Abstract We discuss some aspects of similarity measures in the context of Atanassov’s intuitionistic fuzzy sets (IFSs, for short). IFSs, proposed in 1983, are a relatively new tool for the modeling and simulation and, because of their construction, present us with new challenges as far the similarity measures are concerned. Specifically, we claim that the distances alone are not a proper measure of similarity for the IFSs. We stress the role of a lack of knowledge concerning elements (options, decisions, etc.) and point out the role of the opposing (complementing) elements. We also pay attention to the fact that it is not justified to talk about similarity when one has not enough knowledge about the compared objects/elements. Some novel measures of similarity are presented.
{"title":"Similarity measures for Atanassov’s intuitionistic fuzzy sets: some dilemmas and challenges","authors":"E. Szmidt, J. Kacprzyk, Paweł Bujnowski","doi":"10.2478/candc-2022-0016","DOIUrl":"https://doi.org/10.2478/candc-2022-0016","url":null,"abstract":"Abstract We discuss some aspects of similarity measures in the context of Atanassov’s intuitionistic fuzzy sets (IFSs, for short). IFSs, proposed in 1983, are a relatively new tool for the modeling and simulation and, because of their construction, present us with new challenges as far the similarity measures are concerned. Specifically, we claim that the distances alone are not a proper measure of similarity for the IFSs. We stress the role of a lack of knowledge concerning elements (options, decisions, etc.) and point out the role of the opposing (complementing) elements. We also pay attention to the fact that it is not justified to talk about similarity when one has not enough knowledge about the compared objects/elements. Some novel measures of similarity are presented.","PeriodicalId":55209,"journal":{"name":"Control and Cybernetics","volume":"51 1","pages":"249 - 266"},"PeriodicalIF":0.0,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48446537","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 We consider Helmholtz problems in two and three dimensions. The topological sensitivity of a given cost function J(u∈) with respect to a small hole B∈ around a given point x0 ∈ B∈ ⊂ Ω depends on various parameters, like the frequency k chosen or certain material parameters or even the shape parameters of the hole B∈. These parameters are either deliberately chosen in a certain range, as, e.g., the frequencies, or are known only up to some bounds. The problem arises as to whether one can obtain a uniform design using the topological gradient. We show that for 2-d and 3-d Helmholtz problems such a robust design is achievable.
{"title":"On the robustness of the topological derivative for Helmholtz problems and applications","authors":"G. Leugering, A. Novotny, J. Sokołowski","doi":"10.2478/candc-2022-0015","DOIUrl":"https://doi.org/10.2478/candc-2022-0015","url":null,"abstract":"Abstract We consider Helmholtz problems in two and three dimensions. The topological sensitivity of a given cost function J(u∈) with respect to a small hole B∈ around a given point x0 ∈ B∈ ⊂ Ω depends on various parameters, like the frequency k chosen or certain material parameters or even the shape parameters of the hole B∈. These parameters are either deliberately chosen in a certain range, as, e.g., the frequencies, or are known only up to some bounds. The problem arises as to whether one can obtain a uniform design using the topological gradient. We show that for 2-d and 3-d Helmholtz problems such a robust design is achievable.","PeriodicalId":55209,"journal":{"name":"Control and Cybernetics","volume":"51 1","pages":"227 - 248"},"PeriodicalIF":0.0,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42323572","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 Moore-Gibson-Thompson [MGT] dynamics is considered. This third order in time evolution arises within the context of acoustic wave propagation with applications in high frequency ultrasound technology. The optimal boundary feedback control is constructed in order to have on-line regulation. The above requires wellposedness of the associated Algebraic Riccati Equation. The paper by Lasiecka and Triggiani (2022) recently contributed a comprehensive study of the Optimal Control Problem for the MGT-third order dynamics with boundary control, over an infinite time-horizon. A critical missing point in such a study is the issue of uniqueness (within a specific class) of the corresponding highly non-standard Algebraic Riccati Equation. The present note resolves this problem in the positive, thus completing the study of Lasiecka and Triggiani (2022) with the final goal of having on line feedback control, which is also optimal.
