121 research outputs found
A Posynomial Geometric Programming Restricted to a System of Fuzzy Relation Equations
AbstractA posynomial geometric optimization problem subjected to a system of max-min fuzzy relational equations (FRE) constraints is considered. The complete solution set of FRE is characterized by unique maximal solution and finite number of minimal solutions. A two stage procedure has been suggested to compute the optimal solution for the problem. Firstly all the minimal solutions of fuzzy relation equations are determined. Then a domain specific evolutionary algorithm (EA) is designed to solve the optimization problems obtained after considering the individual sub-feasible region formed with the help of unique maximum solution and each of the minimal solutions separately as the feasible domain with same objective function. A single optimal solution for the problem is determined after solving these optimization problems. The whole procedure is illustrated with a numerical example
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
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
Max-Min Fuzzy Relation Equations for a Problem of Spatial Analysis
We implement an algorithm that uses a system of max-min fuzzy relation equations (SFRE) for solving a problem of spatial analysis. We integrate this algorithm in a Geographical information Systems (GIS) tool. We apply our process to determine the symptoms after that an expert sets the SFRE with the values of the impact coefficients related to some parameters of a geographic zone under study. We also define an index of evaluation about the reliability of the results
The Construction of Type-2 Fuzzy Reasoning Relations for Type-2 Fuzzy Logic Systems
Type-2 fuzzy reasoning relations are the type-2 fuzzy relations obtained from a group of type-2 fuzzy reasonings
by using extended t-(co)norm, which are essential for implementing type-2 fuzzy logic systems. In this paper an
algorithm is provided for constructing type-2 fuzzy reasoning relations of SISO type-2 fuzzy logic systems. First,
we give some properties of extended t-(co)norm and simplify the expression of type-2 fuzzy reasoning relations in
accordance with different input subdomains under certain conditions. And then different techniques are discussed
to solve the simplified expressions on the input subdomains by using the related methods on solving fuzzy relation
equations. Besides, it is pointed out that the computation amount level of the proposed algorithm is the same as that
of polynomials and the possibility of applying the proposed algorithm in the construction of type-2 fuzzy reasoning
relations is illustrated on several examples. Finally, the calculation of an arbitrary extended continuous t-norm can be
obtained as the special case of the proposed algorithm
Fitting aggregation operators to data
Theoretical advances in modelling aggregation of information produced a wide range of aggregation operators, applicable to almost every practical problem. The most important classes of aggregation operators include triangular norms, uninorms, generalised means and OWA operators.With such a variety, an important practical problem has emerged: how to fit the parameters/ weights of these families of aggregation operators to observed data? How to estimate quantitatively whether a given class of operators is suitable as a model in a given practical setting? Aggregation operators are rather special classes of functions, and thus they require specialised regression techniques, which would enforce important theoretical properties, like commutativity or associativity. My presentation will address this issue in detail, and will discuss various regression methods applicable specifically to t-norms, uninorms and generalised means. I will also demonstrate software implementing these regression techniques, which would allow practitioners to paste their data and obtain optimal parameters of the chosen family of operators.<br /
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