International Journal of Advanced Computer and Mathematical Sciences ISSN 2230-9624. Vol 2, Issue 3, 2011, pp 117-125 http://bipublication.com FUZZY PROXIMITY IN PHENOTYPE SPACE Tazid. Ali, Chandra Kanta Phukan Department of mathematics, Dibrugarh University. Dibrugarh, Assam, India ABSTRACT: Evolutionary change in biology is the change in genetic material of a population of organism, through successive generation. The course of biological evolution cannot be understood without the dichotomy of genotype-phenotype. The mapping  from genotype to phenotype hence lies at the heart of any meaningful theory of evolution. Different types of generalized topologies (pretopology, peritopology etc); are being used to model the genotype and phenotype spaces. In this paper we have attempted to study the model using fuzzy topology. We have also discussed the continuity of evolutionary map in this setting. Keywords: Genotype, Phenotype, Evolutionary map, Fuzzy topology. 2010, Mathematical subject classification, Primary 92C40, 92D15, 92D20; Secondary 54A40. 54A05, 1. INTRODUCTION: Evolutionary biology concerns the extent to which the history of life has proceeded gradually or has been punctuated by discontinuous transition at the level of phenotypes. To distinguish continuous from discontinuous evolutionary changes, a relation of nearness between the phenotypes is needed. Genotype and phenotype are two aspects of same molecule, genotype is internally coded, inheritable information possessed by all living organisms, while the phenotype is the physical realization of that information. For example, the collection of genes responsible for eye color in a particular individual is a genotype. The observable eye coloration in the individual is the corresponding phenotype. The idea of phenotype demonstrated on the ribonucleic acid (RNA) is ideally suited to explore the concepts of evolution in a wide context and it is also simple in computational matter. The nucleotide chain that is unfolded is called the genotype (primary structure) for the molecule, composed of letters A, G, C and U namely adenine ,guanine, cytosine and uracil respectively, and the associated bonding diagram of it is called phenotype. It is also referred to as the RNA shape or secondary structure. All the secondary structures used in the discussion is of minimum free energy with fixed length. There is a unique RNA shape which is associated to each genotype sequence; as a result of this we get the canonical map from the set of genotype to phenotype. This canonical map in not one-to-one since, multiple genotype sequences can result in the same RNA shape. Fontana, Stadler, Stadler, and Wagner argue that “continuous” changes in the RNA sequences can lead to apparent jumps at the phenotypic level, so that evolution is not solely influenced by natural selection and genetic drift, but is also directed by internal dynamics[12].If