{"title":"Uniqueness of the Riccati operator of the non-standard ARE of a third order dynamics with boundary control","authors":"I. Lasiecka, R. Triggiani","doi":"10.2478/candc-2022-0013","DOIUrl":"https://doi.org/10.2478/candc-2022-0013","url":null,"abstract":"Abstract The Moore-Gibson-Thompson [MGT] dynamics is considered. This third order in time evolution arises within the context of acoustic wave propagation with applications in high frequency ultrasound technology. The optimal boundary feedback control is constructed in order to have on-line regulation. The above requires wellposedness of the associated Algebraic Riccati Equation. The paper by Lasiecka and Triggiani (2022) recently contributed a comprehensive study of the Optimal Control Problem for the MGT-third order dynamics with boundary control, over an infinite time-horizon. A critical missing point in such a study is the issue of uniqueness (within a specific class) of the corresponding highly non-standard Algebraic Riccati Equation. The present note resolves this problem in the positive, thus completing the study of Lasiecka and Triggiani (2022) with the final goal of having on line feedback control, which is also optimal.","PeriodicalId":55209,"journal":{"name":"Control and Cybernetics","volume":"51 1","pages":"171 - 189"},"PeriodicalIF":0.0,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48992078","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 In this short note, we outline the history of the Journal, present its recent developments, as well as changes that we are going through, with some attempt at sketching the plans for the future. Some illustrations are provided, concerning the publication statistics, especially with respect to the last 15 years.
{"title":"50 years of history, the present and the future","authors":"Z. Nahorski, J. Owsinski","doi":"10.2478/candc-2022-0008","DOIUrl":"https://doi.org/10.2478/candc-2022-0008","url":null,"abstract":"Abstract In this short note, we outline the history of the Journal, present its recent developments, as well as changes that we are going through, with some attempt at sketching the plans for the future. Some illustrations are provided, concerning the publication statistics, especially with respect to the last 15 years.","PeriodicalId":55209,"journal":{"name":"Control and Cybernetics","volume":"51 1","pages":"115 - 123"},"PeriodicalIF":0.0,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44713217","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 purpose of this paper is to provide sufficient conditions for the stabilizability of weak solutions of stochastic differential systems when both the drift and diffusion are affine in the control. This result extends the well–known theorem of Jurdjevic– Quinn (Jurdjevic and Quinn, 1978) to stochastic differential systems under weaker conditions on the system coefficients than those assumed in Florchinger (2002).
{"title":"A Jurdjevic-Quinn theorem for stochastic differential systems under weak conditions","authors":"P. Florchinger","doi":"10.2478/candc-2022-0002","DOIUrl":"https://doi.org/10.2478/candc-2022-0002","url":null,"abstract":"Abstract The purpose of this paper is to provide sufficient conditions for the stabilizability of weak solutions of stochastic differential systems when both the drift and diffusion are affine in the control. This result extends the well–known theorem of Jurdjevic– Quinn (Jurdjevic and Quinn, 1978) to stochastic differential systems under weaker conditions on the system coefficients than those assumed in Florchinger (2002).","PeriodicalId":55209,"journal":{"name":"Control and Cybernetics","volume":"51 1","pages":"21 - 29"},"PeriodicalIF":0.0,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48811998","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}
Amrita Bhadoriya, Mrudul Y. Jani, U. Chaudhari, Aniket C. Tadvi
Abstract This study investigates an inventory model for deteriorating products with a price and stock-dependent demand pattern where the holding cost is a non-linear function of both time and stock level. Moreover, a decreased price and a higher stock level lead to a higher rate of demand. Consequently, in this article, we present a new approach, aiming at maximization of the return on investment by maximizing the profit/cost ratio. If an inventory manager has the potential to invest in a variety of projects, but disposes of only limited resources, it is logical to strategically plan towards a better return on investment. As a result, the manager’s objective will be to develop an inventory policy with a possibly high return on investment. Therefore, a new strategy is considered in this article to optimize the profitability ratio in terms of replenishment time and selling price, which is determined as the proportion between the profit and the overall cost of the inventory scheme. This research demonstrates that optimizing the profitability ratio is equivalent to decreasing the average inventory cost of a product per unit. Also, the optimality is graphically checked and one numerical illustration is discussed to explain the result of the proposed model. Finally, sensitivity analysis of key parameters is performed to show the applicability of the proposed model. The profit/cost ratio is more sensitive to price elasticity markup or purchasing cost compared to the other parameters used. Also, for decision-makers, several helpful management insights are derived.
