Pub Date : 2026-06-15Epub Date: 2026-02-12DOI: 10.1016/j.fss.2026.109820
S. Pallavi, N. Sakthivel, C.A. Suruthi Sri
This work emphasizes the synchronization issue for discrete complex dynamical networks (CDNs) with parameter uncertainties, nonlinearities, and quantization via the Takagi - Sugeno (T-S) fuzzy theory. Specifically, the uncertainties factor in the network are assumed to be linear fractional form. A proportional retarded controller is devised which assures the addressed network model is asymptotically synchronized with a minimum passive disturbance attenuation level. By designing proper time-dependent Lyapunov-Krasovskii functional (LKF) with triple summation terms and utilizing Jensen inequality, the adequate criteria are established and its denoted by linear matrix inequalities (LMIs). Then the desired retarded controller gains can be precisely computed by resolving the developed LMI using the Matlab software. Finally, the numerical simulations are applied to account for the applicability of the obtained theoretical results.
{"title":"Passivity-based synchronization of discrete fuzzy quantized complex dynamical networks with linear fractional uncertainties","authors":"S. Pallavi, N. Sakthivel, C.A. Suruthi Sri","doi":"10.1016/j.fss.2026.109820","DOIUrl":"10.1016/j.fss.2026.109820","url":null,"abstract":"<div><div>This work emphasizes the synchronization issue for discrete complex dynamical networks (CDNs) with parameter uncertainties, nonlinearities, and quantization via the Takagi - Sugeno (T-S) fuzzy theory. Specifically, the uncertainties factor in the network are assumed to be linear fractional form. A proportional retarded controller is devised which assures the addressed network model is asymptotically synchronized with a minimum passive disturbance attenuation level. By designing proper time-dependent Lyapunov-Krasovskii functional (LKF) with triple summation terms and utilizing Jensen inequality, the adequate criteria are established and its denoted by linear matrix inequalities (LMIs). Then the desired retarded controller gains can be precisely computed by resolving the developed LMI using the Matlab software. Finally, the numerical simulations are applied to account for the applicability of the obtained theoretical results.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"533 ","pages":"Article 109820"},"PeriodicalIF":2.7,"publicationDate":"2026-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386209","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 : 2026-06-15Epub Date: 2026-02-12DOI: 10.1016/j.fss.2026.109819
Federico Bacchi , Laura Neri
The implications of population decline have been widely examined in the literature, with particular attention to rural, mountain, and peripheral areas. Most research in the field relies on approaches that measure depopulation by imposing fixed thresholds or by classifying geographical areas as “declining” versus “non-declining”. Such methods suffer from several shortcomings, including the arbitrariness of cut-off values, the treatment of depopulation as a dichotomous phenomenon, and the neglect of the timing and persistence of decline. To address these limitations, this study proposes the Composite Fuzzy Demographic Index (CFDI), defined as the convex combination of two components: one based on the log-differences of the demographic variable P between two subsequent time points, and the other on the persistence of the decreasing state of P. The computation of these components involves a time-weight vector that increases with time proximity and accounts for the variability of P across different time points. The proposed methodology is applied to census data on the resident population of Italian municipalities between 1951 and 2021. Results show that the CFDI produces spatial patterns consistent with established evidence on depopulation, confirming its empirical validity. At the same time, the proposed index uncovers novel insights that traditional threshold-based measures fail to capture.
