5,563 research outputs found
Minimizing and maximizing a linear objective function under a fuzzy relational equation and an inequality constraint
summary:This paper provides an extension of results connected with the problem of the optimization of a linear objective function subject to fuzzy relational equations and an inequality constraint, where is an operation. This research is important because the knowledge and the algorithms presented in the paper can be used in various optimization processes. Previous articles describe an important problem of minimizing a linear objective function under a fuzzy relational equation and an inequality constraint, where is the -norm or mean. The authors present results that generalize this outcome, so the linear optimization problem can be used with any continuous increasing operation with a zero element where includes in particular the previously studied operations. Moreover, operation does not need to be a t-norm nor a pseudo--norm. Due to the fact that optimal solutions are constructed from the greatest and minimal solutions of a relational equation or inequalities, this article presents a method to compute them. We note that the linear optimization problem is valid for both minimization and maximization problems. Therefore, for the optimization problem, we present results to find the largest and the smallest value of the objective function. To illustrate this problem a numerical example is provided
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
An algorithm for solving fuzzy relation programming with the max-t composition operator
This paper studies the problem of minimizing a linear objective function subject to max-T fuzzy relation equation constraints where T is a special class of pseudot-norms. Some sufficient conditions are presented for determination of its optimal solutions. Some procedures are also suggested to simplify the original problem. Some sufficient conditions are given for uniqueness of its optimal solution. Finally, an algorithm is proposed to find its optimal solution.Publisher's Versio
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
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