% Math
\DeclareMathAlphabet{\mathbfit}{OT1}{cmr}{bx}{it}
\newcommand{\Vektor}{\mathbfit}
\newcommand{\Matrix}{\mathbfit}
\newcommand{\EM}{\Matrix{E}}
\newcommand{\Menge}{\mathcal}
\newcommand{\Vgr}{\boldsymbol}

%% Rating Index
\newcommand{\JI}{J}          % Rating Index
\newcommand{\JRI}{J_{RI}}    % Relevance Index
\newcommand{\JRHR}{J_{RHR}}  % Relevant Hitrate
\newcommand{\JCHR}{J_{CHR}}  % Confidente Trefferquote
\newcommand{\JMVB}{J_{MVB}}  % Meanvalue-based Index
\newcommand{\JVBI}{J_{VBI}}  % Variance-based Index
\newcommand{\JNHR}{J_{NHR}}  % Nomralized Hitrate
\newcommand{\JIRI}{J_{IRI}}  % Incrementel Relevance Index
\newcommand{\p}{p}           % Probability
\newcommand{\I}{I}           % Confidence Interval

%% searches
%\newcommand{\CS}{CS}        % complete search
%\newcommand{\CSS}{CSS}      % complete search shortened
%\newcommand{\TOCS}{TOCS}    % tree-oriented complete search
%\newcommand{\MC}{MC}        % monte-carlo search
%\newcommand{\ES}{ES}        % evolutionary search
%\newcommand{\MBES}{MBES}    % metric based evolutionary search
%\newcommand{\HESC}{HESC}    % hybrid evolutionary search concept
%\newcommand{\MDS}{MDS}      % minimal data support restriction
%\newcommand{\SLS}{SLS}      % stepwise local search
%\newcommand{\CSOS}{CSOS}
%\newcommand{\tgen}{t_{gen}} % Generierungszeit
%\newcommand{\tanly}{t_{anly}} % Analysezeit
%\newcommand{\tgenEA}{\tgen^{135}} % Generierungszeit

% variables
\newcommand{\X}{X}              % input variable
\newcommand{\x}{x}              % crisp input value
\newcommand{\M}{M}              % input feature
\newcommand{\m}{m}              % crisp feature value
\newcommand{\Vx}{\Vektor{x}}    % input vector
\newcommand{\VX}{\Vektor{X}}    % input variable vector
\newcommand{\Vm}{\Vektor{m}}    % input feature value vector
\newcommand{\VM}{\Vektor{M}}    % input feature vector
\newcommand{\Vy}{\Vektor{y}}    % output vector
\newcommand{\Y}{Y}              % system output variable
\newcommand{\Ym}{\hat{\Y}}      % model output variable
\newcommand{\y}{y}              % crisp system output value
\newcommand{\ym}{\hat{\y}}      % crisp model output value
\newcommand{\yD}{y_D}           % defuzzified output value
\newcommand{\msf}{\mu}          % membership function
\newcommand{\dt}{d}             % data tupel
\newcommand{\Vd}{\Vektor{d}}    % data point
\newcommand{\sd}{\sigma}        % standard deviation
\newcommand{\pk}{p}             % premise
\newcommand{\SC}{S_c}           % Intervallanzahl
\newcommand{\ab}{\triangle}           % Abstand
\newcommand{\st}{s}             % split point
\newcommand{\Vst}{\Vektor{s}}   % vector of split points
\newcommand{\Hyp}{Q}            % hyperquader
\newcommand{\Ind}{\Vektor{Ind}}   % vector of split points
\newcommand{\Vmut}{{\Vgr{\rho}}}% Mutationsvektor


