From: earlcox@earlcoxreports.com   
      
   I have a difficult time understanding this hierarchy. Why should fuzzy be a   
   last resort? Fuzzy logic is a system of logic in the same way that Boolean   
   logic is a system of logic. It is essentially (but not necessarily always) a   
   logic of continuous variables. It is possible to introduce fuzzy logic as   
   the logic of choice into almost any modeling approach. It is more reasonable   
   to say that fuzzy logic provides a different epistemology of knowledge than   
   Boolean logic and for models that can benefit from this epistemological   
   perspective, fuzzy logic can add robustness, extensibility, simplicity, and   
   computational power.   
      
   I have built and delivered many deterministic as well as stochastic models   
   that use fuzzy logic in this way. Neither deterministic nor stochastic   
   processes exclude or preclude the use of fuzzy logic and the choice is not   
   trivalent. In the sense that fuzzy logic defines the elasticity of fuzzy   
   numbers or fuzzy constraints within a model, that it provides a method of   
   directly incorporating the intrinsic imprecision of set boundaries, that it   
   can be used to define the semantic (or semiotic) properties of data, and   
   that it provides a rational and mathematically sound means of dealing with   
   models that deal with conflicting experts, conflicting evidence, and   
   overlapping set memberships (that is, models where the Boolean laws of the   
   excluded middle and the laws of noncontradiction are inappropriate) it is an   
   ideal logical mechanism.   
      
   The pricing model for a British retailer is an excellent example of a real   
   world fuzzy model that is deterministic but benefits from fuzzy logic. The   
   first four rules of this model are:   
      
   our price must be high;   
   our price must be low;   
   our price must be above around 2*MfgCosts;   
   if the competition_price is not very high   
      then our price should be close to the competition_price;   
      
   these rules are not paraphrased, but are the exact rules used in the model.   
   High and Low are the two basic sigmoidal (growth and decay) fuzzy sets, the   
   hedge "around" turns 2*MfgCosts into a bell shaped fuzzy set with a default   
   expectancy (width), "above" is a hedge that creates a skewed S-fuzzy set   
   that follows the morphology of the bell fuzzy set to generate a membership   
   function that climbs along the left edge of the bell and begins to slowly   
   flatten out above the inflection point, "not very high" is a fuzzy set   
   formed by taking the complement of High and then applying the   
   intensification hedge "very", and "close to the competition_price" is a   
   contrast intensified bell fuzzy set generated by the hedge "close to." It is   
   interesting to note that some of the other rules on shelf life, retail   
   pricing, inventory carrying costs, transportation costs, tariffs, etc. were   
   Gaussian variables coupled to fuzzy measurements, so that Monte Carlo   
   analysis was used to generate normally distributed random values. Thus the   
   pricing model is deterministic for a given set of constraints, but   
   stochastic when tested for data sensitivity and sphere of influence.   
      
   Well, that's all I have on this subject.   
   Until non-academics and business consultants start building real fuzzy   
   models   
   that deal with real, complex, difficult, and nonlinear problems   
   and do this for customers who are paying real dollars for the answers   
   and start bringing their experience to this news group, then   
   all these discussions about the utility of fuzzy logic, when to use   
   fuzzy logic, how to use fuzzy logic, etc. is just so much   
   poorly thought out and ill-informed speculation.   
      
   G'night   
   Earl   
      
      
      
      
      
   "Dmitry A. Kazakov"  wrote in message   
   news:c5te15$58ae3$2@ID-77047.news.uni-berlin.de...   
   > Will Dwinnell wrote:   
   >   
   > > Luko wrote:   
   > > "where and why not use fuzzy?"   
   > >   
   > > "Dmitry A. Kazakov"  wrote:   
   > > "If you know for sure that your case is deterministic or stochastic,   
   > > then do not use fuzzy."   
   > >   
   > > Could you clarify what you mean by this?  By "case", do you mean the   
   > > problem or the solution?   
   >   
   > I intentionally used the word "case", because even if the problem itself   
   is   
   > formulated in a deterministic or stochastic way, there could be place for   
   > fuzzy approach. One should also count in our knowledge about the problem   
   > and the solution space.   
   >   
   > 1. The problem can be ill defined. We might know that a system is, say,   
   > stochastic, but we could be unable to describe in a representative,   
   > correct, unambiguous way.   
   >   
   > 2. This knowledge can be inexact to find a solution in original terms of   
   the   
   > problem.   
   >   
   > 3. The solution can be inappropriate for some reason (numerical   
   complexity,   
   > instability etc).   
   >   
   > > And what other choices do you imagine than   
   > > "deterministic or stochastic"?   
   >   
   > As I see it, in descending order of quality: deterministic, stochastic,   
   > fuzzy. So fuzzy is the last resort approach, there is nothing after it.   
   >   
   > --   
   > Regards,   
   > Dmitry A. Kazakov   
   > www.dmitry-kazakov.de   
      
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