This is to announce the FASS Regression Solver. It is a product of The Fuzzy   
   Analytical & Statistical Software Co. Ltd. (FASS). It solves the general   
   (non-linear) regression problem.   
      
   FASS, as the name implies, is offering software in which there is intimate   
   mixing, yet careful separation, between uncertainty of the probabilistic kind,   
   and that of the fuzzy kind.    
      
   Uncertainty in the fitted parameters of the regression model is fuzzy. This is   
   in general the case for uncertainty regarding a constant known only to within   
   a fuzzy term of description. Uncertainty in the measured data is also   
   represented as fuzzy in    
   general. Thus the data inputs are fuzzy, and the estimated parameters reported   
   as outputs are fuzzy also. Both are standardized as LABR fuzzy sets. The error   
   residuals are assumed to be zero-mean Gaussian.   
      
   Consistent with the LABR fuzzy representation for each parameter, any function   
   of the parameters may likewise have its derived fuzzy uncertainty also   
   represented as an LABR fuzzy set. Thus the prediction function of the mean is   
   represented as a fuzzy    
   LABR swath, grosser or more precise according as the degree of fuzziness   
   inherent in the fitted parameters deriving from the model and the data.   
   Likewise, 5% and 95% probability quantiles are LABR fuzzy swaths w.r.t to the   
   independent variables.    
      
   The fuzzy mapping of the uncertainty in each parameter accomplishes in   
   principle that which the Bayesian approach seeks among others to do, which is   
   to map the marginals describing the uncertainty in each fitted parameter. But   
   it is insisted that the    
   proper calculus that should always have applied to uncertain constants is that   
   of the possibility calculus. The fundamental mathematical object of the   
   possibility calculus is the absolute likelihood function (a.l.f). Under this   
   calculus, the need for a    
   subjective, or any other "prior", is obviated.   
      
   This calculus is a special case of a reformulated fuzzy logic. Jaynes was   
   correct in his assertion that a logic that did not uphold Aristotle, where   
   Aristotle applies, could not be a proper basis for addressing the statistical   
   inference problem. The    
   fuzzy logic here deployed is one in which Aristotle is upheld. The   
   reformulated fuzzy logic allows for flexible connectives, and shows how,   
   within the theory, these may be selected. The max/min rules apply in some   
   situations, the product/product-sum    
   rules in others, and the bounded-sum rules in others, and in general, the   
   reformulated fuzzy logic proposes a linear combination of these three basic   
   rules, mediated through the semantic consistency coefficient. The   
   determination of the latter is    
   internal to the theory under a fairly straight-forward rule easy to motivate   
   and justify.   
      
   The probabiility of the data may be represented as a product-sum (p-s)   
   integral over the a.l.f. This provides an obvious maximization criterion (max   
   p-s) for the general regression problem. It is akin to maximum likelihood   
   obviously, but uses a product-   
   sum rule of disjunction rather than a maximization rule, or bounded-sum rule.   
   Both of the latter are rejected in the light of the reformulated fuzzy logic,   
   which reserves the maximum and bounded-sum rules of disjunction respectively   
   for cases where there    
   is strong positive, or strong negative semantic consistency. In the case of   
   statistical inference, it is a rule of semantic independence that must apply,   
   consistent with the i.i.d assumption for a statistical sample.    
      
   This approach obviates Bayesian priors, as already mentioned. It also   
   sidesteps the known difficulties of the maximum likelihood estimate (MLE) of   
   being sometimes misleading both as to location and precision of the true value   
   sought. And it may be used    
   to give a full mapping of the uncertainty in fitted parameters, as the   
   Bayesian approaches (e.g. MCMC) rightly seek to accomplish.   
      
   The FASS Regression Solver rests on the analytic extensions to ideas explored   
   in an earlier work, "Fuzziness and Probability" (1995). Those extensions are   
   forthcoming in a monograph, "The unified theory of fuzzy logic, the   
   possibility calculus, and    
   statistical inference, with application to Gaussian regression analysis".   
      
   See the website: http://fuzzastat.com, for further details of the FASS   
   Regression Solver.    
      
   For those interested, note in particular that a seminar/tutorial is proposed   
   for Jan 26-Feb 2, 2016, in Port of Spain, Trinidad.   
      
   Sidney   
   --   
   Dr. Sidney Thomas   
   Executive Chairman and Principal   
   The Fuzzy Analytical & Statistical Software Co. Ltd.   
   http://fuzzastat.com   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)