Abstract In this paper the solution for hesitant fuzzy system as AX = B is introduced where A is an n × n known hesitant fuzzy matrix, B is an n × 1 known hesitant fuzzy vector and X is an n × 1 unknown hesitant fuzzy vector. First, L∞-norm and L1-norm of a hesitant fuzzy vector are introduced. Then, the concepts of hesitant fuzzy zero, ’almost equal’ and ’less than’ and ’equal’ are defined for two hesitant fuzzy numbers. Finally, using a minimization problem; the hesitant fuzzy system is solved. At the end, some numerical examples are presented to show the effectiveness of the proposed method.
{"title":"Introducing and solving the hesitant fuzzy system AX = B","authors":"F. Babakordi, T. Allahviranloo","doi":"10.2478/candc-2021-0031","DOIUrl":"https://doi.org/10.2478/candc-2021-0031","url":null,"abstract":"Abstract In this paper the solution for hesitant fuzzy system as AX = B is introduced where A is an n × n known hesitant fuzzy matrix, B is an n × 1 known hesitant fuzzy vector and X is an n × 1 unknown hesitant fuzzy vector. First, L∞-norm and L1-norm of a hesitant fuzzy vector are introduced. Then, the concepts of hesitant fuzzy zero, ’almost equal’ and ’less than’ and ’equal’ are defined for two hesitant fuzzy numbers. Finally, using a minimization problem; the hesitant fuzzy system is solved. At the end, some numerical examples are presented to show the effectiveness of the proposed method.","PeriodicalId":55209,"journal":{"name":"Control and Cybernetics","volume":"50 1","pages":"553 - 574"},"PeriodicalIF":0.0,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48574620","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract This note presents sufficient conditions for the property of strong metric subregularity (SMSr) of the system of first order optimality conditions for a mathematical programming problem in a Banach space (the Karush-Kuhn-Tucker conditions). The constraints of the problem consist of equations in a Banach space setting and a finite number of inequalities. The conditions, under which SMSr is proven, assume that the data are twice continuously Fréchet differentiable, the strict Mangasarian-Fromovitz constraint qualification is satisfied, and the second-order sufficient optimality condition holds. The obtained result extends the one known for finite-dimensional problems. Although the applicability of the result is limited to the Banach space setting (due to the twice Fréchet differentiability assumptions and the finite number of inequality constraints), the paper can be valuable due to the self-contained exposition, and provides a ground for extensions. One possible extension was recently implemented in Osmolovskii and Veliov (2021).
{"title":"On the strong metric subregularity in mathematical programming","authors":"N. Osmolovskii, V. Veliov","doi":"10.2478/candc-2021-0027","DOIUrl":"https://doi.org/10.2478/candc-2021-0027","url":null,"abstract":"Abstract This note presents sufficient conditions for the property of strong metric subregularity (SMSr) of the system of first order optimality conditions for a mathematical programming problem in a Banach space (the Karush-Kuhn-Tucker conditions). The constraints of the problem consist of equations in a Banach space setting and a finite number of inequalities. The conditions, under which SMSr is proven, assume that the data are twice continuously Fréchet differentiable, the strict Mangasarian-Fromovitz constraint qualification is satisfied, and the second-order sufficient optimality condition holds. The obtained result extends the one known for finite-dimensional problems. Although the applicability of the result is limited to the Banach space setting (due to the twice Fréchet differentiability assumptions and the finite number of inequality constraints), the paper can be valuable due to the self-contained exposition, and provides a ground for extensions. One possible extension was recently implemented in Osmolovskii and Veliov (2021).","PeriodicalId":55209,"journal":{"name":"Control and Cybernetics","volume":"50 1","pages":"457 - 471"},"PeriodicalIF":0.0,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69189209","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The convex linear combination of the controllability pairs of linear continuous-time linear systems is defined and its properties are discussed. The main result is obtained using pure algebraic methods. In the illustrative examples different cases of linear convex combinations are analyzed.
{"title":"Convex linear combination of the controllability pairs for linear systems","authors":"T. Kaczorek, J. Klamka","doi":"10.2478/candc-2021-0030","DOIUrl":"https://doi.org/10.2478/candc-2021-0030","url":null,"abstract":"Abstract The convex linear combination of the controllability pairs of linear continuous-time linear systems is defined and its properties are discussed. The main result is obtained using pure algebraic methods. In the illustrative examples different cases of linear convex combinations are analyzed.","PeriodicalId":55209,"journal":{"name":"Control and Cybernetics","volume":"50 1","pages":"541 - 551"},"PeriodicalIF":0.0,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42093200","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Alphabetical list of contributors of volume 50 (2021) AUTHOR, issue number, pages","authors":"","doi":"10.2478/candc-2021-0033","DOIUrl":"https://doi.org/10.2478/candc-2021-0033","url":null,"abstract":"","PeriodicalId":55209,"journal":{"name":"Control and Cybernetics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42056106","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract This paper studies the output controllability of discrete linear time invariant systems (LTI) with non-negative input constraints. Some geometrical arguments and positive invariance concepts are used to derive the necessary and/or sufficient conditions for the positive output controllability of discrete LTI systems. The paper also provides several academic examples, which support the theoretical results.
