By W. B. Vasantha Kandasamy, Florentin Smarandache, K. Ilanthenral
ISBN-10: 1599730057
ISBN-13: 9781599730059
This e-book offers the fundamental notions of fuzzy matrix conception and its purposes to uncomplicated versions. The method is non-traditional for you to allure many scholars to take advantage of this system of their study. the conventional strategy of mathematicians has conditioned scholars of sociology in one of these demeanour that they averse to utilizing mathematical instruments. Six easy sorts of fuzzy types that utilize fuzzy matrices are given. those types are detailed simply because they're time based and will also be used for statistical info. the bushy Cognitive Maps version supplies the hidden trend. Fuzzy Relational Maps version not just provides the inter-relations among units of disjoint attributes. The Bidirectional Associative stories version analyzes facts counting on the time-period whereas the bushy Associative stories version can provide the gradation of significance of every characteristic. eventually, the bushy Relational Equation version is in a position to giving an answer in the direction of the expected answer. all of the equipment are illustrated via difficult examples of specific social difficulties.
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Extra info for Elementary Fuzzy Matrix Theory and Fuzzy Models for Social Scientists
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20% in mood may have fear while meeting him. Thus we see however that this definition eventually leads us to accept all degrees of mood of his boss as in mood no matter how gloomy the boss mood is! In order to resolve this paradox the term mood may introduce vagueness by allowing some sort of gradual transition from degrees of good mood that are considered to be in mood and those that are not. This is infant precisely the basic concept of the fuzzy set, a concept that is both simple and intuitively pleasing and that forms in essence, a generalization of the classical or crisp set.
9 is a complete graph. 10 with four lines is a cycle. 10 It is important to note that in a graph if any two lines intersect it is not essential that their intersection is a point of the graph. , the lines x and y intersect in the diagram their intersection is not a point of the graph. 12. 12 e is loop and {e1, e2} is a set of multiple edges. Thus a graph with loops and multiple edges will be known by some authors as pseudo graphs. But we shall specify graphs with multiple edges and graphs with loops distinctly.
5 7 1 8⎥ ⎥ 2 4 1 4⎦ Now suppose we find max min (bij, aij}. We see max {min {bij, aij}) is not defined. Thus we see even if we use max min operation on the matrices A and B and if this is defined in general max min operation of the matrix B and A may not be defined. Now we see this operation will be used in almost all fuzzy models. Yet one more type of operation which we perform in the fuzzy models is illustrated below. Let ⎡1 4 2 3 0 1 ⎤ ⎢6 0 1 2 1 0 ⎥ ⎢ ⎥ ⎢3 1 0 5 2 6⎥ A= ⎢ ⎥ ⎢1 2 6 1 0 1 ⎥ ⎢0 0 1 0 0 4⎥ ⎢ ⎥ ⎢⎣1 2 1 0 1 0 ⎥⎦ be a 6 × 6 matrix and let X = [0 1 0 0 1 1] be a row vector we calculate XA = [7, 2, 3, 2, 2, 4] = X1 = (a1, a2, a3, a4, a5, a6) = X2 X1A = X3 and so on.