Analytical method for solving max-min inverse fuzzy relation

Wu, Yan-Kuen; Lur, Yung-Yih; Wen, Ching‐Feng; Lee, Shie-Jue

doi:10.1016/j.fss.2021.08.019

Cited by 11 publications

(3 citation statements)

References 15 publications

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“…This work also uses the following: -Methods of system analysis for recognizing situations that have developed in systems described in [27]; -Methods of modeling, optimization and decision-making for technological objects' control, including in a fuzzy environment, studied in the works of [19][20][21][22][23][24]28]; -Methods of expert assessments for collecting expert, fuzzy information about the operating modes of the hydrotreating unit described in the work of [29]; -Methods of fuzzy set theories for formalization and the use of fuzzy information [21][22][23][24][25]30,31]; -Hybrid modeling and optimization methods for constructing models and optimization based on various initial information and methods [22,32], -Methods for planning experiments and processing their results as described in the works of [33,34] used to collect the necessary information about the operating modes of the hydrotreating unit.…”

Section: Formulation Of the Decision-making Problem In The Fuzzy Envi...mentioning

confidence: 99%

“…To effectively solve and obtain a more adequate solution to fuzzy decision-making problems of technological process control, a systematic approach based on the mathematical apparatus of fuzzy mathematics should be applied [22][23][24]. The systematic approach using fuzzy information allows for the development of a package of interrelated CTS models, on the basis of which it is possible to make an adequate decision on the control of technological processes occurring in fuzzy-described CTSs.…”

Section: Introductionmentioning

confidence: 99%

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Decision Making for Control of the Gasoline Fraction Hydrotreating Process in a Fuzzy Environment

Orazbayev,

Tanirbergenova,

Orazbayeva

et al. 2024

Processes

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This article is devoted to the study of decision-making problems of hydrotreating process control in the production of high-quality gasoline under conditions of scarcity and fuzziness of the initial information, ultimately developing an approach to solve them. A systematic method is proposed that makes it possible to develop a package of mathematical models of a complex of interconnected units of chemical-technological systems based on available information of various types. Using the proposed system method, a package of models of the main interconnected units in which the hydrotreating process took place was developed. A decision-making problem was formulated to control the hydrotreating process in a fuzzy environment based on the developed system of models. By modifying the Pareto principle of optimality for fuzzy conditions, a heuristic method for solving the given decision-making problem was developed to control the hydrotreating process in a fuzzy environment. The novelty of the proposed heuristic method lies in the full use of the collected fuzzy information, which represents the knowledge, intuition and experience of the decision makers and experts. Accordingly, the proposed heuristic decision-making method makes it possible to achieve a high adequacy and efficiency of decisions made when solving production problems in a fuzzy environment. The results obtained were applied in practice to solve decision-making problems for hydrotreating process control at the Atyrau refinery. The results obtained show the advantages of the proposed heuristic method for solving decision-making problems of hydrotreating process control over known methods.

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Section: Formulation Of the Decision-making Problem In The Fuzzy Envi...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Decision Making for Control of the Gasoline Fraction Hydrotreating Process in a Fuzzy Environment

Orazbayev,

Tanirbergenova,

Orazbayeva

et al. 2024

Processes

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“…Because of their application potential, it became clear in the early stages of their investigation that it is unreasonable to disregard fuzzy relations that are "close enough" solutions to these systems. For this purpose, numerous techniques for finding such solutions have been developed in many papers [9,10,22,30,35,36,38,54,55,61].…”

Section: A Literature Overviewmentioning

confidence: 99%

On the solvability of weakly linear systems of fuzzy relation equations

Stanimirovic,

Micic

2022

Preprint

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Systems of fuzzy relation equations and inequalities in which an unknown fuzzy relation is on the one side of the equation or inequality are linear systems. They are the most studied ones, and a vast literature on linear systems focuses on finding solutions and solvability criteria for such systems. The situation is quite different with the so-called weakly linear systems, in which an unknown fuzzy relation is on both sides of the equation or inequality. Precisely, the scholars have only given the characterization of the set of exact solutions to such systems. This paper describes the set of fuzzy relations that solve weakly linear systems to a certain degree and provides ways to compute them. We pay special attention to developing the algorithms for computing fuzzy preorders and fuzzy equivalences that are solutions to some extent to weakly linear systems. We establish additional properties for the set of such approximate solutions over some particular types of complete residuated lattices. We demonstrate the advantage of this approach via many examples that arise from the problem of aggregation of fuzzy networks.

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