Pub Date : 2025-11-22DOI: 10.1016/j.fss.2025.109698
Matjaž Omladič , Martin Vuk , Aljaž Zalar
The recent survey [3] nicknamed “Hitchhiker’s Guide” has raised the rating of quasi-copula problems in the dependence modeling community in spite of the lack of statistical interpretation of quasi-copulas. In our previous work we addressed the question of extreme values of the mass distribution associated with a mutidimensional quasi–copulas. Using linear programming approach we were able to settle [3, Open Problem 5] up to and disprove a recent conjecture from [14] on solution to that problem. In this note we use an analytical approach to provide a complete answer to the original question.
{"title":"Extreme mass distributions for quasi-copulas","authors":"Matjaž Omladič , Martin Vuk , Aljaž Zalar","doi":"10.1016/j.fss.2025.109698","DOIUrl":"10.1016/j.fss.2025.109698","url":null,"abstract":"<div><div>The recent survey [3] nicknamed “Hitchhiker’s Guide” has raised the rating of quasi-copula problems in the dependence modeling community in spite of the lack of statistical interpretation of quasi-copulas. In our previous work we addressed the question of extreme values of the mass distribution associated with a mutidimensional quasi–copulas. Using linear programming approach we were able to settle <span><span>[3, Open Problem 5]</span></span> up to <span><math><mrow><mi>d</mi><mo>=</mo><mn>17</mn></mrow></math></span> and disprove a recent conjecture from [14] on solution to that problem. In this note we use an analytical approach to provide a complete answer to the original question.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"527 ","pages":"Article 109698"},"PeriodicalIF":2.7,"publicationDate":"2025-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145625041","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-22DOI: 10.1016/j.fss.2025.109700
Yi Shi , Hui Yang
Dress in 1984 introduced the concept of tight span of a metric space, allowing the space to be isometrically embedded into a larger metric space. This paper aims to extend this theory to fuzzy metric setting. More concretely, we define tight spans of fuzzy metric spaces as a key tool in the study of the appropriate extension. It is shown that any fuzzy metric space can be isometrically embedded into its tight span, with the embedding being an isomorphism when the fuzzy metric space is hyperconvex (or, equivalently, injective). Additionally, we explore tight extensions and essential extensions of fuzzy metric spaces, providing a precise formulation of their hyperconvex hulls and injective hulls.
{"title":"Tight spans of fuzzy metric spaces","authors":"Yi Shi , Hui Yang","doi":"10.1016/j.fss.2025.109700","DOIUrl":"10.1016/j.fss.2025.109700","url":null,"abstract":"<div><div>Dress in 1984 introduced the concept of tight span of a metric space, allowing the space to be isometrically embedded into a larger metric space. This paper aims to extend this theory to fuzzy metric setting. More concretely, we define tight spans of fuzzy metric spaces as a key tool in the study of the appropriate extension. It is shown that any fuzzy metric space can be isometrically embedded into its tight span, with the embedding being an isomorphism when the fuzzy metric space is hyperconvex (or, equivalently, injective). Additionally, we explore tight extensions and essential extensions of fuzzy metric spaces, providing a precise formulation of their hyperconvex hulls and injective hulls.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"527 ","pages":"Article 109700"},"PeriodicalIF":2.7,"publicationDate":"2025-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145694463","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-21DOI: 10.1016/j.fss.2025.109685
Nicolás Madrid, Manuel Ojeda-Aciego
We analyze the use of the composition of mappings as a fuzzy conjunction between indexes of inclusion. Instead of the general approach of the φ-index of inclusion, we consider a fresh approach that computes the φ-index of inclusion when restricted to a join-subsemilattice of indexes of inclusion. Under this restriction, we identify a certain join-subsemilattice which has a biresiduated structure when composition is interpreted as conjunction. The main consequence of this biresiduated structure is a representation theorem of biresiduated lattices on the unit interval in terms of the composition and subsets of indexes of inclusion.
