{"product_id":"bi-level-optimization-in-an-imprecise-and-random-environment-9786203307481","title":"Bi-level Optimization in an Imprecise and Random Environment","description":"\u003cp\u003e • Author(s): Vishnu Pratap Singh | Debjani Chakraborty\u003cbr\u003e • Publisher: LAP Lambert Academic Publishing\u003cbr\u003e • Publisher Imprint: LAP Lambert Academic Publishing\u003cbr\u003e • BISAC: General\u003c\/p\u003e\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","brand":"Atlantic Books","offers":[{"title":"Paperback","offer_id":46452042236055,"sku":"9786203307481","price":3722.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9786203307481.webp?v=1769139361","url":"https:\/\/atlanticbooks.com\/products\/bi-level-optimization-in-an-imprecise-and-random-environment-9786203307481","provider":"Atlantic Books","version":"1.0","type":"link"}