...36, India e-mail: vasantha@iitm.ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Department of Mathematics University of New Mex... ... e-mail: vasantha@iitm.ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Department of Mathematics University of New Mexico Gallu... ...Sciences, Sofia, Bulgaria. Copyright 2005 by W. B. Vasantha Kandasamy and Florentin Smarandache Layout by Kama Kandasamy. Cover design by ... ...ofia, Bulgaria. Copyright 2005 by W. B. Vasantha Kandasamy and Florentin Smarandache Layout by Kama Kandasamy. Cover design by Meena Kanda... ...e world who are bravely battling the AIDS epidemic. W.B.VASANTHA KANDASAMY FLORENTIN SMARANDACHE 7 Chapter One INTRODUCTION ... ...e space. We further assume no intermediate relation exists within the domain elements or node and the range space elements. The number of elements ... ... of elements in the range space need not in general be equal to the number of elements in the domain space. Thus throughout this section we assume t... ...mediate relations exist within the domain and the range spaces. The number of elements or nodes in the range space need not be equal to the number o... ...eory, fuzzy groups, and applications of fuzzy theory of the problems faced in chemical industries and cement industries. Currently, six Ph.D. schola...

... W. B. VASANTHA KANDASAMY FLORENTIN SMARANDACHE FUZZY RELATIONAL MAPS AND NEUTROSOPHIC... ...600036, India e-mail: vasantha@iitm.ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Department of Mathematics University of New M... ...Mysore, Karnataka, India. Copyright 2004 by W. B. Vasantha Kandasamy and Florentin Smarandache Layout by Kama Kandasamy. Cover design by... ...nal products 164 Chapter Two SOME APPLICATIONS OF FRE 2.1 Use of FRE in Chemical Engineering 167 2.2 New FRE to estimate the peak hours o... ... motor-drive system 197 2.10 Application of genetic algorithm to problems in chemical industries 199 2.11 Semantics of implication operators ... ... has 10 sections: we elaborately give the applications of FRE in flow rates in chemical industry problems, preference and determination of peak hou... ...m X to Y, binary relations R(X, Y) may assign to each element of X two or more elements of Y. Some basic operations on functions such as the invers... ...n that each element of Y has to an element of X is equal to the degree of that elements membership in the range of R. In addition, the height of a ... ...responding to one set is distinguished from nodes representing the other set. Elements of X × Y with non-zero membership grades in R(X, Y) are rep...