{"title":"Measuring population decline through a composite fuzzy index: Evidence from Italian municipalities","authors":"Federico Bacchi , Laura Neri","doi":"10.1016/j.fss.2026.109819","DOIUrl":"10.1016/j.fss.2026.109819","url":null,"abstract":"<div><div>The implications of population decline have been widely examined in the literature, with particular attention to rural, mountain, and peripheral areas. Most research in the field relies on approaches that measure depopulation by imposing fixed thresholds or by classifying geographical areas as “declining” versus “non-declining”. Such methods suffer from several shortcomings, including the arbitrariness of cut-off values, the treatment of depopulation as a dichotomous phenomenon, and the neglect of the timing and persistence of decline. To address these limitations, this study proposes the Composite Fuzzy Demographic Index (CFDI), defined as the convex combination of two components: one based on the log-differences of the demographic variable <em>P</em> between two subsequent time points, and the other on the persistence of the decreasing state of <em>P</em>. The computation of these components involves a time-weight vector that increases with time proximity and accounts for the variability of <em>P</em> across different time points. The proposed methodology is applied to census data on the resident population of Italian municipalities between 1951 and 2021. Results show that the CFDI produces spatial patterns consistent with established evidence on depopulation, confirming its empirical validity. At the same time, the proposed index uncovers novel insights that traditional threshold-based measures fail to capture.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"533 ","pages":"Article 109819"},"PeriodicalIF":2.7,"publicationDate":"2026-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386206","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 : 2026-06-15Epub Date: 2026-02-06DOI: 10.1016/j.fss.2026.109816
Sare Alinia Jildani , Hamzeh Agahi , S. Mansour Vaezpour
This paper identifies an error in Propositions 3.13 and 3.14 of Zhang et al. [1], which claims linearity for pseudo-integrals under arbitrary measurable functions. We provide counterexamples demonstrating its invalidity for semirings of Case I and Case III. Corrected versions are established under comonotonicity conditions, while Case II remains valid without restrictions. This clarification enhances mathematical rigor in pseudo-operations theory.
本文指出了Zhang et al.[1]的命题3.13和3.14中的一个错误，该命题声称任意可测函数下伪积分是线性的。我们提供了反例来证明它对于情形1和情形3的半分割是无效的。修正版本是在共单调条件下建立的，而情形II仍然有效，没有限制。这种澄清增强了伪运算理论的数学严谨性。
{"title":"Some notes on the pseudo-integrals based on pseudo-operations","authors":"Sare Alinia Jildani , Hamzeh Agahi , S. Mansour Vaezpour","doi":"10.1016/j.fss.2026.109816","DOIUrl":"10.1016/j.fss.2026.109816","url":null,"abstract":"<div><div>This paper identifies an error in Propositions 3.13 and 3.14 of Zhang et al. [1], which claims linearity for pseudo-integrals under arbitrary measurable functions. We provide counterexamples demonstrating its invalidity for semirings of Case I and Case III. Corrected versions are established under comonotonicity conditions, while Case II remains valid without restrictions. This clarification enhances mathematical rigor in pseudo-operations theory.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"533 ","pages":"Article 109816"},"PeriodicalIF":2.7,"publicationDate":"2026-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146175487","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 : 2026-06-15Epub Date: 2026-02-18DOI: 10.1016/j.fss.2026.109836
Ziyu Wang , Meng Han , Yiming Han , Ge Guo , Zhengsong Wang
In this paper, the controller design of positive interval Type-2 polynomial fuzzy-model-based (PIT2PFMB) systems is investigated, where the PIT2PFMB open-loop system and the controller are permitted to employ distinct premise membership functions. While this premise mismatch enhances controller design flexibility, it introduces conservatism when analyzing stability via Lyapunov stability theory. To mitigate this conservatism, an advanced membership function dependent analysis method is proposed: type-reduction parameters are modeled as system symbolic variables, with their information, together with other information of membership functions, incorporated into the stability conditions. This approach expands the stability regions of the systems. During the type-reduction implementation of the interval Type-2 (IT2) fuzzy controller, the gradient descent approach is employed to optimize the embedded type-1 membership functions of the controllers, thereby improving the control performance. Simulation results will demonstrate the effectiveness of the proposed methodology in expanding the stability region and improving control performance.
