An Efficient Method for Forecasting Using Fuzzy Time Series

Forecasting using fuzzy time series has been applied in several areas including forecasting university enrollments, sales, road accidents, financial forecasting, weather forecasting, etc. Recently, many researchers have paid attention to apply fuzzy time series in time series forecasting problems. In this paper, we present a new model to forecast the enrollments in the University of Alabama and the daily average temperature in Taipei, based on one-factor fuzzy time series. In this model, a new frequency based clustering technique is employed for partitioning the time series data sets into different intervals. For defuzzification function, two new principles are also incorporated in this model. In case of enrollments as well daily temperature forecasting, proposed model exhibits very small error rate.

Classification Techniques in Data Mining

Learning is the ability to improve behavior based on former experiences and observations. Nowadays, mankind continuously attempts to train computers for his purpose, and make them smarter through trainings and experiments. Learning machines are a branch of artificial intelligence with the aim of reaching machines able to extract knowledge (learning) from the environment. Classical, fuzzy classification, as a subcategory of machine learning, has an important role in reaching these goals in this area. In the present chapter, we undertake to elaborate and explain some useful and efficient methods of classical versus fuzzy classification. Moreover, we compare them, investigating their advantages and disadvantages.

Semiring of Generalized Interval-Valued Intuitionistic Fuzzy Matrices

In this paper, the concept of semiring of generalized interval-valued intuitionistic fuzzy matrices are introduced and have shown that the set of GIVIFMs forms a distributive lattice. Also, prove that the GIVIFMs form an generalized interval valued intuitionistic fuzzy algebra and vector space over [0, 1]. Some properties of GIVIFMs are studied using the definition of comparability of GIVIFMs.

Interval-Valued Intuitionistic Fuzzy Partition Matrices

If in an interval-valued intuitionistic fuzzy matrix each element is again a smaller interval-valued intuitionistic fuzzy matrix then the interval-valued intuitionistic fuzzy matrix is called interval-valued intuitionistic fuzzy partion matrix (IVIFPMs). In this paper, the concept of interval-valued intuitionistic fuzzy partion matrices (IVIFPMs) are introduced and defined different types of interval-valued intuitionistic fuzzy partion matrices (IVIFPMs). The operations like direct sum, Kronecker sum, Kronecker product of interval-valued intuitionistic fuzzy matrices are presented and shown that their resultant matrices are also interval-valued intuitionistic fuzzy partion matrices (IVIFPMs).

Multiobjective Optimization of Solar-Powered Irrigation System with Fuzzy Type-2 Noise Modelling

Design optimization has been commonly practiced for many years across various engineering disciplines. Optimization per se is becoming a crucial element in industrial applications involving sustainable alternative energy systems. During the design of such systems, the engineer/decision maker would often encounter noise factors (e.g. solar insolation and ambient temperature fluctuations) when their system interacts with the environment. Therefore, successful modelling and optimization procedures would require a framework that encompasses all these uncertainty features and solves the problem at hand with reasonable accuracy. In this chapter, the sizing and design optimization of the solar powered irrigation system was considered. This problem is multivariate, noisy, nonlinear and multiobjective. This design problem was tackled by first using the Fuzzy Type II approach to model the noise factors. Consequently, the Bacterial Foraging Algorithm (BFA) (in the context of a weighted sum framework) was employed to solve this multiobjective fuzzy design problem. This method was then used to construct the approximate Pareto frontier as well as to identify the best solution option in a fuzzy setting. Comprehensive analyses and discussions were performed on the generated numerical results with respect to the implemented solution methods.

A Three-Level Supply Chain Model with Necessity Measure

In this chapter, a vertical information sharing in terms of inventory replenishment / requirement from the customer(s)? retailer(s)? producer? supplier(s) has been done. The constant imprecise fuzzy demands of the goods are made to the retailers by the customers. These goods are produced (along with defectiveness, which decreases due to learning effects) from the raw materials in the producer's production center with a constant production rate (to be determined). Producer stores these raw materials in a warehouse by purchasing these from a supplier and the suppliers collect these raw materials from open markets at a constant collection rate (to be determined). The whole system is considered in a finite time horizon with fuzzy demand for finished products and fuzzy inventory costs. Here shortages are allowed and fully backlogged. The fuzzy chance constraints on the available space of the producer and transportation costs for both producer, retailers are defuzzified using necessity approach. Results indicate the efficiency of proposed approach in performance measurement. This paper attempts to provide the reader a complete picture of supply chain management through a systematic literature review.

On Bipolar Fuzzy B-Subalgebras of B-Algebras

Based on the concept of bipolar fuzzy set, a theoretical approach of B-subalgebras of B-algebras are established. Some characterizations of bipolar fuzzy B-subalgebras of B-algebras are given. We have shown that the intersection of two bipolar fuzzy B-subalgebras is also a bipolar fuzzy B-subalgebra, but for the union it is not always true. We have also shown that if every bipolar fuzzy B-subalgebras has the finite image, then every descending chain of B-subalgebras terminates at finite step.

Decision Making by Using Intuitionistic Fuzzy Rough Set

This chapter begins with a brief introduction of the theory of rough set. Rough set is an intelligent technique for handling uncertainty aspect in the data. This theory has been hybridized by combining with many other mathematical theories. In recent years, much decision making on rough set theory has been extended by embedding the ideas of fuzzy sets, intuitionistic fuzzy sets and soft sets. In this chapter, the notions of fuzzy rough set and intuitionistic fuzzy rough (IFR) sets are defined, and its properties are studied. Thereafter rough set on two universal sets has been studied. In addition, intuitionistic fuzzy rough set on two universal sets has been extensively studied. Furthermore, we would like to give an application, which shows that intuitionistic fuzzy rough set on two universal sets can be successfully applied to decision making problems.

Non-Linear Intuitionistic Fuzzy Number and Its Application in Partial Differential Equation

In this chapter the concept of non linear intuitionistic fuzzy number is addressed. Mainly the construction of non linear intuitionistic fuzzy number whose membership function is non linear function is taken here. Finally the number is taken with partial differential equation and solve the problem.

Intutionistic Fuzzy Difference Equation

In this chapter we solve linear difference equation with intuitionistic fuzzy initial condition. All possible cases are defined and solved them to obtain the exact solutions. The intuitionistic fuzzy numbers are also taken as trapezoidal intuitionistic fuzzy number. The problems are illustrated by two different numerical examples.