{"product_id":"generalized-concavity-in-fuzzy-optimization-and-decision-analysis-von-jaroslav-ramik-milan-vlach","title":"Generalized Concavity in Fuzzy Optimization and Decision Analysis","description":"\n                                Convexity of sets in linear spaces, and concavity and convexity  of functions, lie at the root of beautiful theoretical results that  are at the same time extremely useful in the analysis and solution of  optimization problems, including problems of either single objective  or multiple objectives. Not all of these results rely necessarily on  convexity and concavity; some of the results can guarantee that each  local optimum is also a global optimum, giving these methods broader  application to a wider class of problems. Hence, the focus of the  first part of the book is concerned with several types of generalized  convex sets and generalized concave functions. In addition to their  applicability to nonconvex optimization, these convex sets and  generalized concave functions are used in the book's second part,  where decision-making and optimization problems under uncertainty are  investigated. \n                \n                \u003cbr\u003e\n                                  Uncertainty in the problem data often cannot be avoided when dealing  with practical problems. Errors occur in real-world data for a host of  reasons. However, over the last thirty years, the fuzzy set approach  has proved to be useful in these situations. It is this approach to  optimization under uncertainty that is extensively used and studied in  the second part of this book. Typically, the membership functions of  fuzzy sets involved in such problems are neither concave nor convex.  They are, however, often quasiconcave or concave in some generalized  sense. This opens possibilities for application of results on  generalized concavity to fuzzy optimization. Despite this obvious  relation, applying the interface of these two areas has been limited  to date. It is hoped that the combination of ideas and results from  the field of generalized concavity on the one hand and fuzzy  optimization on the other hand outlined and discussed in  \n                \n                \u003cem\u003eGeneralized\u003c\/em\u003e\n                                 \n                \n                \u003cem\u003eConcavity in Fuzzy Optimization and Decision  Analysis\u003c\/em\u003e\n                                 will be of interest to both communities. Our aimis to  broaden the classes of problems that the combination of these two  areas can satisfactorily address and solve.\n            \n            \u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9781461355779\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9780792374954\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e","brand":"Libri","offers":[{"title":"Softcover - 9781461355779","offer_id":39415634722909,"sku":"9781461355779","price":106.99,"currency_code":"EUR","in_stock":true},{"title":"Hardcover - 9780792374954","offer_id":50726057670,"sku":"9780792374954","price":106.99,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/57ae8e1e-e427-4482-beca-8ea4a4dddd74.jpg?v=1772172267","url":"https:\/\/shop.autorenwelt.de\/products\/generalized-concavity-in-fuzzy-optimization-and-decision-analysis-von-jaroslav-ramik-milan-vlach","provider":"Autorenwelt Shop","version":"1.0","type":"link"}