Fuzzy number

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

Adaptive fuzzy sliding mode control of nonlinear system

Abstract: In this paper, the fuzzy approximator and sliding mode control (SMC) scheme are considered. We propose two methods of adaptive SMC schemes that the fuzzy logic systems (approximators) are used to approximate the unknown system functions in designing the SMC of nonlinear system. In the first method, a fuzzy logic system is utilized to approximate the unknown function f of the nonlinear system x/sup n=/f(x, t)+b(x, t)u and the robust adaptive law is proposed to reduce the approximation errors between the true nonlinear functions and fuzzy approximators. In the second method, two fuzzy logic systems are utilized to approximate the f and b, respectively, and the control law, which is robust to approximation error is also designed. The stabilities of proposed control schemes are proved and these schemes are applied to an inverted pendulum system. The comparisons between the proposed control schemes are shown in simulations.

A Fuzzy TOPSIS Method for Robot Selection

Abstract: A fuzzy TOPSIS method for robot selection is proposed, where the ratings of various alternatives versus various subjective criteria and the weights of all criteria are assessed in linguistic terms represented by fuzzy numbers. The values of objective criteria are converted into dimensionless indices to ensure compatibility between the values of objective criteria and the linguistic ratings of subjective criteria. The membership function of each weighted rating is developed by interval arithmetic of fuzzy numbers. To avoid complicated aggregation of fuzzy numbers, these weighted ratings are defuzzified into crisp values by the ranking method of mean of removals. A closeness coefficient is defined to determine the ranking order of alternatives by calculating the distances to both the ideal and negative-ideal solutions. A numerical example demonstrates the computational process of the proposed method.

Measuring fuzzy uncertainty

Abstract: First, this paper reviews several well known measures of fuzziness for discrete fuzzy sets. Then new multiplicative and additive classes are defined. We show that each class satisfies five well-known axioms for fuzziness measures, and demonstrate that several existing measures are relatives of these classes. The multiplicative class is based on nonnegative, monotone increasing concave functions. The additive class requires only nonnegative concave functions. Some relationships between several existing and the new measures are established, and some new properties are derived. The relative merits and drawbacks of different measures for applications are discussed. A weighted fuzzy entropy which is flexible enough to incorporate subjectiveness in the measure of fuzziness is also introduced. Finally, we comment on the construction of measures that may assess all of the uncertainties associated with a physical system. >

Limit Theorems for Fuzzy Random Variables

Abstract: A strong law of large numbers and a central limit theorem are proved for independent and identically distributed fuzzy random variables, whose values are fuzzy sets with compact levels. The proofs are based on embedding theorems as well as on probability techniques in Banach space.