Studies On Fuzzy Measure Of Type-2 Fuzzy Logic System And Its Application To Power Load Forecasting

The type-2 fuzzy logic system identification based on type-2 fuzzy logic is an effective branch in the field of nonlinear system identification. The type-2 fuzzy logic, which is an extension version of its conventional type-1 counterpart, is suitable for complex non-linear systems with strongly random disturbance, due to its abilities of effectively making use of linguistic experience of human experts and idiographic predominance in dealing with uncertainties. Compared with the type-1 case, the type-2 fuzzy logic based on type-2 fuzzy sets has more adjustable parameters of membership functions, and its fuzzy reasoning process can be accomplished by the extended sup-star composition, hence it acquires the ability of handling uncertainties in a more effective way.A fuzzy measure can promote a fuzzy logic system to fully play its roles. Type-1 fuzzy measures have shown unique advantage in the field of type-1 fuzzy logic system identification because they can simplify both redundant fuzzy sets and redundant fuzzy rules, but none effort as to it has been done on type-2 case. For that in this paper, type-2 fuzzy measures are introduced to type-2 fuzzy logic system identification to eliminate the harmful effects of redundant fuzzy sets and redundant fuzzy rules, and the model with simplified rule bases is used to power load time series forecasting to improve the prediction accuracy.Power load forecasting is an important work in power industry. As an important basis of many power system behaviors such as planning, construction, production, dispatching and overhauling, etc, accurate power load forecasting can ensure that a power network runs safely and economically, and improve economic and social benefit of an electric power enterprise. However, being affected by various natural and social factors with uncertainties, the fluctuation of power load can be considered as a stochastic non-stationary process, and this leads to difficulties to accurately forecast. As the reform of electricity market continues to deepen, decision-making inevitably has some degree of risk because of different uncertain factors in power system; therefore, uncertainties of power demand must be taken into consideration in decision-making. Under this background, it is significative to find a method that can let us effectively handle uncertainties to improve the accuracy of power load forecasting. The existing traditional forecasting methods cannot obtain ideal results because of their inherent defects; therefore, modern forecasting methods based on some artificial intelligence theories attract more and more researchers'attention, among them type-2 fuzzy logic methods suitable for time series forecasting provide new ideas to power load forecasting because of their abilities of dealing with uncertainties. In this paper, type-2 fuzzy measures are researched because of their important roles in the field of type-2 fuzzy logic system identification. A similarity measure and an inclusion measure between general type-2 fuzzy sets are presented in the constraints of their axiomatic definitions, and the axioms meet human intuitional cognition. The computation formulas of two fuzzy measures are proposed by considering the footprint of uncertainty (FOU) and the secondary membership function, which are the most important factors of a general type-2 fuzzy set. Properties of the proposed fuzzy inclusion measure are analysed. Relations that two fuzzy measures can be transformed by each other are discussed to reveal their inner link. In the end, examples are given to test their performance, and combine the proposed fuzzy similarity measure with Yang and Shih's method for an application to clustering of general type-2 fuzzy data. The clustering results are rational, and show that the proposed fuzzy measures are reasonable and valid for general type-2 fuzzy sets.The interval type-2 fuzzy logic is a hotspot of theoretical research and practical application because it overcomes the deficiency of complex calculation of general type-2 fuzzy logic. According to the characteristics of interval type-2 fuzzy logic, new similarity measure, inclusion measure and entropy of interval type-2 fuzzy sets (IT2 FSs) are proposed based on their axiomatic definitions. The computation formulas are proposed by consideration of a fact that the operations of IT2 FSs depend on the upper and lower membership functions. Properties of the proposed fuzzy inclusion measure are analysed. Relations that three fuzzy measures can be transformed by each other are discussed. In the end, examples are presented to validate their performance to lay a theoretical foundation for the next step applications.In order to introduce the proposed similarity measure between IT2 FSs to interval type-2 fuzzy logic system identification, a singular value decompose-similarity measure-back propagation (SVD-SM-BP) hybrid iterative arithmetic is proposed. The BP arithmetic is used to tune model parameters. The redundant fuzzy sets are identified by the proposed similarity measure between IT2 FSs, and then deleted by merging and deleting methods. Thus, the number of redundant fuzzy sets is reduced and the interpretability of fuzzy rule is enhanced. If the redundancy in the model is high, the number of redundant fuzzy rules may be reduced by the merging method. After identifying, merging and deleting processes, the SVD method is used to choose the optimal fuzzy rules. In a word, the SVD-SM-BP hybrid iterative arithmetic can simplify both redundant fuzzy sets and redundant fuzzy rules, decrease the calculation complexity of fuzzy reasoning, and improve the approximation accuracy of system.Finally, aiming at the problem that it is difficult to accurately forecast power load with strongly random characteristic, the type-2 fuzzy logic method is introduced to improve the prediction accuracy. An interval type-2 non-singleton type-2 Mamdani fuzzy logic model is presented to forecast power load time series, and the proposed SVD-SM-BP hybrid iterative arithmetic is used to simplify both redundant fuzzy sets and redundant fuzzy rules to eliminate the harmful effects. From the forecasting results of power load time series of a certain Chinese city, including time segments of five minutes, one hour, one day and three days, we can draw the conclusion that the forecasting model has high prediction accuracy and excellent tracking characteristics for real power load curve, and show its practicality in the field of power load forecasting.