all architectures such as the Mamdani, the Sugeno and the Tsukamoto fuzzy inferences is proposed.
Abstract: In this paper, we propose a novel fuzzy inference system on picture fuzzy set called picture inference system (PIS) to enhance inference performance of the traditional fuzzy inference system In PIS, the positive, neutral and negative degrees of the picture fuzzy set are computed using the membership graph that is the combination of three Gaussian functions with a common center and different widths expressing a visual view of degrees Then, the positive and negative defuzzification values, synthesized from three degrees of the picture fuzzy set, are used to generate crisp outputs Learning in PIS including training centers, widths, scales and defuzzification parameters is also discussed The system is adapted for all architectures such as the Mamdani, the Sugeno and the Tsukamoto fuzzy inferences Experimental results on benchmark UCI Machine Learning Repository datasets and an example in control theory - the Lorenz system are examined to verify the advantages of PIS
107 citations
TL;DR: By taking advantage of this ranking-based switching mechanism, a class of new fuzzy multi-instant observers are achieved and more relaxed design conditions can be obtained for ensuring the asymptotically stability of the developed state estimation error system.
Abstract: This paper generalizes recent results on multi-instant observer design for discrete-time Takagi–Sugeno fuzzy systems through a valid ranking-based switching approach. The approach hereby develops a concentrated subdivision of spanning space composed of normalized fuzzy weighting functions and then substantially produces a new ranking-based switching mechanism. By taking advantage of this ranking-based switching mechanism, a class of new fuzzy multi-instant observers are achieved and more relaxed design conditions with respect to the recent work can be obtained for ensuring the asymptotically stability of the developed state estimation error system. Two illustrative examples are provided to validate the effectiveness of the result given in this study.
107 citations
TL;DR: Experimental results on six UCI datasets shown that the proposed dynamic algorithm achieves significantly higher efficiency than the static algorithm and the combination of two reference incremental algorithms.
Abstract: In a dynamic environment, the data collected from real applications varies not only with the amount of objects but also with the number of features, which will result in continuous change of knowledge over time. The static methods of updating knowledge need to recompute from scratch when new data are added every time. This makes it potentially very time-consuming to update knowledge, especially as the dataset grows dramatically. Calculation of approximations is one of main mining tasks in rough set theory, like frequent pattern mining in association rules. Considering the fuzzy descriptions of decision states in the universe under fuzzy environment, this paper aims to provide an efficient approach for computing rough approximations of fuzzy concepts in dynamic fuzzy decision systems (FDS) with simultaneous variation of objects and features. We firstly present a matrix-based representation of rough fuzzy approximations by a Boolean matrix associated with a matrix operator in FDS. While adding the objects and features concurrently, incremental mechanisms for updating rough fuzzy approximations are introduced, and the corresponding matrix-based dynamic algorithm is developed. Unlike the static method of computing approximations by updating the whole relation matrix, our new approach partitions it into sub-matrices and updates each sub-matrix locally by utilizing the previous matrix information and the interactive information of each sub-matrix to avoid unnecessary calculations. Experimental results on six UCI datasets shown that the proposed dynamic algorithm achieves significantly higher efficiency than the static algorithm and the combination of two reference incremental algorithms.
85 citations
TL;DR: By a newly proposed inequality bounding technique, the fuzzy sampled-data filtering performance analysis is carried out such that the resultant neural networks is asymptotically stable.
71 citations
TL;DR: It is shown by an illustrative example that by neglecting the information about uncertainty of intensity of preferences the authors lose an important part of knowledge about the decision making problem which can cause the change in ordering of alternatives.
Abstract: The aim of the paper is to highlight the necessity of applying the concept of constrained fuzzy arithmetic instead of the concept of standard fuzzy arithmetic in a fuzzy extension of Analytic Hierarchy Process (AHP). Emphasis is put on preserving the reciprocity of pairwise comparisons during the computations. For deriving fuzzy weights from a fuzzy pairwise comparison matrix, we consider a fuzzy extension of the geometric mean method and simplify the formulas proposed by Enea and Piazza (Fuzzy Optim Decis Mak 3:39---62, 2004). As for the computation of the overall fuzzy weights of alternatives, we reveal the inappropriateness of applying the concept of standard fuzzy arithmetic and propose the proper formulas where the interactions among the fuzzy weights are taken into account. The advantage of our approach is elimination of the false increase of uncertainty of the overall fuzzy weights. Finally, we advocate the validity of the proposed fuzzy extension of AHP; we show by an illustrative example that by neglecting the information about uncertainty of intensity of preferences we lose an important part of knowledge about the decision making problem which can cause the change in ordering of alternatives.
