AND ITS APPLICATION by YU QIU Under the Direction of Yanqing Zhang ABSTRACT In recent years, the type-2 fuzzy sets theory has been used to model and minimize the effects of uncertainties in rule-base fuzzy logic system. In order to make the type-2 fuzzy logic system reasonable and reliable, a new simple and novel statistical method to decide interval-valued fuzzy membership functions and a new ...

The system PICASSO 2 represents the latest version of software package, designed for a comparative evaluation of image processing algorithms. In this paper we discuss the part of the system which evaluates edge detectors and consider its fuzzy extension. Namely, we introduce the ground truth edge maps defined in the fuzzy way and complete the system with several fuzzy similarity measures. The p...

Systems of linear equations, with uncertainty on the parameters, play a major role in various problems in economics and finance. Fuzzy system of linear equations has been discussed in [1] using LU decomposition when the matrix A in Ax = b is a crisp matrix. Also the Adomian decomposition method and iterative methods have been studied in [2, 6] for fuzzy system of linear equations. In this paper...

This paper presents a type-2 fuzzy rule based expert system to handle uncertainty in complex problems such as portfolio selection. In a type-2 fuzzy expert system both antecedent and consequent have type-2 membership function. This research uses indirect approach fuzzy modeling, where the rules are extracted automatically by implementing a clustering approach. For this purpose, a new cluster an...

This paper introduces a new mathematical method for introducing Membership function in fuzzy systems. This new mathematical definition relies on concept of continuousvalued logic (CVL) which can be applied to control the pulse width of generated Pulse Width Modulation. The introduced Membership function is in the form of triangle with curved brim in order of two. For the first time, degree of m...

This paper proposes an optimal design for interval type-2 Takagi-Sugeno-Kang (TSK) fuzzy logic system. In this method, the fuzzy c-means clustering algorithm is used to determine structure of fuzzy rule as well as number of rules. A hybrid between chaos firefly algorithm and genetic algorithms (CFGA) is developed, which is used to find the desirable parameters of membership functions and conseq...

Following the idea of $L$-fuzzy neighborhood system as introduced byFu-Gui Shi, and its generalization to $(L,M)$-fuzzy neighborhood system, the relationship between  $(L,M)$-fuzzy topology and $(L,M)$-fuzzy neighborhood system will be further studied. As an application of the obtained results, we will describe the initial structures of $(L,M)$-fuzzy neighborhood subspaces and $(L,M)$-fuzzy top...

In this paper, the fuzzy dual matrix system as AX + B = CX + D in which A, B, C, D, X are LR fuzzy matrices is studied. At first we solve 1-cut system in order to find the core of LR fuzzy solution; then to obtain the spreads of the LR fuzzy solution, we discuss in several cases. The spreads are obtained by using multiplication, quasi norm and minimization problem with a special objective funct...