A fuzzified neural fuzzy inference network for handling both linguistic and numerical information simultaneously

Abstract

A fuzzified Takagi–Sugeno–Kang (TSK)-type neural fuzzy inference network (FTNFIN) that is capable of handling both linguistic and numerical information simultaneously is proposed in this paper. FTRNFN solves the disadvantages of most existing neural fuzzy systems which can only handle numerical information. The inputs and outputs of FTNFIN may be fuzzy numbers with any shapes or numerical values. Structurally, FTNFIN is a fuzzy network constructed from a series of fuzzy if–then rules with TSK-type consequent parts. The α-cut technique is used in input fuzzification and consequent part computation, which enables the network to simultaneously handle both numerical and linguistic information. There are no rules in FTNFIN initially since they are constructed on-line by concurrent structure and parameter learning. FTNFIN is characterized by small network size and high learning accuracy, and can be applied to linguistic information processing. The network has been applied to the learning of fuzzy if–then rules, a mathematical function with fuzzy inputs and outputs, and truck backing control problem. Good simulation results are achieved from all these applications.

Introduction

In the real world, information usually comes in one of two types, numerical information from measurement and linguistic information according to human opinion. Linguistic information could be represented by fuzzy theory. This paper considers linguistic information represented in the form of fuzzy input and output data pairs. When linguistic information comes from a very large batch of fuzzy input and output pairs, automatic construction of a small fuzzy system from these fuzzy data is necessary. Moreover, for a complex system, it is usually difficult even for an expert to directly describe the solution by linguistic if–then rules, so numerical information from measurement is also necessary. Therefore, a neural fuzzy system that can construct automatically and simultaneously from both numerical and linguistic information is worth studying. However, most current studies focus on the construction of fuzzy rules from numerical information only [1], [4], [7], [8], [9], [11], [15], [17]. To deal with the aforementioned problems, this paper proposes a fuzzified Takagi–Sugeno–Kang (TSK)-type neural fuzzy inference network (FTNFIN) that can learn from both numerical and fuzzy input–output data pairs.

For a neural network to process linguistic information with fuzzy inputs and outputs, several approaches have been proposed [3], [6], [10]. In studies [6], [3], the authors propose an architecture of multilayer feedforward neural networks that can deal with fuzzy input vectors with fuzzy/crisp outputs. In this method, the inputs and outputs of the neural network are fuzzified using fuzzy numbers represented by α-cuts. In addition to the fuzzified neural networks above, fuzzy systems with neural learning for processing fuzzy information have also been proposed [14], [16]. In [14], input fuzzy data are viewed as fuzzy numbers being represented by α-level sets. An unusual fuzzification operation is used, where the fuzzification operation maps level sets onto a real number by measuring total differences of upper and lower limits of the level sets between input fuzzy numbers and fuzzy numbers in the antecedent part, and then uses an activation function to map the difference to the range [0,1]. In [16], fuzzy inputs are assumed to be Gaussian fuzzy sets, and in the fuzzification process, a fuzzy mutual subsethood measure is adopted to define the activation. However, the measurement is performed directly on the Gaussian functions, which is too complex and inefficient. Overall, the neural fuzzy systems above have fuzzy sets used in consequent parts, and the whole network is constructed off-line. In the proposed FTNFIN, fuzzification based on the general sup-min operation [13] is derived and the consequence is of TSK-type. For learning characteristics, FTNFIN is constructed on-line and can learn both numerical information and linguistic information simultaneously.

In the proposed FTNFIN, the input–output crisp/fuzzy data relationship is computed by using α-cut technique. The α-cut arithmetic is a general technique for fuzzy arithmetic computation. Many studies on applying α-cut technique to different fuzzy arithmetic computations have been proposed. In [2], α-cut is applied to rule interpolation. Different methods for fuzzy weighted average operation using α-cut are proposed in [12], [5]. In [18], fuzzy number neural networks using α-cut technique for network output computation and fuzzy chaotic neuron are proposed. As stated above, studies [3], [6], [10] use α-cut to compute fuzzy inputs and fuzzy/crisp outputs of neural networks. Since the fuzzy arithmetic functions in the FTNFIN are different from functions studied in the papers above, the computation process using α-cut differs and a new computation method is proposed this paper. In summary, contributions of the proposed FTNFIN are threefold. First, the proposed FTNFIN can handle fuzzy input–output data or both numerical and fuzzy data simultaneously. Second, derivation of fuzzy input–output mapping of a TSK-type fuzzy system using α-cut is proposed. The result enables FTNFIN to handle fuzzy input/output numbers with any shape. Third, FTNFIN is characterized by simultaneous structure and parameter learning ability, which enables FTNFIN to be constructed on-line. For parameter learning, a simplified learning algorithm is proposed to ease the antecedent parameter update equation and reduce computation time.

This paper is organized as follows. Section 2 introduces the basic structure and mathematical equations of FTNFIN. Structure and parameter learning algorithms of FTNFIN are presented in Section 3. In Section 4, FTNFIN is applied to several examples and comparisons with fuzzified neural networks are made. Conclusions are presented in the last section.