Abstract
This paper presents a developed method for fuzzy multiple-criteria optimization of the rolled-steel heat treatment processes in the modern metallurgical plant. At the first stage of the study, by means of passive industrial experiments or a mathematical simulation of heat transfer processes, and using statistical methods, the regression dependencies of the output parameters of process quality on the input variables that are technological parameters are established. Then, based on the quality parameters, membership functions are formed that represent local criteria of the process quality, and their ranks are calculated using the matrix of pairwise comparisons. The practically useful methodology of the fuzzy multiple-criteria optimization of technological processes is proposed. To illustrate this methodology’s practical efficiency, the solutions of two optimization problems are found by maximizing the global criterion that aggregates local criteria using their ranks. It is shown that the efficiency of the obtained optimal heat treatment modes significantly exceeds the efficiency of the technology used earlier in the plant.
Highlights
In this paper, we will consider fuzzy optimization as the multiple-criteria optimization problem with fuzzy local criteria and constraints of different levels of importance
In real-world optimization problems, we deal with two groups of local criteria: objective criteria based on measured parameters, and subjective criteria based on the verbal expert assessments
Establishment of the membership functions of local criteria based on actual technological instructions, as well as on the experience and intuition of technologists; 3
Summary
We will consider fuzzy optimization as the multiple-criteria optimization problem with fuzzy local criteria and constraints of different levels of importance (weights). A justified methodology, providing an opportunity for synthesized assessments of uncertainty factors, that makes it possible to design comparable local criteria based on measurable quantitative parameters as well as verbal assessments, is needed To solve this problem, the methods of the fuzzy set theory, developed for dealing with uncertainties of a subjective origin, may be used with great efficiency. In [21], a critical analysis of the known approaches to the aggregation of aggregating modes is provided and a new method, based on the synthesis of type 2 and level 2 fuzzy sets, which is free of the revealed drawbacks of existing approaches, is developed This method was successfully used for the solution of the fuzzy multiple-objective optimization problem in logistic [22]; 6.
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