{"title":"Improvement of controller design for positive polynomial fuzzy systems based on symbolic analysis and optimization of reduced-Order parameters of interval type-2 membership functions","authors":"Ziyu Wang , Meng Han , Yiming Han , Ge Guo , Zhengsong Wang","doi":"10.1016/j.fss.2026.109836","DOIUrl":"10.1016/j.fss.2026.109836","url":null,"abstract":"<div><div>In this paper, the controller design of positive interval Type-2 polynomial fuzzy-model-based (PIT2PFMB) systems is investigated, where the PIT2PFMB open-loop system and the controller are permitted to employ distinct premise membership functions. While this premise mismatch enhances controller design flexibility, it introduces conservatism when analyzing stability via Lyapunov stability theory. To mitigate this conservatism, an advanced membership function dependent analysis method is proposed: type-reduction parameters are modeled as system symbolic variables, with their information, together with other information of membership functions, incorporated into the stability conditions. This approach expands the stability regions of the systems. During the type-reduction implementation of the interval Type-2 (IT2) fuzzy controller, the gradient descent approach is employed to optimize the embedded type-1 membership functions of the controllers, thereby improving the control performance. Simulation results will demonstrate the effectiveness of the proposed methodology in expanding the stability region and improving control performance.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"533 ","pages":"Article 109836"},"PeriodicalIF":2.7,"publicationDate":"2026-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386251","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 : 2026-06-15Epub Date: 2026-02-14DOI: 10.1016/j.fss.2026.109823
Liang Cao , Qixia Shen , Yan Lei , Xingjian Sun , Ziyao Pan
A fast finite-time fuzzy adaptive decentralized control strategy is developed for nonlinear interconnected systems under output saturation and time-varying input delays. Firstly, a new auxiliary signal is designed based on fast finite-time theory to counteract the impact of unknown input delay, and the constructed auxiliary signal satisfies fast finite-time stability. Secondly, under the influence of output saturation, a smooth function and fuzzy logic system are introduced to offset the impact of the interconnection term. Then, the dynamic surface technology is integrated in the backstepping technique to avoid the issue of “complexity of explosion”. Finally, the designed Lyapunov functions are used to ensure that all closed-loop signals are fast finite-time stable, although the errors do not absolutely converge to the origin, they can converge into a small neighborhood of the origin. The effectiveness of the designed scheme is validated via simulation results.
{"title":"Fast finite-time fuzzy control for interconnected systems under input delay and output saturation","authors":"Liang Cao , Qixia Shen , Yan Lei , Xingjian Sun , Ziyao Pan","doi":"10.1016/j.fss.2026.109823","DOIUrl":"10.1016/j.fss.2026.109823","url":null,"abstract":"<div><div>A fast finite-time fuzzy adaptive decentralized control strategy is developed for nonlinear interconnected systems under output saturation and time-varying input delays. Firstly, a new auxiliary signal is designed based on fast finite-time theory to counteract the impact of unknown input delay, and the constructed auxiliary signal satisfies fast finite-time stability. Secondly, under the influence of output saturation, a smooth function and fuzzy logic system are introduced to offset the impact of the interconnection term. Then, the dynamic surface technology is integrated in the backstepping technique to avoid the issue of “complexity of explosion”. Finally, the designed Lyapunov functions are used to ensure that all closed-loop signals are fast finite-time stable, although the errors do not absolutely converge to the origin, they can converge into a small neighborhood of the origin. The effectiveness of the designed scheme is validated via simulation results.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"533 ","pages":"Article 109823"},"PeriodicalIF":2.7,"publicationDate":"2026-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386208","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 : 2026-06-15Epub Date: 2026-02-20DOI: 10.1016/j.fss.2026.109835
Ji-Jing Lu, Xiao-Heng Chang
This paper addresses the challenge of nonfragile filtering for networked Takagi-Sugeno (T-S) fuzzy systems subject to hybrid network-induced constraints, including limited communication bandwidth and signal quantization. A multipath dynamic quantization strategy is applied to both measurement and estimated outputs to mitigate quantization effects, while a weighted try-once-discard (WTOD) protocol is employed to schedule data transmission and reduce network congestion. By integrating the scheduling protocol and filter design within a unified co-design framework, we formulate the problem as a nonfragile filtering task under nonideal communication. Using an enhanced Lyapunov-Krasovskii functional approach and average dwell-time (ADT) technique, we derive delay-dependent stability criteria that ensure the resulting filtering error system (FES) is asymptotically stable with a prescribed disturbance attenuation level. The proposed filter is not only robust against external disturbances but also nonfragile to slight variations in its own implementation gains. Simulations on a tunnel diode circuit model validate the proposed method, demonstrating enhanced estimation accuracy and superior performance compared to prior approaches.
