The architecture and learning procedure underlying ANFIS (adaptive-network-based fuzzy inference system) is presented, which is a fuzzy inference system implemented in the framework of adaptive networks. By using a hybrid learning procedure, the proposed ANFIS can construct an input-output mapping based on both human knowledge (in the form of fuzzy if-then rules) and stipulated input-output data pairs. In the simulation, the ANFIS architecture is employed to model nonlinear functions, identify nonlinear components on-line in a control system, and predict a chaotic time series, all yielding remarkable results. Comparisons with artificial neural networks and earlier work on fuzzy modeling are listed and discussed. Other extensions of the proposed ANFIS and promising applications to automatic control and signal processing are also suggested. >

ANFIS: adaptive-network-based fuzzy inference system

Applications of the extent analysis method on fuzzy AHP

We present a new method of finding the fuzzy weights in fuzzy hierarchical analysis which is the direct fuzzification of the original method used by Saaty (1980) in the analytic hierarchy process. We test our new procedure in two cases where there are formulas for the crisp weights. An example is presented where there are five criteria and three alternatives.

Fuzzy hierarchical analysis

Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic

Classification of objects is an important area of research and application in a variety of fields. In the presence of full knowledge of the underlying probabilities, Bayes decision theory gives optimal error rates. In those cases where this information is not present, many algorithms make use of distance or similarity among samples as a means of classification. The K-nearest neighbor decision rule has often been used in these pattern recognition problems. One of the difficulties that arises when utilizing this technique is that each of the labeled samples is given equal importance in deciding the class memberships of the pattern to be classified, regardless of their `typicalness'. The theory of fuzzy sets is introduced into the K-nearest neighbor technique to develop a fuzzy version of the algorithm. Three methods of assigning fuzzy memberships to the labeled samples are proposed, and experimental results and comparisons to the crisp version are presented.

V. K. Rohatgi

Papers

Advances in Fuzzy Set Theory and Applications