Using level-2 fuzzy sets to combine uncertainty and imprecision in fuzzy regions

In many applications, spatial data need to be considered but are prone to uncertainty or imprecision. A fuzzy region - a fuzzy set over a two dimensional domain - allows the representation of such imperfect spatial data. In the original model, points of the fuzzy region where treated independently, making it impossible to model regions where groups of points should be considered as one basic element or subregion. A first extension overcame this, but required points within a group to have the same membership grade. In this contribution, we will extend this further, allowing a fuzzy region to contain subregions in which not all points have the same membership grades. The concept can be used as an underlying model in spatial applications, e.g. websites showing maps and requiring representation of imprecise features or websites with routing functions needing to handle concepts as walking distance or closeby

Fuzzy Supernova Templates II: Parameter Estimation

Wide field surveys will soon be discovering Type Ia supernovae (SNe) at rates of several thousand per year. Spectroscopic follow-up can only scratch the surface for such enormous samples, so these extensive data sets will only be useful to the extent that they can be characterized by the survey photometry alone. In a companion paper (Rodney and Tonry, 2009) we introduced the SOFT method for analyzing SNe using direct comparison to template light curves, and demonstrated its application for photometric SN classification. In this work we extend the SOFT method to derive estimates of redshift and luminosity distance for Type Ia SNe, using light curves from the SDSS and SNLS surveys as a validation set. Redshifts determined by SOFT using light curves alone are consistent with spectroscopic redshifts, showing a root-mean-square scatter in the residuals of RMS_z=0.051. SOFT can also derive simultaneous redshift and distance estimates, yielding results that are consistent with the currently favored Lambda-CDM cosmological model. When SOFT is given spectroscopic information for SN classification and redshift priors, the RMS scatter in Hubble diagram residuals is 0.18 mags for the SDSS data and 0.28 mags for the SNLS objects. Without access to any spectroscopic information, and even without any redshift priors from host galaxy photometry, SOFT can still measure reliable redshifts and distances, with an increase in the Hubble residuals to 0.37 mags for the combined SDSS and SNLS data set. Using Monte Carlo simulations we predict that SOFT will be able to improve constraints on time-variable dark energy models by a factor of 2-3 with each new generation of large-scale SN surveys.Comment: 20 pages, 7 figures, accepted to ApJ; paper 1 is arXiv:0910.370

Retraction and Generalized Extension of Computing with Words

Fuzzy automata, whose input alphabet is a set of numbers or symbols, are a formal model of computing with values. Motivated by Zadeh's paradigm of computing with words rather than numbers, Ying proposed a kind of fuzzy automata, whose input alphabet consists of all fuzzy subsets of a set of symbols, as a formal model of computing with all words. In this paper, we introduce a somewhat general formal model of computing with (some special) words. The new features of the model are that the input alphabet only comprises some (not necessarily all) fuzzy subsets of a set of symbols and the fuzzy transition function can be specified arbitrarily. By employing the methodology of fuzzy control, we establish a retraction principle from computing with words to computing with values for handling crisp inputs and a generalized extension principle from computing with words to computing with all words for handling fuzzy inputs. These principles show that computing with values and computing with all words can be respectively implemented by computing with words. Some algebraic properties of retractions and generalized extensions are addressed as well.Comment: 13 double column pages; 3 figures; to be published in the IEEE Transactions on Fuzzy System

An intelligent system for risk classification of stock investment projects

The proposed paper demonstrates that a hybrid fuzzy neural network can serve as a risk classifier of stock investment projects. The training algorithm for the regular part of the network is based on bidirectional incremental evolution proving more efficient than direct evolution. The approach is compared with other crisp and soft investment appraisal and trading techniques, while building a multimodel domain representation for an intelligent decision support system. Thus the advantages of each model are utilised while looking at the investment problem from different perspectives. The empirical results are based on UK companies traded on the London Stock Exchange

Fuzzy Supernova Templates I: Classification

Modern supernova (SN) surveys are now uncovering stellar explosions at rates that far surpass what the world's spectroscopic resources can handle. In order to make full use of these SN datasets, it is necessary to use analysis methods that depend only on the survey photometry. This paper presents two methods for utilizing a set of SN light curve templates to classify SN objects. In the first case we present an updated version of the Bayesian Adaptive Template Matching program (BATM). To address some shortcomings of that strictly Bayesian approach, we introduce a method for Supernova Ontology with Fuzzy Templates (SOFT), which utilizes Fuzzy Set Theory for the definition and combination of SN light curve models. For well-sampled light curves with a modest signal to noise ratio (S/N>10), the SOFT method can correctly separate thermonuclear (Type Ia) SNe from core collapse SNe with 98% accuracy. In addition, the SOFT method has the potential to classify supernovae into sub-types, providing photometric identification of very rare or peculiar explosions. The accuracy and precision of the SOFT method is verified using Monte Carlo simulations as well as real SN light curves from the Sloan Digital Sky Survey and the SuperNova Legacy Survey. In a subsequent paper the SOFT method is extended to address the problem of parameter estimation, providing estimates of redshift, distance, and host galaxy extinction without any spectroscopy.Comment: 26 pages, 12 figures. Accepted to Ap