66 citations
TL;DR: A state-feedback control criterion is proposed based on the Lyapunov stability theory, and a sufficient condition for synthesis is derived in terms of strict linear matrix inequalities, which eliminates the disadvantages in some existing results, such as same output matrices and the bilinear matrix inequality problem.
Abstract: In this paper, we consider the state-feedback and static output feedback control problems of continuous singular interval-valued Takagi–Sugeno fuzzy systems with mismatched membership functions. First, based on the Lyapunov stability theory, a state-feedback control criterion is proposed to guarantee the closed-loop system to be admissible. Second, the result is extended to the static output feedback control problem, and a sufficient condition for synthesis is derived in terms of strict linear matrix inequalities, which eliminates the disadvantages in some existing results, such as same output matrices and the bilinear matrix inequality problem. To obtain less conservative results, the information of mismatched membership functions is employed. Finally, numerical examples are given to illustrate the effectiveness of the proposed techniques.
51 citations
TL;DR: A new relaxed sufficient condition ensuring a fuzzy descriptor system to be admissible (regular, impulse-free, and stable) is proposed, in which it is not necessary to require every fuzzy subsystem to be stable.
Abstract: The problem of admissibility analysis and control synthesis for Takagi–Sugeno fuzzy descriptor systems is investigated. First, based on Nonquadratic fuzzy Lyapunov function and fully using the information of fuzzy membership functions, a new relaxed sufficient condition ensuring a fuzzy descriptor system to be admissible (regular, impulse-free, and stable) is proposed, in which it is not necessary to require every fuzzy subsystem to be stable. Second, the other sufficient condition for the admissibility is obtained without the information of time derivatives of fuzzy membership functions. Following the analysis, both parallel and nonparallel distributed compensation controllers are designed, linear matrix inequalities conditions are given to construct the controllers. Finally, some examples are provided to illustrate the main results in this paper less conservative than some earlier related results.
50 citations
TL;DR: Experimental results show that except for wine dataset the proposed RST-BatMiner yields high accuracy and comprehensible ruleset when compared to other state-of-the-art bio-inspired based fuzzy rule miners and Fuzzy Rule Based Classification Systems (FRBCS) in the literature.
48 citations
TL;DR: The stability of the fuzzy closed-loop system which is formed by a T-S fuzzy model and a fuzzy dynamic output feedback H∞ controller connected in a closed loop is investigated with Lyapunov stability theory.
Abstract: This paper addresses a fuzzy dynamic output feedback H∞ control design problem for continuous-time nonlinear systems via T-S fuzzy model The stability of the fuzzy closed-loop system which is formed by a T-S fuzzy model and a fuzzy dynamic output feedback H∞ controller connected in a closed loop is investigated with Lyapunov stability theory The proposed fuzzy controller does not share the same membership functions and number of rules with T-S fuzzy systems, which can enhance design flexibility A line-integral fuzzy Lyapunov function is utilized to derive the stability conditions in the form of linear matrix inequalities (LMIs) The boundary information of membership functions is considered in the stability analysis to reduce the conservativeness of the imperfect premise matching design technique Two simulation examples are provided to demonstrate the effectiveness of the proposed approach
45 citations
01 Mar 2017
TL;DR: A comprehensive design process of granular fuzzy rule-based systems emerging during the compression of the rule bases is developed and the cooperative particle swarm optimization to solve optimization problem is implemented.
