Download E-books Generalized Concavity in Fuzzy Optimization and Decision Analysis (International Series in Operations Research & Management Science) PDF

Analysis

By Jaroslav Ramík

Convexity of units in linear areas, and concavity and convexity of features, lie on the root of gorgeous theoretical effects that are whilst super precious within the research and resolution of optimization difficulties, together with difficulties of both unmarried target or a number of pursuits. no longer all of those effects depend unavoidably on convexity and concavity; a few of the effects can be sure that every one neighborhood optimal can be an international optimal, giving those equipment broader software to a much wider category of difficulties. consequently, the point of interest of the first a part of the ebook is worried with various kinds of generalized convex units and generalized concave capabilities. as well as their applicability to nonconvex optimization, those convex units and generalized concave capabilities are utilized in the book's moment half, the place decision-making and optimization difficulties lower than uncertainty are investigated.
Uncertainty within the challenge info usually can't be shunned while dealing with functional difficulties. mistakes take place in real-world facts for a number of purposes. despite the fact that, over the past thirty years, the bushy set procedure has proved to be priceless in those events. it truly is this method of optimization below uncertainty that's generally used and studied in the second one a part of this booklet. regularly, the club features of fuzzy units fascinated with such difficulties are neither concave nor convex. they're, notwithstanding, frequently quasiconcave or concave in a few generalized experience. This opens probabilities for program of effects on generalized concavity to fuzzy optimization. regardless of this noticeable relation, using the interface of those components has been restricted up to now. it really is was hoping that the mix of principles and effects from the sector of generalized concavity at the one hand and fuzzy optimization however defined and mentioned in Generalized Concavity in Fuzzy Optimization and selection Analysis may be of curiosity to either groups. Our objective is to expand the sessions of difficulties that the combo of those parts can satisfactorily deal with and remedy.

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