ABSTRACT
Mathematics has been used in life ever since the very existence of human beings. Mathematical model involving fuzzy systems has become a powerful tool for better modeling and control of processes in different fields of medical science. Conventional epidemics transmission models are used to interpret the spread of epidemic without immunity. There are major communicable diseases, which can be treated with genetically based intrusions. To understand the cure of these diseases, it is equally important to understand the molecular evolution as it reflects the study of inherent dissipative processes that are complicated in nature, particularly for systems where genetic properties play a noteworthy role. While analyzing the complex networks and description of evolutionary processes, concepts such as neighborhood, similarity, connectedness, or continuity of change appear spontaneously. Characteristically, these concepts are topological in nature. The principal sources for natural selection acting on genetic disparity originate from mutation and/or recombination. The recombination can be treated as a binary operator R from C × C to power set of C, P(C) on the set of all chromosomes C. If a and b are two chromosomes, then the recombination set R(a, b) is composed of those chromosomes which are attained by recombining a and b with the help of a certain class of crossover operators. The recombination space can be studied in fuzzy situation by allotting different possibilities of occurrence to each recombinant. Considering fuzzy setting, fuzzy pretopology, in its natural course, is generated in the set of chromosomes. In this chapter, the fuzzy topological features of the recombination space are analyzed. Various crossover models are spontaneously produced in the recombination space, and this can be structured using fuzzy pretopology. In this context, we explore the property of connectedness in fuzzy recombination space in unequal crossover model. Besides that, we examine the property of compactness and separation axioms for the same model.