{"title":"Protocol-scheduled nonfragile H∞ filtering for networked T-S fuzzy systems with multipath quantization","authors":"Ji-Jing Lu, Xiao-Heng Chang","doi":"10.1016/j.fss.2026.109835","DOIUrl":"10.1016/j.fss.2026.109835","url":null,"abstract":"<div><div>This paper addresses the challenge of nonfragile <span><math><msub><mi>H</mi><mi>∞</mi></msub></math></span> filtering for networked Takagi-Sugeno (T-S) fuzzy systems subject to hybrid network-induced constraints, including limited communication bandwidth and signal quantization. A multipath dynamic quantization strategy is applied to both measurement and estimated outputs to mitigate quantization effects, while a weighted try-once-discard (WTOD) protocol is employed to schedule data transmission and reduce network congestion. By integrating the scheduling protocol and filter design within a unified co-design framework, we formulate the problem as a nonfragile <span><math><msub><mi>H</mi><mi>∞</mi></msub></math></span> filtering task under nonideal communication. Using an enhanced Lyapunov-Krasovskii functional approach and average dwell-time (ADT) technique, we derive delay-dependent stability criteria that ensure the resulting filtering error system (FES) is asymptotically stable with a prescribed <span><math><msub><mi>H</mi><mi>∞</mi></msub></math></span> disturbance attenuation level. The proposed filter is not only robust against external disturbances but also nonfragile to slight variations in its own implementation gains. Simulations on a tunnel diode circuit model validate the proposed method, demonstrating enhanced estimation accuracy and superior <span><math><msub><mi>H</mi><mi>∞</mi></msub></math></span> performance compared to prior approaches.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"533 ","pages":"Article 109835"},"PeriodicalIF":2.7,"publicationDate":"2026-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386253","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 : 2026-06-15Epub Date: 2026-02-04DOI: 10.1016/j.fss.2026.109803
Liming Ding , Shen Yan , Yue Cai
Nowadays, the closed-loop glucose-insulin system or artificial pancreas system is becoming an effective and popular insulin therapy for diabetic patients. However, with the integration of extra intelligent devices like communication networks and insulin infusion pumps, some practical constraints on these devices will degrade the therapy effect and even cause serious health problems. In order to improve its practice and reliability, this research is concerned with the secure adaptive fault-tolerant control of networked T-S fuzzy glucose-insulin systems in the presence of insulin pump fault and attack by using an event-triggered protocol and a state observer. First, a T-S fuzzy modeling method is employed to cope with the system nonlinear dynamics and make it easy to be analyzed by using the existing linear system methods. Second, in order to conserve the limited communication bandwidth, an improved dynamic adaptive event-triggered protocol is proposed. This scheme has two merits, the one is that a dynamic triggering threshold is constructed to regulate the releasing frequency along with the system evolution adaptively. The other is that an internal variable related to the traditional triggering condition is introduced to enlarge the event interval. Third, to overcome the state constraint issue and realize the state feedback control, a dynamic state observer by introducing an auxiliary variable related to the integration of the estimation error is designed to get more precise observed state. Fourth, to improve the system reliability and security against the insulin pump with loss of effectiveness fault and malicious attack signal, a secure adaptive fault-tolerant control strategy is constructed based on the observer state, the estimation of the fault factor obtained by an adaptive law and the approximation of the unknown attack signal by an neural network-based attack estimator. Then, resorting to Lyapunov approach, several sufficient co-design conditions of the controller and observer gains and the triggering matrix are derived in terms of linear matrix inequalities. Finally, some comparison simulations are executed to illustrate the advantages of the proposed strategy over some existing methods.
