1,666 research outputs found
Set optimization - a rather short introduction
Recent developments in set optimization are surveyed and extended including
various set relations as well as fundamental constructions of a convex analysis
for set- and vector-valued functions, and duality for set optimization
problems. Extensive sections with bibliographical comments summarize the state
of the art. Applications to vector optimization and financial risk measures are
discussed along with algorithmic approaches to set optimization problems
Fuzzy linear programming problems : models and solutions
We investigate various types of fuzzy linear programming problems based on models and solution methods. First, we review fuzzy linear programming problems with fuzzy decision variables and fuzzy linear programming problems with fuzzy parameters (fuzzy numbers in the definition of the objective function or constraints) along with the associated duality results. Then, we review the fully fuzzy linear programming problems with all variables and parameters being allowed to be fuzzy. Most methods used for solving such problems are based on ranking functions, alpha-cuts, using duality results or penalty functions. In these methods, authors deal with crisp formulations of the fuzzy problems. Recently, some heuristic algorithms have also been proposed. In these methods, some authors solve the fuzzy problem directly, while others solve the crisp problems approximately
Advances in Optimization and Nonlinear Analysis
The present book focuses on that part of calculus of variations, optimization, nonlinear analysis and related applications which combines tools and methods from partial differential equations with geometrical techniques. More precisely, this work is devoted to nonlinear problems coming from different areas, with particular reference to those introducing new techniques capable of solving a wide range of problems. The book is a valuable guide for researchers, engineers and students in the field of mathematics, operations research, optimal control science, artificial intelligence, management science and economics
Fuzzy E.O.Q model with constant demand and shortages: A fuzzy signomial geometric programming (FSGP) approach
In this paper, a fuzzy economic order quantity (E.O.Q) model with shortages under fully backlogging and constant demand is formulated and solved. Here the model is solved by fuzzy signomial geometric programming (FSGP) technique. Fuzzy signomial geometric programming (FSGP) technique provides a powerful technique for solving many non-linear problems. Here we have proposed a new idea that is fuzzy modified signomial geometric programming (FMSGP) and some necessary theorems have been derived. Finally, these are illustrated by some numerical examples and applications
Lexicographic Methods for Fuzzy Linear Programming
Fuzzy Linear Programming (FLP) has addressed the increasing complexity of real-world
decision-making problems that arise in uncertain and ever-changing environments since its
introduction in the 1970s. Built upon the Fuzzy Sets theory and classical Linear Programming
(LP) theory, FLP encompasses an extensive area of theoretical research and algorithmic development.
Unlike classical LP, there is not a unique model for the FLP problem, since fuzziness can
appear in the model components in different ways. Hence, despite fifty years of research,
new formulations of FLP problems and solution methods are still being proposed. Among the
existing formulations, those using fuzzy numbers (FNs) as parameters and/or decision variables
for handling inexactness and vagueness in data have experienced a remarkable development in
recent years. Here, a long-standing issue has been how to deal with FN-valued objective functions
and with constraints whose left- and right-hand sides are FNs. The main objective of this paper is
to present an updated review of advances in this particular area. Consequently, the paper briefly
examines well-known models and methods for FLP, and expands on methods for fuzzy single- and
multi-objective LP that use lexicographic criteria for ranking FNs. A lexicographic approach to the
fuzzy linear assignment (FLA) problem is discussed in detail due to the theoretical and practical
relevance. For this case, computer codes are provided that can be used to reproduce results presented
in the paper and for practical applications. The paper demonstrates that FLP that is focused on
lexicographic methods is an active area with promising research lines and practical implications.Spanish Ministry of Economy and CompetitivenessEuropean Union (EU)
TIN2017-86647-
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