Applied Optimization

By: Jaime Gil-Aluja

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Hardcover | 30 November 1999

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356 Pages

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24.13 x 16.51 x 2.54

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Decisions in uncertainty Scientific reaction to change During latter decades, the basic elements that have traditionally made up the society in wh ich economic activity develops, have been submitted to the effect of multiple aggressions as a consequence of the outcome of events motivated by the nature itself of the human being, always seeking a level of happiness that is never reached. In a very brief manner we are accustomed to mention these by using words such as revolution, profound changes, convulsions . . . . , the results of which are manifest through non-linear reactions that lead to a future charged with uncertainty. To get to know, explain and treat this new world constitutes one of the many objectives of those who desire a society in the service of man, and for those who aspire to the fact of the concept of mutuality transcending the use less limits of the printed word. But for this it will be necessary to overcome a whole realm of obstacles placed in the way by those comfortably embedded in old principles, decrepit ideas and are not willing to open the windows of their mind to receive the fresh air of a new era.

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Introduction: Decisions in Uncertainty
Scientific reaction to change	p. 9
Considerations on the theory of decision	p. 12
The principle of gradual simultaneity	p. 15
Mathematics of uncertainty	p. 18
Fundamental elements of the theory of decision	p. 20
Relations
The basic elements of relations	p. 33
Characteristics of relations between elements of one and the same set	p. 44
The relation as a support to groupings and orders	p. 63
The linking of relations	p. 83
The linking of relation within a set	p. 94
The accumulation of the level of relations	p. 106
Relations of incidence	p. 116
Assignments
Assignment in the theory of decision	p. 125
Algorithm of assignments by elimination of rows and columns	p. 140
Contribution Konig's to the theory of assignment	p. 144
The Hungarian algorithm of assignments	p. 148
Basic aspects of the processes of partition and delimitation	p. 165
Assignment by means of the Branch and Bound algorithm	p. 169
Groupings
The first steps towards grouping processes	p. 183
Concept and contents of affinities	p. 186
Importance of the Moore closings in obtaining affinities	p. 190
Obtaining a Moore closing from a fuzzy graph	p. 197
Transfer toward rectangular relations	p. 205
Algorithms for obtaining affinities	p. 215
Grouping of symmetrical fuzzy relations	p. 222
Maximum sub-relations of similarity	p. 232
Grouping from the concept of clan	p. 247
Order
Order in the theory of decision	p. 265
Obtaining relations between objects that are susceptible to being ordered	p. 267
Towards certain relations of order	p. 277
Importance of grouping indifferent objects for order	p. 287
Establishment of an order from an ordinal function	p. 299
Order by means of the P-latin composition	p. 311
The ordering of objects according to the importance of their characteristics	p. 321
Epilogue	p. 341
References	p. 343
Bibliography	p. 345
Table of Contents provided by Blackwell. All Rights Reserved.

Applied Optimization

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Hardcover

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