{"title":"Positive output controllability of linear discrete–time invariant systems","authors":"Mourad Ouyadri, M. Laabissi, M. E. Achhab","doi":"10.2478/candc-2021-0029","DOIUrl":"https://doi.org/10.2478/candc-2021-0029","url":null,"abstract":"Abstract This paper studies the output controllability of discrete linear time invariant systems (LTI) with non-negative input constraints. Some geometrical arguments and positive invariance concepts are used to derive the necessary and/or sufficient conditions for the positive output controllability of discrete LTI systems. The paper also provides several academic examples, which support the theoretical results.","PeriodicalId":55209,"journal":{"name":"Control and Cybernetics","volume":"50 1","pages":"521 - 539"},"PeriodicalIF":0.0,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69189225","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Deformations of the computational mesh, arising from optimization routines, usually lead to decrease of mesh quality or even destruction of the mesh. We propose a theoretical framework using pre-shapes to generalize the classical shape optimization and calculus. We define pre-shape derivatives and derive corresponding structure and calculus theorems. In particular, tangential directions are featured in pre-shape derivatives, in contrast to classical shape derivatives, featuring only normal directions. Techniques from classical shape optimization and calculus are shown to carry over to this framework. An optimization problem class for mesh quality is introduced, which is solvable with the use of pre-shape derivatives. This class allows for simultaneous optimization of the classical shape objectives and mesh quality without deteriorating the classical shape optimization solution. The new techniques are implemented and numerically tested for 2D and 3D.
{"title":"Pre-shape calculus and its application to mesh quality optimization","authors":"D. Luft, V. Schulz","doi":"10.2478/candc-2021-0019","DOIUrl":"https://doi.org/10.2478/candc-2021-0019","url":null,"abstract":"Abstract Deformations of the computational mesh, arising from optimization routines, usually lead to decrease of mesh quality or even destruction of the mesh. We propose a theoretical framework using pre-shapes to generalize the classical shape optimization and calculus. We define pre-shape derivatives and derive corresponding structure and calculus theorems. In particular, tangential directions are featured in pre-shape derivatives, in contrast to classical shape derivatives, featuring only normal directions. Techniques from classical shape optimization and calculus are shown to carry over to this framework. An optimization problem class for mesh quality is introduced, which is solvable with the use of pre-shape derivatives. This class allows for simultaneous optimization of the classical shape objectives and mesh quality without deteriorating the classical shape optimization solution. The new techniques are implemented and numerically tested for 2D and 3D.","PeriodicalId":55209,"journal":{"name":"Control and Cybernetics","volume":"50 1","pages":"263 - 301"},"PeriodicalIF":0.0,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41427797","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The essay has a twofold objective: primarily, to present an application of voting theory as a possible evaluation method, and concurrently, to offer a pedagogic framework, based on that very application. Evaluation and certain notions of preference and value have common semantic roots. By equating preference and choice, we end up amidst social choice (SC) theory and voting methods, also manageable as joint decisions in multiple-criteria decision making (MCDM). With the aid of the Saari triangle some essential differences of pairwise and positional voting rules for up to three alternatives can be depicted. A voting or decision rule does not necessarily follow the true preferences of the actors, but may mirror the problematics of the chosen rule. The Saari triangle makes it possible to visualize some paradoxical results in the exemplary evaluations of digital websites through an imaginary case description via voting and MCDM. As candidates and voters in SC are put to stand for alternatives and criteria in MCDM, the methodological and pedagogical goals of the study are achieved.
{"title":"Voting and MCDM: the pedagogy of the Saari triangle","authors":"J. Hakula","doi":"10.2478/candc-2021-0024","DOIUrl":"https://doi.org/10.2478/candc-2021-0024","url":null,"abstract":"Abstract The essay has a twofold objective: primarily, to present an application of voting theory as a possible evaluation method, and concurrently, to offer a pedagogic framework, based on that very application. Evaluation and certain notions of preference and value have common semantic roots. By equating preference and choice, we end up amidst social choice (SC) theory and voting methods, also manageable as joint decisions in multiple-criteria decision making (MCDM). With the aid of the Saari triangle some essential differences of pairwise and positional voting rules for up to three alternatives can be depicted. A voting or decision rule does not necessarily follow the true preferences of the actors, but may mirror the problematics of the chosen rule. The Saari triangle makes it possible to visualize some paradoxical results in the exemplary evaluations of digital websites through an imaginary case description via voting and MCDM. As candidates and voters in SC are put to stand for alternatives and criteria in MCDM, the methodological and pedagogical goals of the study are achieved.","PeriodicalId":55209,"journal":{"name":"Control and Cybernetics","volume":"50 1","pages":"401 - 412"},"PeriodicalIF":0.0,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48843453","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The paper presents selected elements of a modelling methodology involving quantization, quantum calculations and dequantization on the example of the neural model of the Day-Ahead Market of the Polish Electricity Exchange. Based on the fundamental assumptions of quantum computing, a new method has been proposed here of converting the real numbers in decimal notation into quantum mixed numbers using the probability modules of quantum mixed number and the principle of superposition, along with a new method of quantum calculations using linear algebra and vectormatrix calculus, and the Artificial Neural Network was taught accordingly. Dequantization of quantum mixed numbers to real numbers in decimal notation using the new method of dequantization has been proposed as well. The operation of the methods introduced was shown on numerical examples.
