Pub Date : 2024-02-07DOI: 10.1007/s10700-024-09420-2
Romain Guillaume, Adam Kasperski, Paweł Zieliński
In this paper, an optimization problem with uncertain constraint coefficients is considered. Possibility theory is used to model the uncertainty. Namely, a joint possibility distribution in constraint coefficient realizations, called scenarios, is specified. This possibility distribution induces a necessity measure in a scenario set, which in turn describes an ambiguity set of probability distributions in a scenario set. The distributionally robust approach is then used to convert the imprecise constraints into deterministic equivalents. Namely, the left-hand side of an imprecise constraint is evaluated by using a risk measure with respect to the worst probability distribution that can occur. In this paper, the Conditional Value at Risk is used as the risk measure, which generalizes the strict robust, and expected value approaches commonly used in literature. A general framework for solving such a class of problems is described. Some cases which can be solved in polynomial time are identified.
{"title":"A framework of distributionally robust possibilistic optimization","authors":"Romain Guillaume, Adam Kasperski, Paweł Zieliński","doi":"10.1007/s10700-024-09420-2","DOIUrl":"https://doi.org/10.1007/s10700-024-09420-2","url":null,"abstract":"<p>In this paper, an optimization problem with uncertain constraint coefficients is considered. Possibility theory is used to model the uncertainty. Namely, a joint possibility distribution in constraint coefficient realizations, called scenarios, is specified. This possibility distribution induces a necessity measure in a scenario set, which in turn describes an ambiguity set of probability distributions in a scenario set. The distributionally robust approach is then used to convert the imprecise constraints into deterministic equivalents. Namely, the left-hand side of an imprecise constraint is evaluated by using a risk measure with respect to the worst probability distribution that can occur. In this paper, the Conditional Value at Risk is used as the risk measure, which generalizes the strict robust, and expected value approaches commonly used in literature. A general framework for solving such a class of problems is described. Some cases which can be solved in polynomial time are identified.</p>","PeriodicalId":55131,"journal":{"name":"Fuzzy Optimization and Decision Making","volume":"65 1","pages":""},"PeriodicalIF":4.7,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139769585","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-20DOI: 10.1007/s10700-023-09417-3
Tingqing Ye
Multivariate uncertain calculus is a branch of mathematics that deals with differentiation and integration of uncertain fields based on uncertainty theory. This paper defines partial derivatives of uncertain fields for the first time by putting forward the concept of Liu field. Then the fundamental theorem, chain rule and integration by parts of multivariate uncertain calculus are derived. Finally, this paper presents an uncertain partial differential equation, and gives its integral form.
{"title":"Partial derivatives of uncertain fields and uncertain partial differential equations","authors":"Tingqing Ye","doi":"10.1007/s10700-023-09417-3","DOIUrl":"https://doi.org/10.1007/s10700-023-09417-3","url":null,"abstract":"<p>Multivariate uncertain calculus is a branch of mathematics that deals with differentiation and integration of uncertain fields based on uncertainty theory. This paper defines partial derivatives of uncertain fields for the first time by putting forward the concept of Liu field. Then the fundamental theorem, chain rule and integration by parts of multivariate uncertain calculus are derived. Finally, this paper presents an uncertain partial differential equation, and gives its integral form.</p>","PeriodicalId":55131,"journal":{"name":"Fuzzy Optimization and Decision Making","volume":"3 4","pages":""},"PeriodicalIF":4.7,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138527256","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-19DOI: 10.1007/s10700-023-09418-2
Yuanguo Zhu
Uncertain partial differential equation (UPDE) was introduced in literature. But the solution of a UPDE was not defined well. In this article, we will rigorously give a suitable concept of a UPDE and define its solution by an integral equation. Then, some examples are given to show the rationality of the definition. Uncertain heat conduction equation is presented as an application of UPDE. For those UPDEs having no analytic solutions, (alpha)-path method is introduced to obtain the inverse uncertainty distributions of solutions to UPDEs.
{"title":"On uncertain partial differential equations","authors":"Yuanguo Zhu","doi":"10.1007/s10700-023-09418-2","DOIUrl":"https://doi.org/10.1007/s10700-023-09418-2","url":null,"abstract":"<p>Uncertain partial differential equation (UPDE) was introduced in literature. But the solution of a UPDE was not defined well. In this article, we will rigorously give a suitable concept of a UPDE and define its solution by an integral equation. Then, some examples are given to show the rationality of the definition. Uncertain heat conduction equation is presented as an application of UPDE. For those UPDEs having no analytic solutions, <span>(alpha)</span>-path method is introduced to obtain the inverse uncertainty distributions of solutions to UPDEs.</p>","PeriodicalId":55131,"journal":{"name":"Fuzzy Optimization and Decision Making","volume":"132 5","pages":""},"PeriodicalIF":4.7,"publicationDate":"2023-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138527220","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-03DOI: 10.1007/s10700-023-09416-4
Bice Cavallo, Jir̆í Mazurek, Jaroslav Ramík
Abstract Pairwise comparisons have been a long-standing technique for comparing alternatives/criteria and their role has been pivotal in the development of modern decision-making methods such as the Analytic Hierarchy/Network Process (AHP/ANP), the Best-Worst method (BWM), PROMETHEE and many others. Pairwise comparisons can be performed within several frameworks such as multiplicative, additive and fuzzy representations of preferences, which are particular instances of a more general framework based on Abelian linearly ordered groups. Though multiplicative, additive and fuzzy representations of preferences are widely used in practice, it is unknown whether decision makers are equally precise in the three aforementioned representations when they measure objective data. Therefore, the aim of this paper is to design, carry out and analyse an experiment with over 200 respondents (undergraduate university students) from two countries, Czechia and Italy, to compare precision of the respondents in all three representations. In the experiment, respondents pairwise compared (by approximation) the areas of four geometric figures and then, the imprecision of their assessments was measured by computing the distance with the exact pairwise comparisons. We grouped the respondents in such a way that each participant was allowed to deal with a unique type of representation. The outcomes of the experiment indicate that the multiplicative approach is the most precise.
