1991) has often proved to be an excellent mathematical tool for the analysis of a vague description of object. The adjective vague referring to the quality of information means inconsistency, or ambiguity which follows from information granulation. The rough set philosophy is based on the assumption that with every object of the universe there is associated a certain amount of information, expressed by means of some attributes used for object description. The indiscernibility relation (similarity), which is a mathematical basis of the rough set theory, induces a partition of the universe in to blocks of indiscernible objects, called elementary sets, which can be used to build knowledge about a real or abstract world. Precise condition rules can be extracted from a discernibility matrix. 

An information system is a pair S=< U, A >, where U is a nonempty finite set called the universe and A is a nonempty finite set of attributes. An attribute a can be regarded as a function from the domain U to some value set Va. An information system can be represented as an attribute-value table, in which rows are labeled by objects of the universe and columns by attributes. With every subset of attributes B⊆ A, one can easily associate an equivalence relation B I on U : 

$I_{B}=\{(x,y)\in U:\mbox{\it for every}\,a\in B,a(x)=a(y)\}$
Then, $I_{B}=\bigcap_{a\in B}I_{a}$.  If $X\subseteq U$,the sets $\left\{x\in U:\left[x\right]_{B}\subseteq X\right\}$ and $\left\{x\in U:\left[x\right]_{B}\bigcap X\neq\varphi\right\}$, where $\left[x\right]_{B}$ denotes the equivalence class of the object $x\in U$ relative to $\left[\mathbf{B}\right]_{B}$ are 
called the B-lower and the B-upper approximation of X in S and denoted by BX and BX , respectively. It may be observed that BX is the greatest B-definable set contained in X and BX is the smallest Bdefinable set containing X To constitute reducts of the system, it will be necessary to obtain irreducible but essential parts of the knowledge encoded by the given information system. So one is, in effect, looking for the maximal sets of attributes taken from the initial set ( ) *A,say* that induce the same partition on the domain as A. In other words, the essence of the information remains intact, and superfluous attributes are removed. Consider U={x1, x2, …,xn} and A={a1, a2, …,an} in the information system S=< U, A >. By the discernibility matrix M(S) of S is meant an n*n matrix such that cij = {a ∈ A :a( xi ) ≠ a( x j )}
A discernibilty function fs is a function of m Boolean variables a1,…,am corresponding to attributes a1,…,am ,respectively, and defined as follows: 
fs( a1 *,...,am* ) = ∧{∨ ( cij ):1≤ i, j ≤ n, j p *i,cij* ≠ ϕ}
where ∨(cij ) is the disjunction of all variables with a. 

ij a ∈c (Pal et al, 2004). With such discriminant matrix the appropriate rules are elicited. 

The existing induction algorithms use one of the following strategies: 
(a) Generation of a minimal set of rules covering all objects from a decision table; 
(b) Generation of an exhaustive set of rules consisting of all possible rules for a decision table; 
(c) Generation of a set of `strong' decision rules, even partly discriminant, covering relatively many objects each but not necessarily all objects from the decision table (Greco et al, 2001). In this study we use first approach in combining with initial crisp granules, adaptively. 

## 3 The Proposed Method Based On Somrst System And Hard Computing Methods

Figure 2, shows a general procedure, in which the 

![0_image_0.png](0_image_0.png) information granulation theory accompanies by a predefined project based rock engineering design. After determining of constraints and the associated rock engineering regards, the initial granulation of information as well as numerical (data base) or linguistic format is accomplished. Developing of modeling instruments based on IGs, whether in independent or associated shape with hard computing methods (such fuzzy finite element, fuzzy boundary element, stochastic finite element…) are new challenges in the current discussion. 