Abstract: In this study, we develop a comprehensive design process of granular fuzzy rule-based systems. These constructs arise as a result of a structural compression of fuzzy rule-based systems in which a subset of originally existing rules is retained. Because of the reduced subset of the originally existing rules, the remaining rules are made more abstract (general) by expressing their conditions in the form of granular fuzzy sets (such as interval-valued fuzzy sets, rough fuzzy sets, probabilistic fuzzy sets, etc.), hence the name of granular fuzzy rule-based systems emerging during the compression of the rule bases. The design of these systems dwells upon an important mechanism of allocation of information granularity using which the granular fuzzy rules are formed. The underlying optimization consists of two phases: structural (being of combinatorial character in which a subset of rules is selected) and parametric (when the conditions of the selected rules are made granular through an optimal allocation of information granularity). We implement the cooperative particle swarm optimization to solve optimization problem. A number of experimental studies are reported; those include fuzzy rule-based systems.
TL;DR: The fuzzy equations are applied as the models for the uncertain nonlinear systems and the neural networks are used to approximate the coefficients of the fuzzy equations.
Abstract: The uncertain nonlinear systems can be modeled with fuzzy equations by incorporating the fuzzy set theory. In this paper, the fuzzy equations are applied as the models for the uncertain nonlinear systems. The nonlinear modeling process is to find the coefficients of the fuzzy equations. We use the neural networks to approximate the coefficients of the fuzzy equations. The approximation theory for crisp models is extended into the fuzzy equation model. The upper bounds of the modeling errors are estimated. Numerical experiments along with comparisons demonstrate the excellent behavior of the proposed method.
TL;DR: Using the Xie–Beni index and an improved particle swarm optimization algorithm, a novel identification method for the Takagi–Sugeno fuzzy model is proposed and it is shown that the proposed method outperforms some existing methods.
TL;DR: A comparison between type-1 fuzzy sets (T1FSs) and intuitionistic fuzzy set (IFSs) is made and operators defined over IFSs that do not have analogues in T2FSs are shown.
Abstract: A comparison between type-1 fuzzy sets (T1FSs) and intuitionistic fuzzy sets (IFSs) is made. The operators defined over IFSs that do not have analogues in T1FSs are shown, and such analogues are introduced whenever possible.
TL;DR: For the first time mathematical models of the simplest Mamdani type fuzzy Proportional Integral (PI)/Proportional Derivative (PD) controllers via CoG defuzzification are presented and two nonlinear plants are considered to show the superiority of thesimple fuzzy controller obtained using CoA or CoGdefuzzification method over the simplest fuzzy controller obtaining using CoS method and reported recently.
Abstract: The mathematical models reported in the literature so far have been found using Center of Sums (CoS) defuzzification method only. It appears that no one has found models using Center of Area (CoA) or Center of Gravity (CoG) defuzzification method. Although there have been some works reported to deal with modeling of fuzzy controllers via Centroid method, all of them have in fact used CoS method only. In this paper, for the first time mathematical models of the simplest Mamdani type fuzzy Proportional Integral (PI)/Proportional Derivative (PD) controllers via CoG defuzzification are presented. L-type and Γ-type membership functions over different Universes of Discourse (UoDs) are considered for the input variables. L-type, Π-type and Γ-type membership functions are considered for the output variable. Three linear fuzzy control rules relating all four input fuzzy sets to three output fuzzy sets are chosen. Two triangular norms namely Algebraic Product (AP) and Minimum (Min), Maximum (Max) triangular co-norm, and two inference methods, Larsen Product (LP) and Mamdani Minimum (MM), are used. Properties of the models are studied. Stability analysis of closed-loop systems containing one of these controller models in the loop is done using the Small Gain theorem. Since digital controllers are implemented using digital processors, computational and memory requirements of these fuzzy controllers and conventional (nonfuzzy) controllers are compared. A rough estimate of the computational time taken by the digital computer while implementing any of these discrete-time fuzzy controllers is given. Two nonlinear plants are considered to show the superiority of the simplest fuzzy controller obtained using CoA or CoG defuzzification method over the simplest fuzzy controller obtained using CoS method and reported recently. Real-time implementation of one of the developed controller models is done on coupled tank experimental setup to show the feasibility of the developed model.
TL;DR: The use of mixed fuzzy clustering (MFC) algorithm to derive Takagi–Sugeno (T–S) fuzzy models (FMs) is proposed, which outperform FCM-based T–S FMs in four out of five datasets and k-nearest neighbors classifiers in five out ofFive datasets.
