A study of the options adaptive analysis of solutions to optimization problems on the basis of logics Reichenbach and Lukasiewicz
Abstract
A study of the options adaptive analysis of solutions to optimization problems on the basis of logics Reichenbach and Lukasiewicz
Incoming article date: 13.06.2015One of the components of the optimization problem is a set of constraints describing the basic requirements for solutions. So as to find a solution that fully satisfies all the wishes of the experts, it is not always possible, the search area extends through analysis of semi-feasible solutions. The adjustment of the system constraints may contribute to changes in the structure and appropriateness of the decisions. The paper shows the ways to form a generalized membership functions of vague constraints of optimization problems based on the logics of Reichenbach and Lukasiewicz. It is known that for the same design procedures in some cases it is necessary to obtain accurate solutions, while others just get approximate solutions. Therefore, we analyzed the features of membership functions obtained using these logics. It is shown that by implication deny rules to allow logic-based Reichenbach membership function takes values equal to one if the value of the function allow rule is one, or if the value of the function deny rule is zero. By implication deny rules in allowing based on Lukasiewicz logic membership function takes values equal to one if the value of the function allow rule is greater than the value of the function deny rules. Therefore, it can be argued that when designing systems with increased reliability (precision) is more expedient to use the function implications for Reichenbach deny rules in a permissive compared with the same implication by Lukasiewicz. The implication deny rules to allow for the Lukasiewicz appropriate to use when designing subsystems that perform secondary functions that are not systemically forming, etc.
Keywords: adaptation, fuzzy system, the implication, intellectual method, membership function, optimization, logic, Reichenbach, Lukasiewicz logic