{"title":"A new approach to maximize the overall return on investment with price and stock dependent demand under the nonlinear holding cost","authors":"Amrita Bhadoriya, Mrudul Y. Jani, U. Chaudhari, Aniket C. Tadvi","doi":"10.2478/candc-2022-0006","DOIUrl":"https://doi.org/10.2478/candc-2022-0006","url":null,"abstract":"Abstract This study investigates an inventory model for deteriorating products with a price and stock-dependent demand pattern where the holding cost is a non-linear function of both time and stock level. Moreover, a decreased price and a higher stock level lead to a higher rate of demand. Consequently, in this article, we present a new approach, aiming at maximization of the return on investment by maximizing the profit/cost ratio. If an inventory manager has the potential to invest in a variety of projects, but disposes of only limited resources, it is logical to strategically plan towards a better return on investment. As a result, the manager’s objective will be to develop an inventory policy with a possibly high return on investment. Therefore, a new strategy is considered in this article to optimize the profitability ratio in terms of replenishment time and selling price, which is determined as the proportion between the profit and the overall cost of the inventory scheme. This research demonstrates that optimizing the profitability ratio is equivalent to decreasing the average inventory cost of a product per unit. Also, the optimality is graphically checked and one numerical illustration is discussed to explain the result of the proposed model. Finally, sensitivity analysis of key parameters is performed to show the applicability of the proposed model. The profit/cost ratio is more sensitive to price elasticity markup or purchasing cost compared to the other parameters used. Also, for decision-makers, several helpful management insights are derived.","PeriodicalId":55209,"journal":{"name":"Control and Cybernetics","volume":"51 1","pages":"91 - 108"},"PeriodicalIF":0.0,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43426211","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 In this paper, we consider a set-valued minimax fractional programming problem (MFP), where the objective as well as constraint maps are set-valued. We introduce the notion of ρ-cone arcwise connectedness of set-valued maps as a generalization of cone arcwise connected set-valued maps. We establish the sufficient Karush-Kuhn-Tucker (KKT) conditions for the existence of minimizers of the problem (MFP) under ρ-cone arcwise connectedness assumption. Further, we study the Mond-Weir (MWD), Wolfe (WD), and mixed (MD) types of duality models and prove the corresponding weak, strong, and converse duality theorems between the primal (MFP) and the corresponding dual problems under ρ-cone arcwise connectedness assumption.
{"title":"Set-valued minimax fractional programming problems under ρ-cone arcwise connectedness","authors":"K. Das","doi":"10.2478/candc-2022-0004","DOIUrl":"https://doi.org/10.2478/candc-2022-0004","url":null,"abstract":"Abstract In this paper, we consider a set-valued minimax fractional programming problem (MFP), where the objective as well as constraint maps are set-valued. We introduce the notion of ρ-cone arcwise connectedness of set-valued maps as a generalization of cone arcwise connected set-valued maps. We establish the sufficient Karush-Kuhn-Tucker (KKT) conditions for the existence of minimizers of the problem (MFP) under ρ-cone arcwise connectedness assumption. Further, we study the Mond-Weir (MWD), Wolfe (WD), and mixed (MD) types of duality models and prove the corresponding weak, strong, and converse duality theorems between the primal (MFP) and the corresponding dual problems under ρ-cone arcwise connectedness assumption.","PeriodicalId":55209,"journal":{"name":"Control and Cybernetics","volume":"51 1","pages":"43 - 69"},"PeriodicalIF":0.0,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43023067","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 There are several classes of decision-making problems that explicitly or implicitly prompt fractional programming problems. Portfolio selection problems, agricultural planning, information transfer, numerical analysis of stochastic processes, and resource allocation problems are just a few examples. The huge number of applications of minimax fractional programming problems inspired us to work on this topic. This paper is concerned with a nondifferentiable minimax fractional programming problem. We study a parametric dual model, corresponding to the primal problem, and derive the sufficient optimality condition for an optimal solution to the considered problem. Further, we obtain the various duality results under (p, r)-ρ-(η, θ)-invexity assumptions. Also, we identify a function lying exclusively in the class of (−1, 1)-ρ-(η, θ)-invex functions but not in the class of (1, −1)-invex functions and convex function already existing in the literature. We have given a non-trivial model of nondifferentiable minimax problem and obtained its optimal solution using optimality results derived in this paper.
