
%Dla tego typu systemów najczęstszą formą reprezentacji wiedzy są reguły twarde (Crisp Rules lub C-rules), które
%zdobytą wiedzę przedstawiają jako serię binarnych operacji porównania na przesłankach
%reguły ({\it jeżeli ... to}) oraz dyskretną wartość konkluzji. Ten typ reguł jest bodaj
%najbardziej rozpowszechniony a jednocześnie wydaje się być najłatwiejszy w późniejszej
%analizie systemu. Jednakże odkrycia psychologiczne i kognitywne ostatnich lat
%\cite{Rul-Sim} pokazują, że reprezentacja wiedzy w naszych mózgach nie odbywa się w
%postaci logicznych reguł {\it jeżeli ... to} lecz na zasadzie podobieństwa do znanych
%przypadków. Ludzki umysł w trakcie wnioskowania porównuje nieznany obiekt lub sytuację z
%różnymi znanymi obiektami lub sytuacjami referencyjnymi zgromadzonymi w pamięci i na
%podstawie podobieństwa do tych obiektów (prototypów) podejmuje ostateczną decyzję.\\
%Podobne podejście od wielu lat było już prezentowane w różnych metodach inteligencji
%obliczeniowej, jak uczenie w oparciu o przypadki (instance-based learning)
%\cite{Aha-IBL}, wnioskowanie pamięciowe (memory-based reasoning) \cite{MBR} czy
%wnioskowanie bazujące na przypadkach (case based reasoning) \cite{CBR}. Jednakże
%wszystkie te grupy metod były raczej używane do poprawienia dokładności klasyfikacji,
%skrócenia jej czasu, lub analizy sposobu podjęcia decyzji niż do przedstawienia prostej i zwięzłej globalnej struktury wiedzy zawartej w analizowanych zbiorach danych.\\
%
% %%
%Sam proces składowania wiedzy przez systemów inteligencji obliczeniowej można podzielić na typu: eksplicite oraz implicite. Pierwsza grupa metod pozwala na bezpośrednią interpretację działania systemu, czyli możliwą do analizy przez człowieka, druga zaś to systemy typu czarne skrzynki (black box), gdzie wiedza ukryta jest przed człowiekiem, lub zapisana w sposób dla niego niezrozumiały. Oczywistym staje się fakt, iż pierwsza grupa systemów będzie preferowana w zagadnieniach gdzie zdolność interpretacji jest własnością nadrzędną, jednakże często spotykaną sytuacją jest konieczność wydobycia wiedzy z systemów już nauczonych, które pozbawione są transparentności.
%%
%
%
%A general idea driven form various similarity based models, and humans cognition
%abilities is a framework on similarity base methods (SBM) proposed by W. Duch in
%\cite{Duch-SBM}. It explains and extends known classification and interpolation models
%into similarity based approach like distance-based multilayer perceptron (SMLP)
%\cite{Duch-D-MLP, Duch-NSBM, Duch-NNSB}. All methods included in SBM framework base on
%closest distance principle either on nearest neighbor or distance with threshold defining
%activation subspace. The conclusion of SBM is that selecting appropriate similarity or
%dissimilarity measure, and reference vectors position allow for knowledge representation
%of any type of system. In other words SBM allow combining knowledge of all known machine
%learning, statistical, neural and fuzzy methods into one general prototype based source
%of information.\\
%As it was earlier noticed some fields of machine learning applications like medicine
%diagnosis or automatic airplane navigation require not only good generalization but also
%general model transparency. In this usage knowledge collected in learning process should
%be denoted human friendly, and this usually leads to logical rules or probabilistic
%models, however both this sources are limited in their comprehensibility. Very often
%obtained set of rules is large, or probability representation is quite complicate with
%many mixture of basic distributions what obscures information of systems behavior.
