By Thomas L. Saaty, Kevin P. Kearns

ISBN-10: 0080325998

ISBN-13: 9780080325996

This booklet provides a methodological method of making plans utilizing the Analytic Hierarchy method (AHP).

Part I, platforms and Complexity, has chapters on Complexity and platforms and the way they relate to the Analytic Hierarchy procedure.

Part II, Strategic making plans, has chapters on present Theories of making plans, Strategic making plans, and Benefit-Cost research and source Allocation.

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Extra resources for Analytical Planning: The Organization of Systems (International Series in Modern Applied Mathematics and Computer Science, Volume 7)

Example text

Then ~l and ){2 equable ==-dp ~l ~/ ~2 equable. Proof. From the set-theoretic equality 18 ,(X l v X2) = I~ X1 u I & . (X I ~ ~2) =~v. ~lV~V. ~2" From this, the lemma follows at once. 6. lg - Equable pseudo-topological vector spaces. e. 2), that each topological vector space is equable. However, not all pseudotopological vector spaces are equable (*). Given any pseudo-topological vector space E, we can introduce on ~ a new pseudo-topology, thus obtaining a new pseudo-topological vector space E I~" .

1) Let ~ E 1 ~ o Hence ~ ~ = ~ E 1 , t(~)~(~) =~ (~V~) = W - [ ( ~ ) ~E 2, ~E2~. , Proposition. 10)). Proof. lO) it is sufficient to show that b: El~ x E 2 ~ E 3 ~ • i~Ei ~ , i = 1,2. is continuous at the point (0~0). So let Hence ~i ~ ~ i = ~ V ~ i ~ E i , and b(~l,~2)~-b(~l,~2 ) = b(W~l,~2) shows that b(~l, @2 ) ~ E 3 ~ " =~V b ( N l , ~ 2 ) ~E 3, which - § 3. 32 - DIFFERENTIABILITY AND DERIVATIVES. In this section, the definition of differentiability is given and the most elementary results of calculus are proved.

X ( U and - x ( U o is convex , then z = ~x, where Since ~ O , ~ . U = U, ~x = I ~ l (~x) @ U. Thus we have V ~ I l ~ / , which shows that V e ~ V ~ o e) Let V 6 1 ~ , also ½U e ~ ; and choose U as before. By (c) we have and since ½U is also convex it follows that ½U ~ . 2)). 7) are necessary and sufficient in order that ~ i s the neighborhood-filter of zero for a unique compatible topology on ~ (cf. [Q] ). 9) Proposition. 24 - For any pseudo-topological vector space E, the space E° defined above is a locally convex topological vector space.

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Analytical Planning: The Organization of Systems (International Series in Modern Applied Mathematics and Computer Science, Volume 7) by Thomas L. Saaty, Kevin P. Kearns


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