2,063 research outputs found
An exact algorithm for linear optimization problem subject to max-product fuzzy relational inequalities with fuzzy constraints
Fuzzy relational inequalities with fuzzy constraints (FRI-FC) are the
generalized form of fuzzy relational inequalities (FRI) in which fuzzy
inequality replaces ordinary inequality in the constraints. Fuzzy constraints
enable us to attain optimal points (called super-optima) that are better
solutions than those resulted from the resolution of the similar problems with
ordinary inequality constraints. This paper considers the linear objective
function optimization with respect to max-product FRI-FC problems. It is proved
that there is a set of optimization problems equivalent to the primal problem.
Based on the algebraic structure of the primal problem and its equivalent
forms, some simplification operations are presented to convert the main problem
into a more simplified one. Finally, by some appropriate mathematical
manipulations, the main problem is transformed into an optimization model whose
constraints are linear. The proposed linearization method not only provides a
super-optimum (that is better solution than ordinary feasible optimal
solutions) but also finds the best super-optimum for the main problem. The
current approach is compared with our previous work and some well-known
heuristic algorithms by applying them to random test problems in different
sizes.Comment: 29 pages, 8 figures, 7 table
Weighted minimax programming subject to the max-min fuzzy relation inequalities
Recently, max-min fuzzy relation inequalities (FRIs) have been used to model a (peer-to-peer) P2P network system. Any feasible scheme in the P2P network system is reflected by a solution of the max-min FRIs. One of the objectives of system managers is to decrease network congestion. To satisfy this objective, we attempt to minimize a weighted minimax function motivated by existing research. As a consequence, we establish a weighted minimax programming model in which the constraint is the max-min FRIs. Our goal in this work is to develop an effective algorithm to obtain the optimal solution of the optimization model. The so-called SCP-based algorithm is proposed to find the optimal solution. A numerical example shows the efficiency of our proposed SCP-based algorithm
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
Methods in Industrial Biotechnology for Chemical Engineers
In keeping with the definition that biotechnology is really no more than a
name given to a set of techniques and processes, the authors apply some set of
fuzzy techniques to chemical industry problems such as finding the proper
proportion of raw mix to control pollution, to study flow rates, to find out
the better quality of products. We use fuzzy control theory, fuzzy neural
networks, fuzzy relational equations, genetic algorithms to these problems for
solutions. When the solution to the problem can have certain concepts or
attributes as indeterminate, the only model that can tackle such a situation is
the neutrosophic model. The authors have also used these models in this book to
study the use of biotechnology in chemical industries.
This book has six chapters. First chapter gives a brief description of
biotechnology. Second chapter deals will proper proportion of mix of raw
materials in cement industries to minimize pollution using fuzzy control
theory. Chapter three gives the method of determination of temperature set
point for crude oil in oil refineries. Chapter four studies the flow rates in
chemical industries using fuzzy neutral networks. Chapter five gives the method
of minimization of waste gas flow in chemical industries using fuzzy linear
programming. The final chapter suggests when in these studies indeterminancy is
an attribute or concept involved, the notion of neutrosophic methods can be
adopted.Comment: 125 pages, 20 figure
Fuzzifying [sic] Markov decision process
Markov decision processes have become an indispensable tool in applications as diverse as equipment maintenance, manufacturing systems, inventory control, queuing networks and investment analysis. Typically we have a controlled Markov chain on a suitable state space in which transitional probabilities depend on the policy (or decision maker) which comes from a set of possible actions. The main problem of interest would be to find an optimal policy that minimizes the associated cost. Linear Programming has been widely used to find the optimal Markov decision policy. It requires solutions of large systems of simultaneous linear equations. By the fact that the complexity in linear programming increases much faster with the increase in the number of states which is often called curse of dimensionality, the linear programming method can handle only small models. This thesis presents a new method to lessen the curse of dimensionality. By assuming certain monotonicity property for the transition probability, it is shown that a fuzzy membership function can be used to reduce the number of states. The use of membership functions help to reduce the number of the states. However all the states remain intact through the use of the membership value. That is, those states eliminated can be recovered through interpolation with the aid of membership functions. This new proposed method is shown to be effective in coping with the curse of dimensionality
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