{"title":"Secure adaptive fault-tolerant control of networked T-S fuzzy glucose-insulin system against pump fault and attack under dynamic adaptive event-trigger and dynamic observer","authors":"Liming Ding , Shen Yan , Yue Cai","doi":"10.1016/j.fss.2026.109803","DOIUrl":"10.1016/j.fss.2026.109803","url":null,"abstract":"<div><div>Nowadays, the closed-loop glucose-insulin system or artificial pancreas system is becoming an effective and popular insulin therapy for diabetic patients. However, with the integration of extra intelligent devices like communication networks and insulin infusion pumps, some practical constraints on these devices will degrade the therapy effect and even cause serious health problems. In order to improve its practice and reliability, this research is concerned with the secure adaptive fault-tolerant control of networked T-S fuzzy glucose-insulin systems in the presence of insulin pump fault and attack by using an event-triggered protocol and a state observer. First, a T-S fuzzy modeling method is employed to cope with the system nonlinear dynamics and make it easy to be analyzed by using the existing linear system methods. Second, in order to conserve the limited communication bandwidth, an improved dynamic adaptive event-triggered protocol is proposed. This scheme has two merits, the one is that a dynamic triggering threshold is constructed to regulate the releasing frequency along with the system evolution adaptively. The other is that an internal variable related to the traditional triggering condition is introduced to enlarge the event interval. Third, to overcome the state constraint issue and realize the state feedback control, a dynamic state observer by introducing an auxiliary variable related to the integration of the estimation error is designed to get more precise observed state. Fourth, to improve the system reliability and security against the insulin pump with loss of effectiveness fault and malicious attack signal, a secure adaptive fault-tolerant control strategy is constructed based on the observer state, the estimation of the fault factor obtained by an adaptive law and the approximation of the unknown attack signal by an neural network-based attack estimator. Then, resorting to Lyapunov approach, several sufficient co-design conditions of the controller and observer gains and the triggering matrix are derived in terms of linear matrix inequalities. Finally, some comparison simulations are executed to illustrate the advantages of the proposed strategy over some existing methods.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"533 ","pages":"Article 109803"},"PeriodicalIF":2.7,"publicationDate":"2026-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146175486","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 : 2026-06-15Epub Date: 2026-02-18DOI: 10.1016/j.fss.2026.109834
Stanislav Basarik , Lenka Halčinová , Barbora Hennelová , Ondrej Hutník , Mária Slovinská
We investigate the concept of generalized level measures within the discrete setting and explore their relationship with the standard level measure by providing necessary and sufficient conditions under which these two functions coincide. Building on this foundation, we develop a comprehensive calculus for the generalized Choquet integral on the discrete universe, defined in terms of the generalized level measure. When restricted to symmetric monotone measures, we introduce a novel class of operators: an extension of OWA operators, based on conditional aggregation operators. This new formulation enables a more flexible approach to data aggregation, preserving the essence of OWA while introducing additional functionality through conditional dependencies. We further examine the fundamental properties of this extended framework and establish its relationship with the traditional OWA operator.
{"title":"Generalized level measures, discrete Choquet-like integrals and conditional OWA operators","authors":"Stanislav Basarik , Lenka Halčinová , Barbora Hennelová , Ondrej Hutník , Mária Slovinská","doi":"10.1016/j.fss.2026.109834","DOIUrl":"10.1016/j.fss.2026.109834","url":null,"abstract":"<div><div>We investigate the concept of generalized level measures within the discrete setting and explore their relationship with the standard level measure by providing necessary and sufficient conditions under which these two functions coincide. Building on this foundation, we develop a comprehensive calculus for the generalized Choquet integral on the discrete universe, defined in terms of the generalized level measure. When restricted to symmetric monotone measures, we introduce a novel class of operators: an extension of OWA operators, based on conditional aggregation operators. This new formulation enables a more flexible approach to data aggregation, preserving the essence of OWA while introducing additional functionality through conditional dependencies. We further examine the fundamental properties of this extended framework and establish its relationship with the traditional OWA operator.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"533 ","pages":"Article 109834"},"PeriodicalIF":2.7,"publicationDate":"2026-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386249","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 : 2026-06-15Epub Date: 2026-02-19DOI: 10.1016/j.fss.2026.109824
Ting-hai Zhang , Feng Qin , Jie Wan , Wenhuang Li
In this work, we extend the existing ordinal sum constructions of fuzzy negations and fuzzy Sheffer strokes, which are based on the standard negation, to general ordinal sum structures derived from arbitrary negations. We also establish equivalent characterizations of their fundamental properties. Building upon this foundation and leveraging the completeness of the fuzzy Sheffer stroke, which provides a robust theoretical basis for designing fuzzy logic operators, we construct general ordinal sum structures for overlap (grouping) functions and pseudo-quasi overlap (grouping) functions. In these novel constructions, the range of function values within each summand interval is extended from the summand interval itself to an interval determined jointly by the summand interval and an arbitrary automorphism or quasi automorphism. Similarly, the function values outside the summand intervals are generalized from the identity mapping to an automorphism or quasi automorphism on [0,1]. This approach not only generalizes the existing corresponding ordinal sum structures but also substantially broadens their scope, thereby offering new perspectives for developing richer and more flexible ordinal sum constructions for other fuzzy logic operators.
