Toward Fuzzy block theory

This study, fundamentals of fuzzy block theory, and its application in assessment of stability in underground openings, has surveyed. Using fuzzy topics and inserting them in to key block theory, in two ways, fundamentals of fuzzy block theory has been presented. In indirect combining, by coupling of adaptive Neuro Fuzzy Inference System (NFIS) and classic block theory, we could extract possible damage parts around a tunnel. In direct solution, some principles of block theory, by means of different fuzzy facets theory, were rewritten. 2 INDIRECT METHOD: PARRLILIZATON OF KEY BLOCK THEORY Figure (1) summaries two branches of uncertainty .Modern uncertainty theory has been extended by Lotfi..A.Zadeh (Zadeh.1965):”fuzzy set theory”. Fuzzy logic (FL) is essentially coextension with fuzzy set theory and in narrow sense; fuzzy logic is logical system which is aimed at a formalization of modes of reasoning which are approximate rather than exact. FL in wide sense has four principal facets: The logical facet, FL/L; the set-theoretic facet (FL/S), the relational facet (FL/R) and the epistemic facet FL/E. (Dubois&Prade.2000) Figure1.schamatizatio of the uncertainty theory (Ayyub& Gupta, 1994-Zadeh, 2005) 2.1 An algorithm to combining KBT &FIS Figure 3 shows a combining of KBT (key block theory) and TSK type inference system. One way to extension of this algorithm, can be carried out using multiple inputs/outputs systems, for example, CANFIS or MANFIS: coactive neuro-fuzzy inference systems; multiple ANFIS (Adaptive Neuro Fuzzy Inference System), respectively. (Jang etal.1997). In this study input parameters were dived in two facets :( 1) Fixed parameters (2) changeable parameters. Fixed parameters can be taken in such as shape of tunnel, unit weight of rock, some properties of joints....Changeable parameters must be inserted in different values, namely, in random data set, for example: joint properties, in situ stresses...After producing of KBT output, input data (changeable) and outputs of KBT must be rearranged. So these data sets must be normalized in defined range (for example in [-1, 1] -Step 1). Then normalized S.F, obtained from KBT, and mentioned data sets are gotten in ANFIS algorithm. In this step (2), the rules in if-then shape between input and output variables are obtained. Thus new predictions on S.F for new input can be performed. Uncertainty theory Classic 1. set theory (interval analysis) 2. Probability theory Modern 1. Fuzzy set theory 2. Possibility theory 3. Evidence theory ... 4-generlized uncertainty theory (Zadeh, 2005) Figure3. A combined algorithm on KBT, TSK Some results of the proposed algorithm can be highlighted as follows: 1-Detection of membership functions (MFs) for any input and output (figure 4) 2-The dominated rules in if-then format between inputs and output (safety factor for any block) 3-Possible damage parts around tunnel. In similar conditions; a compression between DDA (discontinuous deformation analysis)-MacLaughlin&Sitar.1995and results of mentioned algorithm has been accomplished. See figure5. Figure4. MFs for phi (φ ) and volume of blocks, vertical axis show MFs degree. (a) Input parameters