% reductions
\newcommand{\OCR}{\mbox{OCR}}      % Optimizing Conflict Reduction

%% build up a rule
\newcommand{\cmax}{c_{max}}         % maximum combination depth
\newcommand{\tmax}{t_{max}}         % maximum time depth
\newcommand{\cd}{c}                 % combination depth
\newcommand{\LE}{A}                 % linguistic expression
%\newcommand{\LEn}{\tilde\LE}        % nummerierter ling. Ausdruck
%\newcommand{\If}{IF }
\newcommand{\WENN}{WENN}
\newcommand{\AND}{\mbox{AND }}
\newcommand{\UND}{\mbox{UND }}
\newcommand{\NOT}{\mbox{NOT }}
\newcommand{\THEN}{\mbox{THEN }}
\newcommand{\DANN}{DANN}
\newcommand{\prem}{P}               % premise
\newcommand{\conc}{C}               % conclusion
%\newcommand{\prempart}[1]{\mbox{\If}#1}                    % premise part
%\newcommand{\concpart}[1]{\mbox{\THEN}#1\mbox{}}           % conclusion part
%\newcommand{\Rule}[2]{\prempart{#1}\mbox{ }\concpart{#2}}  % rule
\newcommand{\PremTeil}[1]{\mbox{\WENN}\; #1}               % premise part
\newcommand{\praemissenteil}[1]{\mbox{\WENN}\;#1}
\newcommand{\ConcTeil}[1]{\mbox{\DANN}\; #1}               % conclusion part
\newcommand{\FuncTeil}[1]{\mbox{\DANN}\; #1}               % conclusion part
\newcommand{\Regel}[2]{\PremTeil{#1}\;\; \ConcTeil{#2}}    % rule
\newcommand{\RegelTSK}[2]{\PremTeil{#1}\;\; \FuncTeil{#2}} % rule
%\newcommand{\rl}{r}                                        % rule
%\newcommand{\RS}{{\cal R}}                                 % rule set

% TSK stuff

%\newcommand{\FS}{f_{S}}
%\newcommand{\ZFY}[1]{\mu_{Y,c_#1}}
%\newcommand{\FSY}[1]{\FS(\ZFY{#1})}
\newcommand{\TSK}{Takagi--Sugeno}
\newcommand{\Mam}{Mamdani}
\newcommand{\FR}{Fuzzy--ROSA}




% Examples Abriviations
\newcommand{\HE}{HE}
\newcommand{\MGT}{MGT}
\newcommand{\MAE}{$\overline{\mbox{MAE}}$}

% Sets
\newcommand{\SD}{{\mathcal D}}                         % set of all data points
\newcommand{\SX}{{\mathcal X}}                         % set of all input data vectors
\newcommand{\SY}{{\mathcal Y}}                         % set of all output data points
\newcommand{\SDL}{{\mathcal D}_L}                      % set of learning data points
\newcommand{\SDV}{{\mathcal D}_V}                      % set of validation data points
\newcommand{\SDin}{{\mathcal D}_{\prem}}               % set of data points in prem
\newcommand{\SDiin}{{\mathcal D}_{\prem,i}}            % set of data points in prem for an variable
\newcommand{\SDinY}{{\mathcal D}_{\prem \wedge \conc}} % set data points in prem and conc
\newcommand{\s}{\mathcal F}                            % Fuzzy set
\newcommand{\ls}{\mathcal L}                           % linguistic set
\newcommand{\SR}{\mathcal R}                           % set of rules
\newcommand{\SM}{\mathcal M}                           % set of relevant input variables
\newcommand{\Nei}{\mathcal N}                          % neighborhood function
\newcommand{\Rek}{\mathcal E}                        % reconstruktion function
\newcommand{\NeiG}{\mathcal Z}                         % global neighborhood function
\newcommand{\Ss}{\mathcal S}                           % set of splitpoints
\newcommand{\SHyp}{\mathcal Q}                          % set of hyperquader

\newcommand{\SInd}{{\mathcal P}}                       % set of all individuums


\newcommand{\ntt}{\normalfont\ttfamily}
\newcommand{\fn}[1]{{\protect\ntt#1}}
\newcommand{\cn}[1]{{\protect\ntt\bslash#1}}
\newcommand{\pkg}[1]{{\protect\ntt#1}}
\newcommand{\env}[1]{{\protect\ntt#1}}
%\hfuzz1pc

\newcommand{\keyw}[1]{{\bf #1}}
\newcommand{\code}[1]{{\texttt #1}}
\newcommand{\tif}[1]{\textrm {#1}}
%\newcommand{\mbf}[1]{\mathbf{#1}}
\newcommand{\mc}[1]{\mathcal{#1}}
\newcommand{\mbf}[1]{\textbf{\textit{#1}}}

