| This research is concerned with linguistic algorithms with linguistic vectors as inputs. These algorithms are developed based on the extension principle and the decomposition theorem. In particular these algorithms are a linguistic Choquet fuzzy integral (LCFI), linguistic Sugeno fuzzy integral (LSFI), linguistic nearest prototype (LNP), linguistic Hard C-Means (LHCM), linguistic Fuzzy C-Means (LFCM), and linguistic Possibilistic C-Means (LPCM). We analytically examined the extensions and proved that these algorithms behave properly, i.e., in a similar fashion to their counterparts (numeric algorithms) which they reduce to in the degenerate linguistic case.; Using the extension principle to extend the capability of the standard update equation in linguistic clustering algorithms to deal with linguistic vectors has huge computational complexity. To handle this problem, an efficient method has been analyzed and developed based on fuzzy arithmetic and optimization. The shape of the centers can be an indicator for the closeness of the cluster and also they can indicate whether there is a bad point, i.e., a vector with high uncertainty, in the data set.; We compared the performance of the LCFI and the LSFI through a synthetic data set. Both algorithms produce the results that are based on the extension principle and decomposition theorem. For example, for a particular fuzzy measure such that the linguistic fuzzy integral will give the minimum/maximum, the results from both algorithms are minimum/maximum according to the concept of the extension principle.; We also developed a linguistic fusion using the LCFI or the LSFI. This fusion algorithm was applied to land mine recognition problem. The result showed an improvement in the probability of detection and a reduction in the false alarm rate.; We developed tools for detection error prediction and d-metric (the ratio of a target's signal to the clutter's signal) prediction. The characteristic of a new sensor added can be determined in order to gain a desired performance from the fusion. Also the performance of a system when a new sensor with a certain characteristic is added can be foreseen. |