%Possible solution for this problem brings fuzzy logic and fuzzy rules (F-rules) which are
%much more flexible then crisp rules, and for many real word application this approach
%lead to good balance between transparency (unfortunately fuzzy rules are less
%comprehension then crisp rules)
%and model generalization.\\
%The strength of F-rules is their inference system, however the studies of L. Kuncheva and
%J. Bezdek lead to {\it Generalized Nearest Prototype Classifier} \cite{Kunch-GNPC}, with
%a common inference for different minimum distance classifiers (like nearest neighbor,
%Parzen or radial basis function networks), which from the mathematic perspective is
%equivalent to most fuzzy system \cite{Kunch-Book}.\\
%Joining SMB framework with GNPC lead to an alternative to F-rules which are prototype
%based rules (P-rules) \cite{Grudz-P-rules}. P-rules tends to represent knowledge as set
%of prototypes with appropriate similarity metric, and an inference system.\\
%Unfortunately at the moment P-rules doesn't have any strong mathematical theory, and this
%problem is still evaluated, but many of P-rules systems (depending on similarity metrics)
%can be directly transformed to well mathematically described F-rules, and this topic will
%be discussed in chapter \ref{chap:P2F-rules}
%
%
%
%\section{Reguły prototypowe w stosunku do innych metod}
%The most popular inference system based on reference examples is case based reasoning (CBR). This
%approach allow for simple analysis of systems decision on particular input example through
%reasoning based on closest case or cases to its input (nearest neighbor approach). However real
%applications of CBR usually lead to large number of stored cases, and their number usually increase
%during system exploitation while new cases are added to the systems memory. This is both the source
%of strength and many problems and weaknesses of CBR approach. On the one hand CBR systems are very
%powerful specially in precedence problems like common low or some medical applications but on the
%other hand CBR has general low transparency, what makes CBR useless for data mining application,
%where system transparency and comprehension is one of major aims. Another important problem of CBR
%systems is computational cost and memory requirements, where large number of stored cases extend
%inference speed. However this problem can be solved by Kd-tree \cite{KDTree}algorithm or classical
%decision trees like C4.5, which are used for cases indexing and selecting \cite{Plaza-CBR}.\\
%Problem of system transparency usually is solved by logical rules, however if number of obtained
%rules increase then the simplicity of model decrease, in other words transparency is inverse
%proportion to the rules number. Before fuzzy logic and F-rules, rules extraction processes used to
%base on classical - crisp logical rules (C-rules), which in applications to real world problems may
%lead to huge set of useless rules with week generalization and small intelligible. The simplest
%example of this problem describes fig. \ref{fi:CrispRulesProb}.a%
%
%
%
%where for decision border reconstruction large number of C-rules is required, moreover obtained by
%the system shape of classification border is far from Bayesian optimal decision
%\ref{fi:CrispRulesProb}.b. There are two possible ways to build optimal rule-based system solving
%described earlier example - via F-rules and P-rules both with just 2 rules. \\
%Main differences between P and F-rules drive from different interpretation and different
%meaning of each of this rules. This topic will be deeply considered in the chapter
%\ref{chap:P2F-rules}, however it has to be noticed that P-rules looks more general:
%\begin{itemize}
%    \item Many of popular distance functions cannot be decomposed
%    into equivalent membership functions
%    \item Probabilistic and heterogeneous distance functions allow
%    operations on all type of attributes
%    \item P-rules may be interpreted using both cases or instances approach and
%     using logical paradigms as in fuzzy logic
%    \item Unlike to P-rules, F-rules assume attribute independence while usually
%    this assumption is not valid
%\end{itemize}
%In the background of F-rules stand linguistic interpretation usually described as
%adjectives which describes values of particular attributes, like temperature: small,
%medium, high, while the background of P-rules is constituted by a set of reference
%examples (vectors) which can be understood as concepts. Linguistic interpretation of
%F-rules is noticed as their strength, however on the other hand it bounds itself, while
%obtained rules are strongly context dependent, while representing data as concepts like
%prototypes is context independent. An example of this problem is representation of
%variable {\it humans hight} which in context of teenagers and  adults has different
%membership functions representation of the same term {\it tall}. In P-rules such
%prototype representation is not changed but linguistic interpretation can be dynamically
%changed according to temporal situation or
%context. \\
%Another strength of P-rules is attribute type independence. In many real world problems
%structure of data consist of different types of attributes like discrete, symbolic,
%nominal or linear what makes the model optimization much harder. Many popular data mining
%models can't handle this problem, requiring previous attribute transformation to common
%feature type. This leads to sequential data transformation where each transformation
%module bring its own variance increasing overall model variance. This problem specially
%concern F-rules where most of fuzzy data mining tools require linear attributes, while in
%the literature it's possible to find different distance functions which allow
%calculations of any type of attributes, what is used in P-rules.\\
%

%-------------------------END Introduction ------------------------

%\section{Measures of Classification and Generalization Quality}
%ACC, BACC, Resubstitution, ROC, Confusion Matrix, CV, Bootstrap
%
%\be \label{eq:ErrRate} %
%err=\frac{m^{err}}{m} %
%\ee
%
%\be \label{eq:ACC}%
%acc=1-err
% \ee
%
%\be \label{eq:BER}%
%ber=\mathop{mean}\limits_{i=1\ldots c}\left({\frac{m_i^{err}}{m_i}}\right) %
%\ee
%
%\be \label{eq:BACC}%
%bacc=1-ber%
% \ee