{"title":"Composition as a fuzzy conjunction between indexes of inclusion","authors":"Nicolás Madrid, Manuel Ojeda-Aciego","doi":"10.1016/j.fss.2025.109685","DOIUrl":"10.1016/j.fss.2025.109685","url":null,"abstract":"<div><div>We analyze the use of the composition of mappings as a fuzzy conjunction between indexes of inclusion. Instead of the general approach of the φ-index of inclusion, we consider a fresh approach that computes the φ-index of inclusion when restricted to a join-subsemilattice of indexes of inclusion. Under this restriction, we identify a certain join-subsemilattice which has a biresiduated structure when composition is interpreted as conjunction. The main consequence of this biresiduated structure is a representation theorem of biresiduated lattices on the unit interval in terms of the composition and subsets of indexes of inclusion.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"527 ","pages":"Article 109685"},"PeriodicalIF":2.7,"publicationDate":"2025-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145694061","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-20DOI: 10.1016/j.fss.2025.109695
Ta Zhou , Yuanqing Yang , Wei Yan , Weiqin Liu , Xibei Yang , Weiping Ding , Jing Cai , Shitong Wang
Distant metastasis (DM) as a major cause of treatment failure of nasopharyngeal cancer (NPC) actually occurs with a considerably gradual development in the early stage. Therefore, an ideal DM prediction model should be an efficient and interpretable model and simultaneously reflect/simulate this characteristic during its training. Towards such a goal, this study proposes a hierarchical Takagi-Sugeno-Kang (TSK) fuzzy classifier (H-TSKFC) to assure both enhanced classification performance and diversified generation of interpretable fuzzy rules therein through full-partial-rule-transmission fusion for simulating gradual development of DM. Profiting from full-partial-rule-transmission fusion between sub-classifiers, H-TSKFC was endowed with the following benefits. Firstly, a novel stacking mechanism without any use of residuals between sub-classifiers enhances its generalization capability. Secondly, the generation of interpretable fuzzy rules from the second TSK fuzzy sub-classifier provides a diversified way. That is, its useful rules fusion transmitted fully or partially from previous sub-classifier guarantees considerable consistency between sub-classifiers, while its remaining rules reflect gradual difference between them. In this way, the H-TSKFC’s structure naturally mimics the gradual development of DM. Finally, each sub-classifier therein can be trained sequentially and quickly with an analytical solution to accomplish an individual prediction on the original inputs and outputs. Experimental results indeed demonstrate that H-TSKFC possesses linguistic interpretability, along with considerable classification and generalization performance.
{"title":"Fully & partially-transmitted-rule fusion: A novel hierarchical fuzzy classification with application to nasopharyngeal cancer’s metastasis prediction","authors":"Ta Zhou , Yuanqing Yang , Wei Yan , Weiqin Liu , Xibei Yang , Weiping Ding , Jing Cai , Shitong Wang","doi":"10.1016/j.fss.2025.109695","DOIUrl":"10.1016/j.fss.2025.109695","url":null,"abstract":"<div><div>Distant metastasis (DM) as a major cause of treatment failure of nasopharyngeal cancer (NPC) actually occurs with a considerably gradual development in the early stage. Therefore, an ideal DM prediction model should be an efficient and interpretable model and simultaneously reflect/simulate this characteristic during its training. Towards such a goal, this study proposes a hierarchical Takagi-Sugeno-Kang (TSK) fuzzy classifier (H-TSKFC) to assure both enhanced classification performance and diversified generation of interpretable fuzzy rules therein through full-partial-rule-transmission fusion for simulating gradual development of DM. Profiting from full-partial-rule-transmission fusion between sub-classifiers, H-TSKFC was endowed with the following benefits. Firstly, a novel stacking mechanism without any use of residuals between sub-classifiers enhances its generalization capability. Secondly, the generation of interpretable fuzzy rules from the second TSK fuzzy sub-classifier provides a diversified way. That is, its useful rules fusion transmitted fully or partially from previous sub-classifier guarantees considerable consistency between sub-classifiers, while its remaining rules reflect gradual difference between them. In this way, the H-TSKFC’s structure naturally mimics the gradual development of DM. Finally, each sub-classifier therein can be trained sequentially and quickly with an analytical solution to accomplish an individual prediction on the original inputs and outputs. Experimental results indeed demonstrate that H-TSKFC possesses linguistic interpretability, along with considerable classification and generalization performance.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"527 ","pages":"Article 109695"},"PeriodicalIF":2.7,"publicationDate":"2025-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145625047","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-19DOI: 10.1016/j.fss.2025.109664
Serafina Lapenta , Sebastiano Napolitano
We investigate the computational complexity of various satisfiability problems in Łukasiewicz logic, restricting attention to valuations in the standard MV-algebra [0,1]. Specifically, we focus on maximal r-satisfiability – the task of maximizing the number of formulas whose valuation is at least a given rational r ∈ (0, 1]. We also consider the decisional and weighted versions of this problem, as well as the partial (weighted) r-satisfiability problem.