Abstract: This paper proposes the use of mixed fuzzy clustering (MFC) algorithm to derive Takagi–Sugeno (T–S) fuzzy models (FMs). Mixed fuzzy clustering handles both time invariant and multivariate time variant features, allowing the user to control the weight of each component in the clustering process. Two model designs based on MFC are investigated. In the first, the antecedent fuzzy sets of the T–S model are obtained from the clusters obtained by the MFC algorithm. In the second, FMs based on fuzzy c-means (FCM) are constructed over the input space of the partition matrix generated by MFC. The proposed fuzzy modeling approaches are used in health care classification problems, where time series of unequal lengths are very common. MFC-based T–S FMs outperform FCM-based T–S FMs in four out of five datasets and k -nearest neighbors classifiers in five out of five datasets. Dynamic time warping performs better than the Euclidean distance in one dataset and similarly in the remaining. Given the different nature of time variant and invariant data, the choice of a clustering algorithm that treats data differently should be considered for model construction.
TL;DR: An approach for deriving the fuzzy priority vector from triangular fuzzy compare wise judgment matrices based on the row weighted arithmetic mean method, which indicates the decision maker’s optimistic and pessimistic attitudes.
Abstract: To cope with the uncertainty in the process of decision making, fuzzy preference relations are proposed and commonly applied in many fields. In practical decision-making problems, the decision maker may use triangular fuzzy preference relations to express his/her uncertainty. Based on the row weighted arithmetic mean method, this paper develops an approach for deriving the fuzzy priority vector from triangular fuzzy compare wise judgment matrices. To do this, this paper first analyzes the upper and lower bounds of the triangular fuzzy priority weight of each alternative, which indicates the decision maker’s optimistic and pessimistic attitudes. Based on (acceptably) consistent multiplicative preference relations, the triangular fuzzy priority vector is obtained. Meanwhile, a consistency concept of triangular fuzzy compare wise judgment matrices is defined, and the consistent relationship between triangular fuzzy and crisp preference relations is studied. Different to the existing methods, the new approach calculates the triangular fuzzy priority weights separately. Furthermore, the fuzzy priority vector from trapezoidal fuzzy reciprocal preference relations is considered. Finally, the application of the new method to new product development (NDP) project screening is tested, and comparative analyses are also offered.
TL;DR: This study introduces an augmentation of fuzzy models by facilitating interaction among the rules leading to more flexible type membership functions of fuzzy sets forming conditions of the rules (thus resulting in substantially advanced topology of the partition of the input space).
TL;DR: The notion of product bipolar fuzzy line graph is introduced and some of its properties are investigated and a necessary and sufficient condition is given for a productipolar fuzzy graph to be isomorphic to its corresponding product bipolar fuzziness line graph.
Abstract: Recently, bipolar fuzzy graph is a vastly growing research area as it is the generalization of the fuzzy graphs. In this paper, at first the concepts of regular and totally regular product bipolar fuzzy graphs is introduced. Then necessary and sufficient conditions are established under which regular and totally regular product bipolar fuzzy graph becomes equivalent. The notion of product bipolar fuzzy line graph is introduced and investigated some of its properties. A necessary and sufficient condition is given for a product bipolar fuzzy graph to be isomorphic to its corresponding product bipolar fuzzy line graph. It is also examined when an isomorphism between two product bipolar fuzzy graphs follows from an isomorphism of their corresponding fuzzy line graphs.
TL;DR: A proper fuzzy extension of the maximal eigenvector method is proposed that preserves the reciprocity of pairwise comparisons and eliminates redundant information in the method.
01 Jul 2017
TL;DR: A generic architecture of multi-layered network developed from Takagi Sugeno fuzzy inference systems as basic units is proposed and it is compared with performance of artificial neural network with same architecture.
