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Journal of Engineering and Applied Sciences

Fuzzy Logic Application to Coaxial and Non-Coaxial Components of Shear Strength of Soils
J. Rajaraman, K. Thiruvenkatasamy and S. Narasimha Rao

Abstract: Fuzziness is explored as an alternative to randomness for describing uncertainty. The new sets as points geometric view of fuzzy sets is developed. This view identifies a fuzzy set with a point in a unit hyper cube and a non-fuzzy set with a vertex of the cube. In fuzzy logic a crisp set is a set in which all members match the class concept and the class boundaries are sharp. The degree to which an individual observation z is a member of the set is expressed by the membership function F which can take the value of 0 or 1 for Boolean sets. In fuzzy logic the membership function is a number in the range of 0.1 with 0 representing non-membership of the set and 1 representing full membership of the set. In fuzzy sets, the grade of membership is reflected in terms of a scale that can fluctuate continuously between 0 and 1. Normally, we can visualize the membership function by having x axis with the element of the fuzzy set and y axis with the value of the membership function. There are better ways of visualization. AKosko cube@ is the starting point. Kosko uses the term@ fit@ values to designate the value of the membership function. This is to contrast the term Abit@ which is used for binary values the f stands for Afuzzy@. To achieve better results the fuzzy power set F(2x) is examined. Thus, the 2x is the set of all sub-sets of x and x is our universe of discourse. The set of all sub-sets equals the unit hyper cube In = [0.1]n. A two dimensional version of Kosko cube is considered. In Geology/sediments/soil samples usually consists of clay and sand in ideal conditions. If p is percentage of clay then (1-p) is % of sand. Clay properties relate to pure shear or cohesion or coaxial shear component of the sample. Similarly the sand % represents simple shear or friction or non-coaxial shear component. Fuzzy logic suits this problem when % are expressed in the range 0, 0.1, 0.2, etc., up to 1.0. The membership functions in the combination of coaxial and non-coaxial shear component is represented in kosko cube. Taking Skempton's experimental data (clay+sand) points distributed in quadrants 1-4 inside the cube as points in are interpreted through simple geological processes.

How to cite this article
J. Rajaraman, K. Thiruvenkatasamy and S. Narasimha Rao, 2018. Fuzzy Logic Application to Coaxial and Non-Coaxial Components of Shear Strength of Soils. Journal of Engineering and Applied Sciences, 13: 9431-9437.

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