...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...

....6: Let G(I) be a neutrosophic vector space over the field K. The number of elements in the neutrosophic basis is called the neutrosophic dimension ... ...g neutrosophic vector space over the neutrosophic field K(I). The number of elements in the strong neutrosophic basis is called the strong neutrosop... ...tinguished from the others), with point of degree at most 4 and finally the chemical problem of trees in which every point has degree 1 or 4. Jorda... ...e that Jordan did so without having any suspicion of its bearing on modern chemical doctrine. The most famous problem in graph theory and perhaps i... ...nite non empty set V = V (G) of p points. (vertex, node, junction O-simplex elements) together with a prescribed set X of q unordered pairs of disti... ...Each pair x = {u, v} of points in X is a line (edge, arc, branch, 1-simplex elements) of G and x is said to join u and v. We write x = uv and say t... ...graph is a complete graph. Thus in a tournament for every pair of distinct elements u and v either (u, v) or (v, u) but not both is an arc of D. To... ...ry, fuzzy groups, and applications of fuzzy theory of the problems faced in chemical industries and cement industries. Currently, six Ph.D. scholars...

...∪ (B 1 + B 2 ). Thus two bimatrices are added by adding the corresponding elements only when compatibility of usual matrix addition exists. ... ...dence maps that associates with each element of E i (G) an unordered pair of elements of V i (G) i = 1, 2. It is to be noted that E 1 (G 1 ) ... ...simple. A bigraph G = G 1 ∪ G 2 is bisimple if |G| = n that is number of elements in G 1 and G 2 without repetition i.e. o (G 1 ∪ G 2 ) = o(... ...ion between the health hazards the agricultural labourer suffers 94 due to chemical pollution. Let us taken the 11 attributes (P 1 , P 2 ,…, P 11... ... – Ulcer / skin ailments in legs and hands P 3 – Manuring the fields with chemical fertilizers P 4 – Vomiting P 5 – Mouth and stomach ... ...e at a fixed bipoint as the bihidden pattern. Thus manuring the field with of chemical fertilizers makes all the coordinates on except P 4 which im... ...ey may not suffer the symptom of vomiting because of manuring the field with chemical fertilizers. Now we study the effect of the attribute Head... ...ed by them due to spray of pesticides insecticides and manuring the plants by chemical fertilizers. At the first stage we take arbitrary attributes ... ...concepts. We further assume no intermediate relation exists within the domain elements or node and the range spaces elements. The number of elements...