{"title":"Computational complexity of some MaxSAT problems in Łukasiewicz logic","authors":"Serafina Lapenta , Sebastiano Napolitano","doi":"10.1016/j.fss.2025.109664","DOIUrl":"10.1016/j.fss.2025.109664","url":null,"abstract":"<div><div>We investigate the computational complexity of various satisfiability problems in Łukasiewicz logic, restricting attention to valuations in the standard MV-algebra [0,1]. Specifically, we focus on maximal <em>r</em>-satisfiability – the task of maximizing the number of formulas whose valuation is at least a given rational <em>r</em> ∈ (0, 1]. We also consider the decisional and weighted versions of this problem, as well as the partial (weighted) <em>r</em>-satisfiability problem.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"527 ","pages":"Article 109664"},"PeriodicalIF":2.7,"publicationDate":"2025-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145625042","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-19DOI: 10.1016/j.fss.2025.109676
Gleb Beliakov , Peiqi Sun , Jian-Zhang Wu
Random generation of fuzzy measures plays a pivotal role in large-scale decision-making and optimization that involve fuzzy integrals as a model to aggregate dependent inputs. We address the problem of random generation of fuzzy measures with specific additional constraints on their values and their combinations that reflect decision maker preferences. We present a range of approaches to handle sparse linear equality constraints and analyse their computational complexity. Some approaches involve random walks in the affine subspaces while others are based on projecting random points in an order polytope onto those affine spaces. We also examine special cases of linear constraints that arise in generation of k-additive fuzzy measures, and provide recommendations on the applicability of the approaches that we examined.
{"title":"Random projections of constrained fuzzy measures","authors":"Gleb Beliakov , Peiqi Sun , Jian-Zhang Wu","doi":"10.1016/j.fss.2025.109676","DOIUrl":"10.1016/j.fss.2025.109676","url":null,"abstract":"<div><div>Random generation of fuzzy measures plays a pivotal role in large-scale decision-making and optimization that involve fuzzy integrals as a model to aggregate dependent inputs. We address the problem of random generation of fuzzy measures with specific additional constraints on their values and their combinations that reflect decision maker preferences. We present a range of approaches to handle sparse linear equality constraints and analyse their computational complexity. Some approaches involve random walks in the affine subspaces while others are based on projecting random points in an order polytope onto those affine spaces. We also examine special cases of linear constraints that arise in generation of k-additive fuzzy measures, and provide recommendations on the applicability of the approaches that we examined.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"528 ","pages":"Article 109676"},"PeriodicalIF":2.7,"publicationDate":"2025-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145790848","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-19DOI: 10.1016/j.fss.2025.109684
Alessandro Gallo, Francesca Adele Giambona
Economic insecurity has gained increasing attention over the last decade, particularly in terms of its measurement and how it affects everyday life. This paper contributes to the literature on measurement by proposing a new individual-level, multidimensional index based on a fuzzy sets approach. The fuzzy logic moves beyond the classic binary framework of set theory, which classifies elements strictly as 0 or 1. In the fuzzy sets approach, each set is defined by a membership function that indicates the degree to which each element belongs to the set. This flexibility makes it particularly well suited for capturing complex socio-economic conditions such as economic insecurity. The proposed measure incorporates a range of economic insecurity indicators and offers some advantages. First, it produces an individual score that can be easily aggregated for geographical and socio-demographic comparisons. Second, the methodology allows for precise estimation of the variance, which is useful for assessing the reliability of aggregate estimates. The new index is applied to the Italian context using the most recent EU-SILC data. Aggregate estimates by region and socio-demographic group are derived and compared. Results indicate that the well-known North-South gradient persists and that economic insecurity is higher among the most disadvantaged sub-populations. In particular, individuals with low educational attainment and those who are unemployed or inactive experience the highest levels of economic insecurity.