{"title":"Sufficient optimality condition and duality of nondifferentiable minimax ratio constraint problems under (p, r)-ρ-(η, θ)-invexity","authors":"N. Kailey, Sonali Sethi, Shivani Saini","doi":"10.2478/candc-2022-0005","DOIUrl":"https://doi.org/10.2478/candc-2022-0005","url":null,"abstract":"Abstract There are several classes of decision-making problems that explicitly or implicitly prompt fractional programming problems. Portfolio selection problems, agricultural planning, information transfer, numerical analysis of stochastic processes, and resource allocation problems are just a few examples. The huge number of applications of minimax fractional programming problems inspired us to work on this topic. This paper is concerned with a nondifferentiable minimax fractional programming problem. We study a parametric dual model, corresponding to the primal problem, and derive the sufficient optimality condition for an optimal solution to the considered problem. Further, we obtain the various duality results under (p, r)-ρ-(η, θ)-invexity assumptions. Also, we identify a function lying exclusively in the class of (−1, 1)-ρ-(η, θ)-invex functions but not in the class of (1, −1)-invex functions and convex function already existing in the literature. We have given a non-trivial model of nondifferentiable minimax problem and obtained its optimal solution using optimality results derived in this paper.","PeriodicalId":55209,"journal":{"name":"Control and Cybernetics","volume":"51 1","pages":"71 - 89"},"PeriodicalIF":0.0,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43839322","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 parametric concept of equilibrium in a finite cooperative game of several players in a normal form is introduced. This concept is defined by the partitioning of a set of players into coalitions. Two extreme cases of such partitioning correspond to Pareto optimal and Nash equilibrium outcomes, respectively. The game is characterized by its matrix, in which each element is a subject for independent perturbations., i.e. a set of perturbing matrices is formed by a set of additive matrices, with two arbitrary Hölder norms specified independently in the outcome and criterion spaces. We undertake post-optimal analysis for the so-called stability kernel. The analytical expression for supreme levels of such perturbations is found. Numerical examples illustrate some of the pertinent cases.
{"title":"Stability kernel in finite games with perturbed payoffs","authors":"V. Emelichev, Y. Nikulin","doi":"10.2478/candc-2022-0001","DOIUrl":"https://doi.org/10.2478/candc-2022-0001","url":null,"abstract":"Abstract The parametric concept of equilibrium in a finite cooperative game of several players in a normal form is introduced. This concept is defined by the partitioning of a set of players into coalitions. Two extreme cases of such partitioning correspond to Pareto optimal and Nash equilibrium outcomes, respectively. The game is characterized by its matrix, in which each element is a subject for independent perturbations., i.e. a set of perturbing matrices is formed by a set of additive matrices, with two arbitrary Hölder norms specified independently in the outcome and criterion spaces. We undertake post-optimal analysis for the so-called stability kernel. The analytical expression for supreme levels of such perturbations is found. Numerical examples illustrate some of the pertinent cases.","PeriodicalId":55209,"journal":{"name":"Control and Cybernetics","volume":"51 1","pages":"6 - 20"},"PeriodicalIF":0.0,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42548257","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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