{"title":"General ordinal sums of (pseudo-quasi) overlap and grouping functions","authors":"Ting-hai Zhang , Feng Qin , Jie Wan , Wenhuang Li","doi":"10.1016/j.fss.2026.109824","DOIUrl":"10.1016/j.fss.2026.109824","url":null,"abstract":"<div><div>In this work, we extend the existing ordinal sum constructions of fuzzy negations and fuzzy Sheffer strokes, which are based on the standard negation, to general ordinal sum structures derived from arbitrary negations. We also establish equivalent characterizations of their fundamental properties. Building upon this foundation and leveraging the completeness of the fuzzy Sheffer stroke, which provides a robust theoretical basis for designing fuzzy logic operators, we construct general ordinal sum structures for overlap (grouping) functions and pseudo-quasi overlap (grouping) functions. In these novel constructions, the range of function values within each summand interval is extended from the summand interval itself to an interval determined jointly by the summand interval and an arbitrary automorphism or quasi automorphism. Similarly, the function values outside the summand intervals are generalized from the identity mapping to an automorphism or quasi automorphism on [0,1]. This approach not only generalizes the existing corresponding ordinal sum structures but also substantially broadens their scope, thereby offering new perspectives for developing richer and more flexible ordinal sum constructions for other fuzzy logic operators.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"533 ","pages":"Article 109824"},"PeriodicalIF":2.7,"publicationDate":"2026-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386254","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 : 2026-06-15Epub Date: 2026-01-29DOI: 10.1016/j.fss.2026.109796
Mustafa Demirci
Ω⋆-lax objects, providing a categorical framework for fuzzy sets on structured sets, are generalization of L-fuzzy sets in an abstract category C on the basis of a fixed partially ordered object Ω⋆. One of the main objectives of this paper is to exhibit how they are used to define the notions of fuzzy sets on fuzzy sets, fuzzy sets on sets with fuzzy equalities and fuzzy sets on typed sets and to investigate some categorical properties of Ω⋆-lax objects. Categorical many-valued functions are special Ω⋆-lax objects that enable us to formulate the notions of fuzzy functions between sets with the same kind of structures. It is another main objective of this paper to study them. Referring to a symmetric, partially ordered Ω-monoidal relation system Υ on C having a symmetric, closed monoidal structure, we formalize categorical many-valued functions as Υ-functions and give their some basic properties. Furthermore, the results are applied to fuzzy functions between two sets, two fuzzy sets, two sets with fuzzy equalities, two typed sets.
{"title":"Lax objects and categorical many-valued functions","authors":"Mustafa Demirci","doi":"10.1016/j.fss.2026.109796","DOIUrl":"10.1016/j.fss.2026.109796","url":null,"abstract":"<div><div>Ω<sup>⋆</sup>-lax objects, providing a categorical framework for fuzzy sets on structured sets, are generalization of <em>L</em>-fuzzy sets in an abstract category <strong>C</strong> on the basis of a fixed partially ordered object Ω<sup>⋆</sup>. One of the main objectives of this paper is to exhibit how they are used to define the notions of fuzzy sets on fuzzy sets, fuzzy sets on sets with fuzzy equalities and fuzzy sets on typed sets and to investigate some categorical properties of Ω<sup>⋆</sup>-lax objects. Categorical many-valued functions are special Ω<sup>⋆</sup>-lax objects that enable us to formulate the notions of fuzzy functions between sets with the same kind of structures. It is another main objective of this paper to study them. Referring to a symmetric, partially ordered Ω-monoidal relation system Υ on <strong>C</strong> having a symmetric, closed monoidal structure, we formalize categorical many-valued functions as Υ-functions and give their some basic properties. Furthermore, the results are applied to fuzzy functions between two sets, two fuzzy sets, two sets with fuzzy equalities, two typed sets.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"533 ","pages":"Article 109796"},"PeriodicalIF":2.7,"publicationDate":"2026-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146175575","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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