{"title":"Measuring economic insecurity using a fuzzy sets approach","authors":"Alessandro Gallo, Francesca Adele Giambona","doi":"10.1016/j.fss.2025.109684","DOIUrl":"10.1016/j.fss.2025.109684","url":null,"abstract":"<div><div>Economic insecurity has gained increasing attention over the last decade, particularly in terms of its measurement and how it affects everyday life. This paper contributes to the literature on measurement by proposing a new individual-level, multidimensional index based on a fuzzy sets approach. The fuzzy logic moves beyond the classic binary framework of set theory, which classifies elements strictly as 0 or 1. In the fuzzy sets approach, each set is defined by a membership function that indicates the degree to which each element belongs to the set. This flexibility makes it particularly well suited for capturing complex socio-economic conditions such as economic insecurity. The proposed measure incorporates a range of economic insecurity indicators and offers some advantages. First, it produces an individual score that can be easily aggregated for geographical and socio-demographic comparisons. Second, the methodology allows for precise estimation of the variance, which is useful for assessing the reliability of aggregate estimates. The new index is applied to the Italian context using the most recent EU-SILC data. Aggregate estimates by region and socio-demographic group are derived and compared. Results indicate that the well-known North-South gradient persists and that economic insecurity is higher among the most disadvantaged sub-populations. In particular, individuals with low educational attainment and those who are unemployed or inactive experience the highest levels of economic insecurity.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"527 ","pages":"Article 109684"},"PeriodicalIF":2.7,"publicationDate":"2025-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145584369","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-19DOI: 10.1016/j.fss.2025.109673
Bo Xu , Changzhong Wang , Shuang An , Yang Huang
Fuzzy rough set theory offers an effective approach for feature selection; however, traditional methods lack an adaptive learning mechanism to adjust feature weights, making it difficult to accurately measure the contribution of each feature to classification. To address this issue, this paper introduces a novel dynamic optimization feature selection method based on maximum likelihood estimation. The method leverages the fuzzy similarity relation strategy from fuzzy rough sets to handle data uncertainty, while employing maximum likelihood estimation to assess feature importance. Specifically, the proposed model treats class labels as observed data and sample features as hidden variables, evaluating the classification ability of features by constructing a maximum likelihood function. Feature weights and class variances are integrated into the fuzzy similarity relation, and they are dynamically adjusted in accordance with the data characteristics through collaborative optimization. The inclusion degrees of samples are utilized to derive the empirical estimation of the conditional probability of classes relative to features. Finally, maximum likelihood estimation is applied to optimize the weighted features, assess their impact on the target variable, and select those that best explain the variation of the target variable. In this way, the model combines the strengths of fuzzy similarity relations in addressing uncertainty and the power of maximum likelihood estimation in parameter estimation, significantly enhancing the accuracy and robustness of feature selection. The experimental results show that the proposed algorithm has significant advantages over mainstream comparison methods on 18 benchmark data sets and provides a novel solution for feature selection in the field of uncertain data.
{"title":"Feature selection driven by maximum likelihood estimation and fuzzy similarity relation learning","authors":"Bo Xu , Changzhong Wang , Shuang An , Yang Huang","doi":"10.1016/j.fss.2025.109673","DOIUrl":"10.1016/j.fss.2025.109673","url":null,"abstract":"<div><div>Fuzzy rough set theory offers an effective approach for feature selection; however, traditional methods lack an adaptive learning mechanism to adjust feature weights, making it difficult to accurately measure the contribution of each feature to classification. To address this issue, this paper introduces a novel dynamic optimization feature selection method based on maximum likelihood estimation. The method leverages the fuzzy similarity relation strategy from fuzzy rough sets to handle data uncertainty, while employing maximum likelihood estimation to assess feature importance. Specifically, the proposed model treats class labels as observed data and sample features as hidden variables, evaluating the classification ability of features by constructing a maximum likelihood function. Feature weights and class variances are integrated into the fuzzy similarity relation, and they are dynamically adjusted in accordance with the data characteristics through collaborative optimization. The inclusion degrees of samples are utilized to derive the empirical estimation of the conditional probability of classes relative to features. Finally, maximum likelihood estimation is applied to optimize the weighted features, assess their impact on the target variable, and select those that best explain the variation of the target variable. In this way, the model combines the strengths of fuzzy similarity relations in addressing uncertainty and the power of maximum likelihood estimation in parameter estimation, significantly enhancing the accuracy and robustness of feature selection. The experimental results show that the proposed algorithm has significant advantages over mainstream comparison methods on 18 benchmark data sets and provides a novel solution for feature selection in the field of uncertain data.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"527 ","pages":"Article 109673"},"PeriodicalIF":2.7,"publicationDate":"2025-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145625045","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-17DOI: 10.1016/j.fss.2025.109683
Qian Hu , Jiapeng Bai , Jun Zhang , Yafei Song , Jusheng Mi
Outlier detection, as an important direction of data mining, aims to identify data objects that deviate from normal patterns and is widely used in fields such as financial fraud, network security, and medical diagnosis. Functioning as an essential tool in knowledge acquisition and data mining, granular computing provides a novel framework that emulates human cognitive patterns for resolving large-scale complex problems. However, traditional outlier detection methods based on granular computing are difficult to balance data diversity and fuzziness. Therefore, this article constructs an outlier detection model based on fuzzy neighborhood combination entropy using neighborhood fuzzy granules and combination entropy. Firstly, the fuzzy neighborhood combination entropy of the information system is defined, and the relative fuzzy neighborhood combination entropy of the object is defined by the change in neighborhood fuzzy entropy caused by the object. Secondly, the relative fuzzy cardinality of the object is defined by the difference degree between its fuzzy neighborhoods, and the anomaly factor of the object is measured by its relative fuzzy neighborhoods combination entropy and relative fuzzy cardinality. Then, an outlier detection model based on the combination entropy of fuzzy neighborhoods is constructed and the relevant algorithm is designed. Finally, the effectiveness and efficiency of the proposed method were verified through publicly available datasets.
