Download Elementary Fuzzy Matrix Theory and Fuzzy Models for Social by W. B. Vasantha Kandasamy, Florentin Smarandache, K. PDF

By W. B. Vasantha Kandasamy, Florentin Smarandache, K. Ilanthenral

ISBN-10: 1599730057

ISBN-13: 9781599730059

This publication supplies the elemental notions of fuzzy matrix idea and its functions to easy versions. The technique is non-traditional in an effort to allure many scholars to take advantage of this technique of their learn. the conventional strategy of mathematicians has conditioned scholars of sociology in the sort of demeanour that they averse to utilizing mathematical instruments. Six easy varieties 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 facts. the bushy Cognitive Maps version provides the hidden trend. Fuzzy Relational Maps version not just supplies the inter-relations among units of disjoint attributes. The Bidirectional Associative thoughts version analyzes facts looking on the time-period whereas the bushy Associative thoughts version may give the gradation of value of every characteristic. eventually, the bushy Relational Equation version is in a position to giving an answer in the direction of the expected resolution. all of the equipment are illustrated via complicated examples of specific social difficulties.

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Using the opinion we obtain the hidden patterns. The following concepts are taken as the nodes relative to the employee. We can have several more nodes and also several experts' opinions for it a clearly evident theory which professes that more the number of experts the better is the result. We have taken as the concepts / nodes of domain only 8 notions which pertain to the employee.

6 0 0 0 0 The related graph for the binary relation. 4 Further in the description of the fuzzy compatibility relations also the graphs were used. The notion of graph theory was used in describing the fuzzy ordering relations. In fact one can say that the graph theory method was more simple and an easy representation even by a lay man. Thus we can say whenever the data had a fuzzy matrix representation it is bound to get the digraph representation. , in finite machines we do not study in this direction in this book.

We also call the unit interval as a fuzzy interval. We say [a, b] is a fuzzy sub interval of the fuzzy interval [0, 1] if 0 ≤ a < b ≤ 1: we denote this by [a, b] ⊆ [0, 1]. We also use the convention of calling [–1, 1] to be also a fuzzy interval. x ∈ [–1, 1] if –1 ≤ x ≤ 1. , 0 < x < 1} is uncountable; hence [0, 1] is an infinite set as [0, 1] is an uncountable set. Let X be any universal set. The characteristic function maps elements of X to elements of the set to elements of the set {0, 1}, which is formally expressed by χA: X → [0, 1].

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Elementary Fuzzy Matrix Theory and Fuzzy Models for Social Scientists by W. B. Vasantha Kandasamy, Florentin Smarandache, K. Ilanthenral

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