{"product_id":"bi-level-optimization-in-an-imprecise-and-random-environment-von-vishnu-pratap-singh-debjani-chakraborty","title":"Bi-level Optimization in an Imprecise and Random Environment","description":"\u003cp\u003eIn classical bi-level programming problems, coefficients of objective functions of the leader and the follower are crisp. But in real-life situations, uncertainties arise in almost every aspect. Thus, to include more realistic cases in classical bi-level programming problems, a fuzzy stochastic bi-level programming model has been developed using fuzzy random variable coefficients. A fuzzy random variable is a mathematical tool to deal with a sort of hybrid uncertainty. The novelty of the fuzzy random variable is that it contains the structure of twofold distribution which can carry a joint oneness of the simultaneous random and imprecise information which goes beyond the contrast of information contained in a random variable in probability theory and fuzzy variable in fuzzy set theory. Though the book deals to solve bi-level optimization models in the fuzzy or fuzzy random environment through a multi-stage decision-making approach. The main contribution of this book is twofold. It introduced the fuzzy stochastic and fuzzy rule-base bi-level optimization model to overcome the uncertainties present due to impreciseness and randomness.\u003c\/p\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9786203307481\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e","brand":"Libri","offers":[{"title":"Softcover - 9786203307481","offer_id":39449675759709,"sku":"9786203307481","price":39.9,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/8467970a-7a76-4cd6-9488-874a4d88fc4a.jpg?v=1769925555","url":"https:\/\/shop.autorenwelt.de\/products\/bi-level-optimization-in-an-imprecise-and-random-environment-von-vishnu-pratap-singh-debjani-chakraborty","provider":"Autorenwelt Shop","version":"1.0","type":"link"}