Fuzzy number

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

Multicriteria analysis with fuzzy pairwise comparison

Abstract: Presents an approach for solving qualitative multicriteria analysis (MA) problems using fuzzy pairwise comparison. Fuzzy numbers are used to approximate the decision-maker's (DM's) subjective assessments in assessing alternative performance and criteria importance. The concept of fuzzy extent analysis is applied for solving the reciprocal judgement matrices. To avoid the complex and unreliable process of comparing fuzzy utilities, the /spl alpha/-cut technique is applied to transform the fuzzy performance matrix into an interval matrix. Incorporated with the DM's attitude towards risk, an overall performance index is obtained for each alternative across all criteria in line with the ideal solution concept. An empirical study of a tender selection problem in Australia is conducted. The result shows that the approach developed is simple and comprehensible in concept, efficient in computation, and robust and flexible in modeling the human evaluation process, thus making it of general use for solving practical MA problems.

A procedure for multiple-aspect decision making using fuzzy sets

Abstract: In many situations one has to find the best alternative on the basis of many aspects which have varying degrees of importance. The problem is more complex if the ratings of the alternatives and the importance of the aspects are expressed using qualitative variables like good, fair, very important, etc. This paper presents a method for decision making in such situations. The qualitative terms are represented quantitatively using fuzzy sots and then the fuzzy optimal alternative is computed. The fuzzy set representing the optimal alternative gives the relative merit of each alternative and thus helps in decision making.

Stabilization of Nonlinear Systems Under Variable Sampling: A Fuzzy Control Approach

Abstract: This paper investigates the problem of stabilization for a Takagi-Sugeno (T-S) fuzzy system with nonuniform uncertain sampling. The sampling is not required to be periodic, and the only assumption is that the distance between any two consecutive sampling instants is less than a given bound. By using the input delay approach, the T-S fuzzy system with variable uncertain sampling is transformed into a continuous-time T-S fuzzy system with a delay in the state. Though the resulting closed-loop state-delayed T-S fuzzy system takes a standard form, the existing results on delay T-S fuzzy systems cannot be used for our purpose due to their restrictive assumptions on the derivative of state delay. A new condition guaranteeing asymptotic stability of the closed-loop sampled-data system is derived by a Lyapunov approach plus the free weighting matrix technique. Based on this stability condition, two procedures for designing state-feedback control laws are given: one casts the controller design into a convex optimization by introducing some over design and the other utilizes the cone complementarity linearization idea to cast the controller design into a sequential minimization problem subject to linear matrix inequality constraints, which can be readily solved using standard numerical software. An illustrative example is provided to show the applicability and effectiveness of the proposed controller design methodology.