Abstract: The state-of-art algorithms in computational intelligence have become better than human intelligence in some of pattern recognition areas. Most of these state-of-art algorithms have been developed from the concept of multi-layered artificial neural networks. Large amount of numerical and linguistic rule data has been created in recent years. Fuzzy sets are useful in modeling uncertainty due to vagueness, ambiguity and imprecision. Fuzzy inference systems incorporate linguistic rules intelligible to human beings. Many attempts have been made to combine assets of fuzzy sets, fuzzy inference systems and artificial neural networks. Use of a single fuzzy inference system limits the performance. In this paper, we propose a generic architecture of multi-layered network developed from Takagi Sugeno fuzzy inference systems as basic units. This generic architecture is called “Takagi Sugeno Deep Fuzzy Network”. Multiple distinct fuzzy inference structures can be identified using proposed architecture. A general three layered TS deep fuzzy network is explained in detail in this paper. The generic algorithm for identification of all network parameters of three layered deep fuzzy network using error backpropagation is presented in the paper. The proposed architecture as well as its identification procedure are validated using two experimental case studies. The performance of proposed architecture is evaluated in normal, imprecise and vague situations and it is compared with performance of artificial neural network with same architecture. The results illustrate that the proposed architecture eclipses over three layered feedforward artificial neural network in all situations.
01 Jul 2017
TL;DR: The authors developed a two-stage method for fuzzy rule base (RB) correction in the case of changing the structure of the input vector and the fuzzy DSS with a hierarchical structure for the best selection of the marine delivery company was developed.
Abstract: The article is a review of the perspective methods and approaches to the design of fuzzy decision support systems (DSS) with the application of discrete fuzzy inference engine. The authors also developed a two-stage method for fuzzy rule base (RB) correction in the case of changing the structure of the input vector. In addition, the fuzzy DSS with a hierarchical structure for the best selection of the marine delivery company was developed. Simulation results confirm the effectiveness and feasibility of fuzzy DSS structure with variable input coordinates vector, in particular, in marine practice.
TL;DR: The proposed fuzzy regression model performs more convenient and efficient results in regard to six goodness-of-fit criteria which concludes that the proposed model could be a rational substituted model of some common fuzzy regression models in many practical studies of fuzzy regressionmodel in expert and intelligent systems.
Abstract: We use semi-parametric methods to improve fuzzy linear regression models.We present a detailed comparison of proposed method via sumulation data.Efficiency of proposed method is demonstrated via some real-world applications. A large number of accounting studies have focused on parametric or non-parametric forms of fuzzy regression relationships between dependent and independent variables. Notably, semi-parametric partially linear model as a powerful tool to incorporate statistical parametric and non-parametric regression analyses has gained attentions in many real-life applications recently. However, fuzzy data find application in many real studies. This study is an investigation of semi-parametric partially linear model for such cases to improve the conventional fuzzy linear regression models with fuzzy inputs, fuzzy outputs, fuzzy smooth function and non-fuzzy coefficients. For this purpose, a hybrid procedure is suggested based on curve fitting methods and least absolutes deviations to estimate the fuzzy smooth function and fuzzy coefficients. The proposed method is also examined to be compared with a common fuzzy linear regression model via a simulation data set and some real fuzzy data sets. It is shown that the proposed fuzzy regression model performs more convenient and efficient results in regard to six goodness-of-fit criteria which concludes that the proposed model could be a rational substituted model of some common fuzzy regression models in many practical studies of fuzzy regression model in expert and intelligent systems.
TL;DR: In this article, the verification of fuzzy regular safety properties and fuzzy ω-regular properties using fuzzy finite automata are thoroughly studied, and several examples are given to illustrate the methods presented in this paper.
TL;DR: This work proposes the use of Type-2 fuzzy logic for the dynamic adaptation of the variables of the system of predator-prey equations and proposes a new variant of the bio-inspired optimization algorithm based on the self-defense mechanisms of plants in the nature.
Abstract: Fuzzy logic is a soft computing technique that has been very successful in recent years when it is used as a complement to improve meta-heuristic optimization. In this paper, we present a new variant of the bio-inspired optimization algorithm based on the self-defense mechanisms of plants in the nature. The optimization algorithm proposed in this work is based on the predator-prey model originally presented by Lotka and Volterra, where two populations interact with each other and the objective is to maintain a balance. The system of predator-prey equations use four variables (α, β, λ, δ) and the values of these variables are very important since they are in charge of maintaining a balance between the pair of equations. In this work, we propose the use of Type-2 fuzzy logic for the dynamic adaptation of the variables of the system. This time a fuzzy controller is in charge of finding the optimal values for the model variables, the use of this technique will allow the algorithm to have a higher performance and accuracy in the exploration of the values.
