...S AND NEUTROSOPHIC RELATIONAL MAPS W. B. Vasantha Kandasamy Department of Mathematics Indian Institute of Technology, Madras Chennai – 600... ...tm.ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Department of Mathematics University of New Mexico Gallup, NM 87301, USA e-ma... ...their properties It is well known fact that binary relations are generalized mathematical functions. Contrary to functions from X to Y, binary re... ...s R(X, Y) may assign to each element of X two or more elements of Y. Some basic operations on functions such as the inverse and composition are appl... ...of genetic algorithms cannot provide measurement for the performance empirical computational testing is necessary. Test problems for computational ... ...ominated criterion vectors is called the non-dominated set. In the absence of a mathematical specification of the decision maker’s utility function,... ...icient set. A system of FRE may be manipulated in a way such that the required computational effort of the proposed genetic algorithm is reduced. D... ...n [6] tell us whether a fuzzy relation equation has solution? No. Due to the complexity in fact these problems exist not only in [6] but also in ... ...lties of saying anything meaningful about a system increase enormously with its complexity. The vogue for, and success of, statistical methods are e...

...The aim of this book is two fold. At the outset the book gives most of the available literature about Fuzzy Relational Equations (FREs) and its properties for there is no book that solely caters to FREs and its applications. Though w...