Bi-level Optimization in an Imprecise and Random Environment - Singh, Vishnu Pratap;Chakraborty, Debjani
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In 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…mehr

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Produktbeschreibung
In 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.
Autorenporträt
Dr. Vishnu Pratap Singh has completed M.Sc. and Ph.D. from Department of Mathematics, IIT Kharagpur. Currently, He is working as an assistant professor in the Department of Mathematics, Visvesvaraya National Institute of Technology, Nagpur.