{"title":"Quantum-inspired method of neural modeling of the day-ahead market of the Polish electricity exchange","authors":"Jerzy Tchórzewsk, Dariusz Ruciński","doi":"10.2478/candc-2021-0023","DOIUrl":"https://doi.org/10.2478/candc-2021-0023","url":null,"abstract":"Abstract The paper presents selected elements of a modelling methodology involving quantization, quantum calculations and dequantization on the example of the neural model of the Day-Ahead Market of the Polish Electricity Exchange. Based on the fundamental assumptions of quantum computing, a new method has been proposed here of converting the real numbers in decimal notation into quantum mixed numbers using the probability modules of quantum mixed number and the principle of superposition, along with a new method of quantum calculations using linear algebra and vectormatrix calculus, and the Artificial Neural Network was taught accordingly. Dequantization of quantum mixed numbers to real numbers in decimal notation using the new method of dequantization has been proposed as well. The operation of the methods introduced was shown on numerical examples.","PeriodicalId":55209,"journal":{"name":"Control and Cybernetics","volume":"50 1","pages":"383 - 399"},"PeriodicalIF":0.0,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46707763","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract A vast majority of research has been performed in the field of hesitant fuzzy sets (HFSs), involving the introduction of some properties, operations, relations and modifications of such sets or considering the application of HFSs in MCDM (multicriteria decision making). On the other hand, no research has been performed in the field of fully hesitant fuzzy equations. Therefore, in this paper, fully hesitant fuzzy equations and dual hesitant fuzzy equations are introduced. First, a method is proposed to solve one-element hesitant fuzzy equations. Then, the proposed method is extended to solve n-element hesitant fuzzy equations effectively. Moreover, to show the applicability of the proposed method, it is used to solve a real world problem. Thus, the proposed method is applied to determine market equilibrium price. Also, some other numerical examples are presented to better show the performance of the proposed method.
{"title":"Introducing hesitant fuzzy equations and determining market equilibrium price","authors":"F. Babakordi, N. Taghi-Nezhad","doi":"10.2478/candc-2021-0022","DOIUrl":"https://doi.org/10.2478/candc-2021-0022","url":null,"abstract":"Abstract A vast majority of research has been performed in the field of hesitant fuzzy sets (HFSs), involving the introduction of some properties, operations, relations and modifications of such sets or considering the application of HFSs in MCDM (multicriteria decision making). On the other hand, no research has been performed in the field of fully hesitant fuzzy equations. Therefore, in this paper, fully hesitant fuzzy equations and dual hesitant fuzzy equations are introduced. First, a method is proposed to solve one-element hesitant fuzzy equations. Then, the proposed method is extended to solve n-element hesitant fuzzy equations effectively. Moreover, to show the applicability of the proposed method, it is used to solve a real world problem. Thus, the proposed method is applied to determine market equilibrium price. Also, some other numerical examples are presented to better show the performance of the proposed method.","PeriodicalId":55209,"journal":{"name":"Control and Cybernetics","volume":"50 1","pages":"363 - 382"},"PeriodicalIF":0.0,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44776111","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Taking as an example the very interesting and motivating paper by Sousa Ribeiro et al. (2021) an attempt is made of providing a couple of insights into the decision making process from the point of view of the potentially helpful aspects of data analysis and OR-related modelling. These are just hints and suggestions, meant primarily to emphasise the multifaceted character of the decision making situations and processes, especially when concerning more complex issues. While the course of the procedure proposed and exemplified in Sousa Ribeiro et al. (2021) is treated as fully correctly and successfully carried out to the end, we wish to show the potential use of information, constituting in a sense a “by-product” of such a procedure, or, actually, of any similar procedure, aimed at supporting decision making.
{"title":"On the use of data analysis and OR modelling in MCDM problems: a case analysis – a rejoinder to the paper by Sousa Ribeiro et al","authors":"J. Owsinski","doi":"10.2478/candc-2021-0025","DOIUrl":"https://doi.org/10.2478/candc-2021-0025","url":null,"abstract":"Abstract Taking as an example the very interesting and motivating paper by Sousa Ribeiro et al. (2021) an attempt is made of providing a couple of insights into the decision making process from the point of view of the potentially helpful aspects of data analysis and OR-related modelling. These are just hints and suggestions, meant primarily to emphasise the multifaceted character of the decision making situations and processes, especially when concerning more complex issues. While the course of the procedure proposed and exemplified in Sousa Ribeiro et al. (2021) is treated as fully correctly and successfully carried out to the end, we wish to show the potential use of information, constituting in a sense a “by-product” of such a procedure, or, actually, of any similar procedure, aimed at supporting decision making.","PeriodicalId":55209,"journal":{"name":"Control and Cybernetics","volume":"50 1","pages":"413 - 422"},"PeriodicalIF":0.0,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49035307","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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