0000000000046872
AUTHOR
Pavels Orlovs
Upper and lower generalized factoraggregations based on fuzzy equivalence relation
We develop the concept of a general factoraggre-gation operator introduced by the authors on the basis of an equivalence relation and applied in two recent papers for analysis of bilevel linear programming solving parameters. In the paper this concept is generalized by using a fuzzy equivalence relation instead of the crisp one. By using a left-continuous t-norm and its residuum we define and investigate two modifications of such generalized construction: upper and lower generalized factoraggregations. These generalized factoraggregations can be used for construction of extensional fuzzy sets.
Fuzzy Metric Approach to Aggregation of Risk Levels
In this paper we propose a special construction of a general aggregation operator. The construction allows to aggregate fuzzy sets taking into account the distance between elements of the universe. We consider the case when fuzzy sets to be aggregated represent the risk level evaluation by several experts. We describe how the proposed construction could be applied for risk level assessment in the case when a strong fuzzy metric is used to characterize the similarity of objects under evaluation.
Aggregation of Risk Level Assessments Based on Fuzzy Equivalence Relation
The paper deals with the problem of aggregation of risk level assessments. We describe the technique of a risk level evaluation taking into account values of the risk level obtained for objects which are in some sense equivalent. For this purpose we propose to use the construction of a general aggregation operator based on the corresponding fuzzy equivalence relation. Numerical example of the investment risk level aggregation using an equivalence relation obtained on the basis of different macroeconomic factors for countries of one region is considered.
On Extensional Fuzzy Sets Generated by Factoraggregation
We develop the concept of a general factoraggregation operator introduced by the authors on the basis of an equivalence relation and applied in two recent papers for analysis of bilevel linear programming solving parameters. In the paper this concept is generalized by using a fuzzy equivalence relation instead of the crisp one. We show how the generalized factoraggregation can be used for construction of extensional fuzzy sets and consider approximations of arbitrary fuzzy sets by extensional ones.
An Analysis of Bilevel Linear Programming Solving Parameters Based on Factoraggregation Approach
We introduce the notion of factoraggregation,which is a special construction of general aggregation operators, and apply it for an analysis of optimal solution parameters for bilevel linear programming problems. The aggregation observes lower level objective functions considering the classes of equivalence generated by an objective function on the upper level. The proposed method is illustrated with numerical and graphical examples.
General aggregation operators based on a fuzzy equivalence relation in the context of approximate systems
Our paper deals with special constructions of general aggregation operators, which are based on a fuzzy equivalence relation and provide upper and lower approximations of the pointwise extension of an ordinary aggregation operator. We consider properties of these approximations and explore their role in the context of extensional fuzzy sets with respect to the corresponding equivalence relation. We consider also upper and lower approximations of a t-norm extension of an ordinary aggregation operator. Finally, we describe an approximate system, considering the lattice of all general aggregation operators and the lattice of all fuzzy equivalence relations.
Upper and lower approximations of general aggregation operators based on fuzzy rough sets
Our paper deals with constructions of upper and lower general aggregation operators which act on fuzzy sets. These constructions are based on fuzzy rough sets and provide two approximations (upper and lower) of the pointwise extension and the t-extension of an ordinary aggregation operator. Considering two lattices of corresponding general aggregation operators we describe two approximate systems with respect to a lattice of fuzzy equivalence relations.
A choice of bilevel linear programming solving parameters: factoraggregation approach
Our paper deals with the problem of choosing correct parameters for the bilevel linear program- ming solving algorithm proposed by M. Sakawa and I. Nishizaki. We suggest an approach based on fac- toraggregation, which is a specially designed general aggregation operator. The idea of factoraggregation arises from factorization by the equivalence relation generated by the upper level objective function. We prove several important properties of the factorag- gregation result regarding the analysis of param- eters in order to find an optimal solution for the problem. We illustrate the proposed method with some numerical and graphical examples, in particu- lar we consider a modification of the m…