The Cauchy Mean Value Theorem for Intuitionistic Fuzzy Functions

In this paper, we first study the arithmetic properties of intuitionistic fuzzy number, the monotonicity of intuitionistic fuzzy function and the derivative of intuitionistic fuzzy functions and then we study the fundamental properties on monotone function. After that, we proposed a mean value theorem for differentiable function in intuitionistic fuzzy calculus, from which we derived a general version using Cauchy mean value theorem for intuitionistic fuzzy calculus. At last, we give some examples and we also show as a corollary that the mean value theorem is a special case of the Cauchy version of mean value theorem.Comment: 36 pages, 3 graphic

Intuitionistic Fuzzy Time Series Functions Approach for Time Series Forecasting

Fuzzy inference systems have been commonly used for time series forecasting in the literature. Adaptive network fuzzy inference system, fuzzy time series approaches and fuzzy regression functions approaches are popular among fuzzy inference systems. In recent years, intuitionistic fuzzy sets have been preferred in the fuzzy modeling and new fuzzy inference systems have been proposed based on intuitionistic fuzzy sets. In this paper, a new intuitionistic fuzzy regression functions approach is proposed based on intuitionistic fuzzy sets for forecasting purpose. This new inference system is called an intuitionistic fuzzy time series functions approach. The contribution of the paper is proposing a new intuitionistic fuzzy inference system. To evaluate the performance of intuitionistic fuzzy time series functions, twenty-three real-world time series data sets are analyzed. The results obtained from the intuitionistic fuzzy time series functions approach are compared with some other methods according to a root mean square error and mean absolute percentage error criteria. The proposed method has superior forecasting performance among all methods

Himpunan Fuzzy dan Rough Sets

The concept of a fuzzy set was introduced by Zadeh in 1965. Fuzzy set is a mathematical model of vague qualitative or quantitative data, frequently generated by means of the natural language. The model is based on the generalization of the classical concepts of set and its characteristic function. Intuitionistic fuzzy sets are sets whose elements have degrees of membership and non-membership. Intuitionistic fuzzy sets have been introduced by Atanassov in 1983 as an extension fuzzy sets. On the other hand, the concept of rough set was proposed by Pawlak 1982. Since then the subject has been investigated in many papers. The overall aim of this paper is to present an introduction to some of main concepts related to fuzzy sets, intuitionistic fuzzy sets and rough sets. We investigate Crisp sets and characteristic functions, fuzzy sets, intuitionistic fuzzy sets, rough sets and probabilistic rough sets

On Intuitionistic Fuzzy Context-Free Languages

Taking intuitionistic fuzzy sets as the structures of truth values, we propose the notions of intuitionistic fuzzy context-free grammars (IFCFGs, for short) and pushdown automata with final states (IFPDAs). Then we investigate algebraic characterization of intuitionistic fuzzy recognizable languages including decomposition form and representation theorem. By introducing the generalized subset construction method, we show that IFPDAs are equivalent to their simple form, called intuitionistic fuzzy simple pushdown automata (IF-SPDAs), and then prove that intuitionistic fuzzy recognizable step functions are the same as those accepted by IFPDAs. It follows that intuitionistic fuzzy pushdown automata with empty stack and IFPDAs are equivalent by classical automata theory. Additionally, we introduce the concepts of Chomsky normal form grammar (IFCNF) and Greibach normal form grammar (IFGNF) based on intuitionistic fuzzy sets. The results of our study indicate that intuitionistic fuzzy context-free languages generated by IFCFGs are equivalent to those generated by IFGNFs and IFCNFs, respectively, and they are also equivalent to intuitionistic fuzzy recognizable step functions. Then some operations on the family of intuitionistic fuzzy context-free languages are discussed. Finally, pumping lemma for intuitionistic fuzzy context-free languages is investigated