{"product_id":"bi-level-optimization-in-an-imprecise-and-random-environment-paperback","title":"Bi-level Optimization in an Imprecise and Random Environment - Paperback","description":"\u003cp\u003eby \u003cb\u003eVishnu Pratap Singh\u003c\/b\u003e (Author), \u003cb\u003eDebjani Chakraborty\u003c\/b\u003e (Author)\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\u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 84\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 0.2 x 9 x 6 IN\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e May 14, 2021\u003c\/div\u003e","brand":"Books by splitShops","offers":[{"title":"Default Title","offer_id":42708267630655,"sku":"9786203307481","price":74.46,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0105\/8226\/1823\/files\/abb27bc477dc6bf2130a3270a0999415.webp?v=1765047179","url":"https:\/\/dhlswag.com\/products\/bi-level-optimization-in-an-imprecise-and-random-environment-paperback","provider":"BBB","version":"1.0","type":"link"}