 (b) 

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In this analysis, inputs were joint and tunnel properties (such: dip, dip directions-trend, plunge,φ ) and volume of block (all of random data sets were 283).Because of small samples 
(data sets), applying of results in practical may not be correct, but mentioned results give an overview about stability of possible blocks around tunnel. 

## 3 Remarks On Possibilty Theory And Fuzzy Geometry 3.1 Possibility Theory (Epistemic Facet Of Fuzzy Logic)

The concept of possibility proposed by Zadeh forms one of the most useful foundations in fuzzy set theory. Possibility measure can be defined either based on confidence measure or based on fuzzy set. The former gives the connection between possibility measure and evidence theory and the later gives the connection between possibility and fuzzy membership function. 

Evidence theory is known as upper and lower probability. The advantage based on fuzzy set is that the approach offers easy means to obtain numerical values of the representation while the confidence approach is based on a set of basic axioms. One of the central concepts in possibility theory is possibility distribution, which serves the same purpose in possibility theory as probability distribution in probability theory. Let F be a fuzzy subset of universe of discourse U, 
which is characterized by its membership function µ F , with the grade of membership ( ) F µ u . 

Let X be a variable taking on values in U and let F act as a fuzzy restriction, R(x),associated with X. then the proposition "x is F"(R(x)=F),associates a possibility distribution function associated with X , Πx ,can be defined to be numerically equal to the membership function of F 
,that is, π x F ≡ µ where π x represents the possibility distribution function of Πx .mathematically, Poss(X is u X is F) = µ F (u),u∈U, which is conditional possibility expression parallel to the conditional probability expression. 

Now, let A be a non-fuzzy subset of U and π x be the possibility distribution function ofΠx . 

Then the possibility measure,Π( ) A , of A is defined as a number in the interval [0,1] and is given by: Π( ) A = sup ( ) *uA x* π u .The possibility measure can also be interpreted as the possibility that the value of X belongs to A, or, Poss(x∈A) = Π( ) A =sup ( ) *uA x* π u =sup ( ) *uA F* µ u ∈ . 

If, A is a fuzzy subset of U, then the possibility measure of A is defined by: 
Poss{x is A} =Π( ) A =
sup min ( ), ( ) A x u u u U
⎡ ⎤ µ π ⎣ ⎦ ∈
A good discussion about possibility and probability can be found in (Dubois & Prade 
(edit).2000).in section (4), we will use the ranking or compression of fuzzy numbers, based on 