P% ( ) α to point a point inQ% ( ) α }.The fuzzy line segment Lpq % is: 
µ ( ) ( ) *xy L xy* , sup ( : ( , ) *pq l* = ∈Ω { α α( )} % .now let 1,..., L Ln % % be fuzzy line segments from 

$\mu\left(\left(x,y\right)\left|\tilde{L}_{pq}\right.\right)=\sup\left\{\left(x,y\right)\left|\tilde{\Sigma}\right.\right\}=\max_{1\leq i\leq n}\left\{\mu\left(x,y\right)\left|\tilde{L}_{i}\right.\right\}$.  
Mentioned definitions on fuzzy polygons may be as solution to detection of distances of blocks and determination of real fuzzy area and perimeter of blocks. Fuzzy distance between two blocks, and using possibility theory, as a real brain's perception, can be summarized in "new contact detection algorithm". See (Owladeghaffari, unpublished). Fuzzy half spaces by applying fuzzy line and possibility ranking eliminate difficulty in definition of half planes and spaces. 

## 4 Direct Fuzzy Block Theory

Let Inequality equations system,{ } 1,..., i i i n L D =
% % ≥ present set of fuzzy half planes or non crisp boundary of blocks in 2-D. by referring to fuzzy line (section 3.2) and the strict exceedence possibility (section 3.1): 

⎧ ⎫ ⎧ ⎪ ⎪ ⎪⎨ ⎪⎩ 11 1 1 % % Poss L D ( ) ≥ = δ 0 . . . 1 Poss{ } 1,..., i i i n L D = % % ≥ = ; with conditions  ⎨ ⎬ ⎪ ⎪ ⎧ ⎪⎨ ⎪ ⎩ ⎭ ⎩ ( ) % % Poss L D ≥ = δ 0 ii i

In witch, Li
% and Di
% are real fuzzy line and fuzzy number, respectively. For a block obtained from intersection of half-plans: fuzzy joint block = { } 1,..., i i i n L D =
% % ≥ .so, 

$\bigcap\limits_{i=1}^{n}\left\{Pos\left(\tilde{L}_{i}\geq\tilde{D}_{i}\right)\right\}\leq Min\left\{Pos\left(\tilde{L}_{i}\geq\tilde{D}_{i}\right)\right\}\Rightarrow\approx Min\left\{Pos\left(\tilde{L}_{i}\geq\tilde{D}_{i}\right)\right\}=$ possibility of 
i n joint block (PJB). In fact, we select upper limitation in inequality. (See chapter 7, in Dubois &Prade, 2000). In Goodman-Shi terminology, and associated with mentioned theories, block pyramid has been defined as: 