Your explanation is not entirely clear, and it would be useful to have a complete output example. Although you write that "I mean data(2,2)=2, so it should be replaced by map(2,2)", you do not explain why this is so: is it because they both are indexed at (2,2), or do the indices map(2,2) use the value of the element data(2,2)?
In any case it is not required to use arrayfun when indexing will do the job perfectly. Perhaps you want something like this, where I used the values of the cell array elements as indices into map:
X = { 1, 1, 1,45.7600;...
1, 2, 2,52.9200;...
2, 1, 2,59.7600;...
2, 2, 1,50.4200;...
98.6800, 105.5200, 96.1800, 0;...
110.1800, 103.3400, 112.6800, 0;...
27.8280, 1, 57.2868, 0;...
161.4476,4.0522e+03,1.6211e+04, 1.1881};
R = 1:4;
C = 1:3;
M = cell2mat(X(R,C));
map = {'10 min','2.2g','5.0kg';...
'20 min','3.0g','7.0kg'};
Z = map(M);
X(R,C) = Z;
Of course linear indexing in MATLAB is column-wise, so to access all six values of map the original cell array would need to have values up to six. Currently the cell array only has values 1 and 2, so with the given values it only accesses those two elements of map's first column.