TL;DR: The objective of this study is to develop a new design methodology of constructing incremental fuzzy rules formed through fuzzy clustering with the aid of context-based Fuzzy C-Means (C-FCM) clustering.
Abstract: This paper is concerned with a reinforced rule-based fuzzy model and its design realized with the aid of fuzzy clustering. The objective of this study is to develop a new design methodology of constructing incremental fuzzy rules formed through fuzzy clustering. The proposed model consists of four functional modules. The premise part of the fuzzy rules involves membership functions designed with the aid of the Fuzzy C-Means (FCM) clustering algorithm. The consequent part comprises local models (linear functions). The parameters of the local models are estimated by Weighted Least Squares (WLS). In the inference part, after determining the error associated with each fuzzy rule, the rule with the highest error is identified and refined. The selected rule is split into two or more specialized more detailed rules providing a better insight and detailed view into the system. These new rules are formed with the aid of the context-based Fuzzy C-Means (C-FCM) clustering. Along with the refinement of the rule, the linear conclusion part can be also refined by admitting quadratic functions. The effectiveness of the proposed rule-based model is discussed and illustrated with the aid of some numeric studies including both synthetic and machine learning data.
TL;DR: The arithmetic operation of a particular type of pentagonal fuzzy number is addressed here and an illustrative example is taken with the useful graph and table for usefulness for attained to the proposed concept.
TL;DR: This study proposes a novel conceptual and algorithmic approach by elevating existing fuzzy models to granular fuzzy models in the form of fuzzy sets, and establishes a way of an optimal allocation of information granularity across the parameters of the original model and making them fuzzy sets (fuzzy numbers).
Abstract: In recent years, granular fuzzy models have become an intensively studied category of fuzzy models. Granular fuzzy models help elevate the existing models to the higher level of abstraction subsequently making the resulting constructs in a better rapport with real-world systems. In contrast to numeric models, granular models produce results in the form of information granules (such as intervals, fuzzy sets, rough sets and alike). A number of studies have been focused on efficient designing granular fuzzy models where the information granularity has been formalized in the form of intervals. In this study, we propose a novel conceptual and algorithmic approach by elevating existing fuzzy models to granular fuzzy models in the form of fuzzy sets. Concentrating on Takagi-Sugeno fuzzy rule-based models (being commonly used in the literature), we establish a way of an optimal allocation of information granularity across the parameters of the original model and making them fuzzy sets (fuzzy numbers). As a result, the outputs of the granular fuzzy model become fuzzy sets. In the process of allocation of information granularity, we resort ourselves to some population-based meta-heuristic optimization techniques such as particle swarm optimization and differential evolution. To evaluate the performance of granular fuzzy models, we engage the principle of justifiable information granularity leading to the assessment and optimization of the coverage and specificity of the resulting fuzzy set. Besides, we involve the defuzzification (decoding) process to evaluate the impact of granular parameters on the quality of the numeric manifestation of the model. Comprehensive experimental studies involving synthetic and publicly available data sets are reported to demonstrate the performance of the granular fuzzy models.
TL;DR: The defuzzification-free hierarchical fuzzy inference system (DF-HFS) is proposed in which the misleading defuzzified steps are eliminated from the hierarchical inference flow, and the fuzziness is propagated up to the highest layer without being exposed to any degeneration.
TL;DR: This paper presents a sufficient condition for stability of a class of multiple input multiple output recurrent type-2 TSK fuzzy systems using spectrum analysis and shows the effectiveness of the proposed method.
Abstract: This paper presents a sufficient condition for stability of a class of multiple input multiple output recurrent type-2 TSK fuzzy systems using spectrum analysis. In this class of type-2 TSK fuzzy systems, the antecedent part is interval Gaussian type-2 fuzzy sets and the consequent part is a linear combination of inputs with crisp coefficients. In the proposed method, at first a type-2 fuzzy model is built and then the stability of the model is analyzed. It should be noted that this method is suitable for strictly ascending and strictly decreasing systems. Two first-order systems and two second-order systems are simulated by type-2 and type-1 fuzzy systems. The simulation results show the effectiveness of the proposed method.