Fuzzy number

About: Fuzzy number is a research topic. Over the lifetime, 35606 publications have been published within this topic receiving 972544 citations.

Fuzzy risk analysis based on the ranking of generalized trapezoidal fuzzy numbers

Abstract: In this paper, we present a new method for fuzzy risk analysis based on the ranking of generalized trapezoidal fuzzy numbers. The proposed method considers the centroid points and the standard deviations of generalized trapezoidal fuzzy numbers for ranking generalized trapezoidal fuzzy numbers. We also use an example to compare the ranking results of the proposed method with the existing centroid-index ranking methods. The proposed ranking method can overcome the drawbacks of the existing centroid-index ranking methods. Based on the proposed ranking method, we also present an algorithm to deal with fuzzy risk analysis problems. The proposed fuzzy risk analysis algorithm can overcome the drawbacks of the one we presented in [7].

Expected value operator of random fuzzy variable and random fuzzy expected value models

Abstract: Random fuzzy variable is a mapping from a possibility space to a collection of random variables This paper first presents a new definition of the expected value operator of a random fuzzy variable, and proves the linearity of the operator Then, a random fuzzy simulation approach, which combines fuzzy simulation and random simulation, is designed to estimate the expected value of a random fuzzy variable Based on the new expected value operator, three types of random fuzzy expected value models are presented to model decision systems where fuzziness and randomness appear simultaneously In addition, random fuzzy simulation, neural networks and genetic algorithm are integrated to produce a hybrid intelligent algorithm for solving those random fuzzy expected valued models Finally, three numerical examples are provided to illustrate the feasibility and the effectiveness of the proposed algorithm

Intuitionistic fuzzy interpretations of multi-criteria multi-person and multi-measurement tool decision making

Abstract: Intuitionistic fuzzy sets are extensions of fuzzy sets. Their elements have two degrees – a degree of membership and a degree of non-membership so that their sum is smaller or equal to 1. Intuitionistic fuzzy interpretations of the processes of multi-person and of multi-measurement tool multi-criteria decision makings are discussed in this paper.

Control Design for Interval Type-2 Fuzzy Systems Under Imperfect Premise Matching

Abstract: This paper focuses on designing interval type-2 (IT2) control for nonlinear systems subject to parameter uncertainties. To facilitate the stability analysis and control synthesis, an IT2 Takagi-Sugeno (T-S) fuzzy model is employed to represent the dynamics of nonlinear systems of which the parameter uncertainties are captured by IT2 membership functions characterized by the lower and upper membership functions. A novel IT2 fuzzy controller is proposed to perform the control process, where the membership functions and number of rules can be freely chosen and different from those of the IT2 T-S fuzzy model. Consequently, the IT2 fuzzy-model-based (FMB) control system is with imperfectly matched membership functions, which hinders the stability analysis. To relax the stability analysis for this class of IT2 FMB control systems, the information of footprint of uncertainties and the lower and upper membership functions are taken into account for the stability analysis. Based on the Lyapunov stability theory, some stability conditions in terms of linear matrix inequalities are obtained to determine the system stability and achieve the control design. Finally, simulation and experimental examples are provided to demonstrate the effectiveness and the merit of the proposed approach.