{"title":"FNCEOD: Fuzzy neighborhood combination entropy-based outlier detection","authors":"Qian Hu , Jiapeng Bai , Jun Zhang , Yafei Song , Jusheng Mi","doi":"10.1016/j.fss.2025.109683","DOIUrl":"10.1016/j.fss.2025.109683","url":null,"abstract":"<div><div>Outlier detection, as an important direction of data mining, aims to identify data objects that deviate from normal patterns and is widely used in fields such as financial fraud, network security, and medical diagnosis. Functioning as an essential tool in knowledge acquisition and data mining, granular computing provides a novel framework that emulates human cognitive patterns for resolving large-scale complex problems. However, traditional outlier detection methods based on granular computing are difficult to balance data diversity and fuzziness. Therefore, this article constructs an outlier detection model based on fuzzy neighborhood combination entropy using neighborhood fuzzy granules and combination entropy. Firstly, the fuzzy neighborhood combination entropy of the information system is defined, and the relative fuzzy neighborhood combination entropy of the object is defined by the change in neighborhood fuzzy entropy caused by the object. Secondly, the relative fuzzy cardinality of the object is defined by the difference degree between its fuzzy neighborhoods, and the anomaly factor of the object is measured by its relative fuzzy neighborhoods combination entropy and relative fuzzy cardinality. Then, an outlier detection model based on the combination entropy of fuzzy neighborhoods is constructed and the relevant algorithm is designed. Finally, the effectiveness and efficiency of the proposed method were verified through publicly available datasets.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"526 ","pages":"Article 109683"},"PeriodicalIF":2.7,"publicationDate":"2025-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145580332","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-16DOI: 10.1016/j.fss.2025.109677
José R. González de Mendívil , Zorana Jančić , Aitor González de Mendívil Grau , Ivana Micić , Stefan Stanimirović
Minimization of fuzzy deterministic finite automata (FDfAs) is a challenging problem due to two main reasons. First, the graded nature of transitions and state memberships makes traditional minimization techniques difficult to apply. Second, a minimal FDfA is not necessarily unique, as multiple equivalent FDfAs of the same size may exist. In this paper, we focus on finding a polynomial-time minimization method that constructs a minimal FDfA for a given FDfA. Our approach is based on establishing isomorphisms between well-known polynomial-time constructions, providing a mathematical foundation for the proposed method. Specifically, we introduce the notion of quasi-deterministic fuzzy finite automata (QDFfAs) and explore their isomorphism properties with the Myhill-Nerode automaton of a fuzzy language. We show that the determinization via factorization of a QDFfA preserves strong isomorphism with the generalized Myhill-Nerode automaton of the recognized fuzzy language. This insight enables the development of an efficient minimization method by leveraging the interpretable backward replica of an FDfA.
{"title":"Quasi-deterministic fuzzy automata: Isomorphisms and fuzzy deterministic automata minimization","authors":"José R. González de Mendívil , Zorana Jančić , Aitor González de Mendívil Grau , Ivana Micić , Stefan Stanimirović","doi":"10.1016/j.fss.2025.109677","DOIUrl":"10.1016/j.fss.2025.109677","url":null,"abstract":"<div><div>Minimization of fuzzy deterministic finite automata (FDfAs) is a challenging problem due to two main reasons. First, the graded nature of transitions and state memberships makes traditional minimization techniques difficult to apply. Second, a minimal FDfA is not necessarily unique, as multiple equivalent FDfAs of the same size may exist. In this paper, we focus on finding a polynomial-time minimization method that constructs a minimal FDfA for a given FDfA. Our approach is based on establishing isomorphisms between well-known polynomial-time constructions, providing a mathematical foundation for the proposed method. Specifically, we introduce the notion of quasi-deterministic fuzzy finite automata (QDFfAs) and explore their isomorphism properties with the Myhill-Nerode automaton of a fuzzy language. We show that the determinization via factorization of a QDFfA preserves strong isomorphism with the generalized Myhill-Nerode automaton of the recognized fuzzy language. This insight enables the development of an efficient minimization method by leveraging the interpretable backward replica of an FDfA.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"527 ","pages":"Article 109677"},"PeriodicalIF":2.7,"publicationDate":"2025-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145584368","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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