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...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... ... ik ] ° [q kj ] where r ij = k max min (p ik q kj ). Observe that the same elements of P and Q are used in the calculation of R as would be use... ... give several of the applications of fuzzy relational equations in studies like chemical engineering, transportation, medicine etc. The fuzzy relati... ... applied to special problem. [81, 85, 100-101,111, 114] 2.1 Use of FRE in chemical engineering The use of fuzzy relational equations (FRE) f...