{"title":"A comparative study on precision of pairwise comparison matrices","authors":"Bice Cavallo, Jir̆í Mazurek, Jaroslav Ramík","doi":"10.1007/s10700-023-09416-4","DOIUrl":"https://doi.org/10.1007/s10700-023-09416-4","url":null,"abstract":"Abstract Pairwise comparisons have been a long-standing technique for comparing alternatives/criteria and their role has been pivotal in the development of modern decision-making methods such as the Analytic Hierarchy/Network Process (AHP/ANP), the Best-Worst method (BWM), PROMETHEE and many others. Pairwise comparisons can be performed within several frameworks such as multiplicative, additive and fuzzy representations of preferences, which are particular instances of a more general framework based on Abelian linearly ordered groups. Though multiplicative, additive and fuzzy representations of preferences are widely used in practice, it is unknown whether decision makers are equally precise in the three aforementioned representations when they measure objective data. Therefore, the aim of this paper is to design, carry out and analyse an experiment with over 200 respondents (undergraduate university students) from two countries, Czechia and Italy, to compare precision of the respondents in all three representations. In the experiment, respondents pairwise compared (by approximation) the areas of four geometric figures and then, the imprecision of their assessments was measured by computing the distance with the exact pairwise comparisons. We grouped the respondents in such a way that each participant was allowed to deal with a unique type of representation. The outcomes of the experiment indicate that the multiplicative approach is the most precise.","PeriodicalId":55131,"journal":{"name":"Fuzzy Optimization and Decision Making","volume":"24 33","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135818602","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-01DOI: 10.1007/s10700-023-09415-5
Lu Yang, Yang Liu
{"title":"Solution method and parameter estimation of uncertain partial differential equation with application to China’s population","authors":"Lu Yang, Yang Liu","doi":"10.1007/s10700-023-09415-5","DOIUrl":"https://doi.org/10.1007/s10700-023-09415-5","url":null,"abstract":"","PeriodicalId":55131,"journal":{"name":"Fuzzy Optimization and Decision Making","volume":"1 1","pages":""},"PeriodicalIF":4.7,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43010805","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-08DOI: 10.1007/s10700-023-09413-7
Jin Peng, Bo Zhang, Lin Chen, Hui Li
{"title":"A survey on uncertain graph and uncertain network optimization","authors":"Jin Peng, Bo Zhang, Lin Chen, Hui Li","doi":"10.1007/s10700-023-09413-7","DOIUrl":"https://doi.org/10.1007/s10700-023-09413-7","url":null,"abstract":"","PeriodicalId":55131,"journal":{"name":"Fuzzy Optimization and Decision Making","volume":" ","pages":""},"PeriodicalIF":4.7,"publicationDate":"2023-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49462300","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-04DOI: 10.1007/s10700-023-09410-w
Yejun Xu, Dayong Wang
{"title":"Some methods to derive the priority weights from the best–worst method matrix and weight efficiency test in view of incomplete pairwise comparison matrix","authors":"Yejun Xu, Dayong Wang","doi":"10.1007/s10700-023-09410-w","DOIUrl":"https://doi.org/10.1007/s10700-023-09410-w","url":null,"abstract":"","PeriodicalId":55131,"journal":{"name":"Fuzzy Optimization and Decision Making","volume":" ","pages":""},"PeriodicalIF":4.7,"publicationDate":"2023-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44276367","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-02DOI: 10.1007/s10700-023-09412-8
F. Goodarzian, P. Ghasemi, A. Gunasekaran, A. Labib
{"title":"A fuzzy sustainable model for COVID-19 medical waste supply chain network","authors":"F. Goodarzian, P. Ghasemi, A. Gunasekaran, A. Labib","doi":"10.1007/s10700-023-09412-8","DOIUrl":"https://doi.org/10.1007/s10700-023-09412-8","url":null,"abstract":"","PeriodicalId":55131,"journal":{"name":"Fuzzy Optimization and Decision Making","volume":"1 1","pages":"1 - 35"},"PeriodicalIF":4.7,"publicationDate":"2023-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41718260","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Correction: Medical health resources allocation evaluation in public health emergencies by an improved ORESTE method with linguistic preference orderings","authors":"Xunjie Gou, Xinru Xu, Fumin Deng, Wei Zhou, Enrique Herrera-Viedma","doi":"10.1007/s10700-023-09414-6","DOIUrl":"https://doi.org/10.1007/s10700-023-09414-6","url":null,"abstract":"","PeriodicalId":55131,"journal":{"name":"Fuzzy Optimization and Decision Making","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135912572","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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