\newcommand{\ML}{\textsc{MATLAB}}



% Number of...
\newcommand{\NR}{R}                 % number of rules
\newcommand{\iR}{r}                 % index of rules
%\newcommand{\NRf}{\NR_f}            % number of found rules for prob. searches
\newcommand{\ND}{N}                 % number of data sets
\newcommand{\iD}{j}                 % index of data sets
%\newcommand{\NDL}{D_L}              % number of learning data sets
%\newcommand{\NDV}{D_V}              % number of validation data sets
%\newcommand{\NCD}{\ND_{nc}}         % number of not covered data sets
\newcommand{\Nls}{L}                % number of linguistic sets per Variable
\newcommand{\ils}{j}                % index  of linguistic sets per Variable
\newcommand{\NE}{E}                 % number of linguistic expressions
\newcommand{\iE}{e}                 % index  of linguistic expressions
\newcommand{\NV}{n}                 % number of all input variables
\newcommand{\iV}{i}                 % index  of all input variables
\newcommand{\iM}{i}                 % index  of all selected features
\newcommand{\sit}{j}                  % Zeitpunkt
\newcommand{\NVsel}{q}              % number of the selected input variables
\newcommand{\iVsel}{i}              % index  of the selected input variables
\newcommand{\NDS}{\ND_{sup}}        % datasupport


%\newcommand{\NDin}{\ND_{\prem}}     % number of data sets with p_k(\Vektor{x}_\ND)>0
%\newcommand{\NDinY}{\ND_{\prem \wedge \conc}} % number of data sets with p_k(\Vektor{x}_d)>0 \wedge \mu_{Y,c_k}(y_d)>0


% Errors
\newcommand{\e}{\epsilon}                  % Modellation error
\newcommand{\Evali}{\e_{vali}}       % Error on validation data
\newcommand{\Elearn}{\e_{learn}}     % Error on learning data



% Combinatorial Stuff

% hypotheses
%\newcommand{\NHTot}{H_{tot}}      % total number of hypotheses
%\newcommand{\NHPos}{H_{pos}}      % number of possible hypotheses
%\newcommand{\NHTest}{H_{tst}}    % number of tested hypotheses
%\newcommand{\NHGen}{H_{gen}}      % number of generated hypothese
%\newcommand{\RateEffGenH}{r_H}    % rate tested/generated hypothese in %
%\newcommand{\NHRestr}{H_{res}}

% possible premises
%\newcommand{\PMaxPos}{\prem_{tot}}
%\newcommand{\PMaxPosC}{\PMaxPos^\cd}
%\newcommand{\PTot}{\prem_{pos}}
%\newcommand{\PPos}{\prem_{pos}}
%\newcommand{\PPosC}{\PPos^\cd}
%\newcommand{\PPosTot}{\PPos}
%\newcommand{\PPosDatC}{\prem_{dat}^\cd}
%\newcommand{\PPosDat}{\prem_{dat}}
%\newcommand{\PTest}{\prem_{tst}}
%\newcommand{\PRestr}{\prem_{res}}

% supported premises
%\newcommand{\PSup}{\prem_{sup}}
%\newcommand{\PSupC}{\PSup^\cd}
%\newcommand{\PSupTot}{\PSup}
%\newcommand{\PSupOneDatC}{\prem_{max}^{c}}
%\newcommand{\Ddensity}{\varrho_{dat}}


% saved hypotheses
%\newcommand{\PSave}{\prem_{sve}}
%\newcommand{\PSaveC}{\PSave^\cd}
%\newcommand{\PSaveTot}{\bar\PSave}

% generated premises
%\newcommand{\PGen}{\prem_{gen}}
%\newcommand{\PGenC}{\PGen^\cd}
%\newcommand{\PGenTot}{\bar\PGen}

%


% More stuff
%
%\newcommand{\HR}{H_\RS}     % Entropie Rule Set
%\newcommand{\RR}{H^{*}_\RS} % Redundancy Rule Set
%\newcommand{\gen}{\geq_g}   % more general
%\newcommand{\spez}{\leq_g}  % more special
%\newcommand{\K}{K}          % Consistence
%\newcommand{\IK}{\K^*}      % Inconsistence
%\newcommand{\IS}{I}         % Input Situation
%\newcommand{\Inull}{{\cal\I}_0}
%\newcommand{\Incv}{{\cal\IS}^*}
%\newcommand{\Vol}{\mbox{\em Vol}}
