Search Results (18)

The objective of this study is to measure T2* relaxation time in the triangular fibrocartilage (TFC) disc in asymptomatic volunteers and evaluate its variation with factors such as age, hand dominance, sex, and ulnar variance, using a dedicated MRI sequence. The MRI protocol included anatomical sequences as well as a 3D ultra-short echo time (UTE)-T2* mapping sequence. A linear regression model was used to assess the potential influence of age, sex, and hand dominance on T2* values measured in the TFC disc and to evaluate the correlation between T2* values and ulnar variance. T2* relaxation time was positively correlated with age. The higher T2* relaxation times may reflect early degeneration of the fibrocartilage microstructure, which is associated with both biomechanical factors and the aging process. However, T2* was not significantly influenced by sex or hand dominance, nor was it correlated with ulnar variance (this later being limited by the fact that none of our subject had positive ulnar variance). In conclusion, UTE-T2* is a promising MRI technique showing positive correlation with age in the TFC of healthy subjects. These findings are a first step to establish normative T2* values and will help interpreting deviations observed in patient with suspected pathology in future studies. Full article

In this paper, we explore the application of fuzzy set theory in the context of triangular norms, with a focus on strong Sheffer stroke NMV-algebras. We introduce the concepts of $\mathfrak{T}$-fuzzy subalgebras and $\mathfrak{T}$-fuzzy filters, analyze their properties, and provide several illustrative examples. Our study demonstrates that $\mathfrak{T}$-fuzzy subalgebras and filters generalize classical subalgebras and filters, with level subsets preserving algebraic structures under t-norms. Notably, $\mathfrak{T}$-fuzzy sets exhibit strong closure properties, and homomorphisms between SSNMV-algebras extend naturally to fuzzy settings. Furthermore, we examine the relationships between $\mathfrak{T}$-fuzzy subalgebras (or filters) and their classical counterparts, as well as their corresponding level subsets and homomorphisms. These results contribute to refined uncertainty modeling in logical systems, with potential applications in fuzzy control and AI. Full article

The avionics network supports high-safety-level flight operations, with the analysis of transmission failures serving as a crucial means for its safety evaluation. Due to the time-dependent nature of the failure probability in avionics networks, traditional constant and unchangeable probability values can deviate from the actual situation under specific conditions. This deviation may lead to inadequate responses to occasional events and potentially cause flight accidents. A Dynamic Fault Tree (DFT) model for civil aircraft avionics network transmission failures, based on an optimized extended fuzzy algorithm, is introduced in this paper. Initially focusing on event correlations, a DFT is established for the transmission failure of the Avionics Full Duplex Switched Ethernet (AFDX). Subsequently, considering the variations between events, triangular fuzzy processing is applied to the event failure rates based on relative confidence levels. Finally, by optimizing the weakest t-norm operator, the failure probability intervals are aggregated and the fuzzy scale is regulated. Experimental results demonstrate that, compared to the static-minimum t-norm and traditional weakest t-norm methods, the proposed approach enhances the accuracy of the fuzzy failure probability intervals by 66.15% and 40.59%, respectively. Concurrently, it maintains consistency in the ranking of event importance, highlighting the superior effectiveness of the proposed method in analyzing transmission failures in avionics networks. Full article

Machine learning and image processing are closely related fields that have undergone major development and application in recent years. Machine learning algorithms are being used to develop sophisticated techniques for analyzing and interpreting images, such as object detection, image classification, and image segmentation. One important aspect of image processing is the ability to compare and measure the similarity between different images by providing a way to quantify the similarity between images using various features such as contrast, luminance, and structure. Generally, the flexibility of similarity measures enables fine-tuning the comparison process to achieve the desired outcomes. This is while the existing similarity measures are not flexible enough to address diverse and comprehensive practical aspects. To this end, we utilize triangular norms (t-norms) to construct an inclusive class of similarity measures in this article. As is well-known, each t-norm possesses distinctive attributes that allow for novel interpretations of image similarities. The proposed class of t-norm-based structural similarity measures offers numerous options for decisionmakers to consider various issues and interpret results more broadly in line with their objectives. For more details, in the Experiments section, the proposed method is applied to grayscale and binarized images and a specific experiment related to meteorology. Eventually, the presented diverse case studies confirm the efficiency and key features of the t-norm-based structural similarity. Full article

There are some drawbacks to arithmetic and logic operations of general discrete fuzzy numbers, which limit their application. For example, the result of the addition operation of general discrete fuzzy numbers defined by the Zadeh’s extension principle may not satisfy the condition of becoming a discrete fuzzy number. In order to solve these problems, special discrete fuzzy numbers on countable sets are investigated in this paper. Since the representation theorem of fuzzy numbers is the basic tool of fuzzy analysis, two kinds of representation theorems of special discrete fuzzy numbers on countable sets are studied first. Then, the metrics of special discrete fuzzy numbers on countable sets are defined, and the relationship between these metrics and the uniform Hausdorff metric (i.e., supremum metric) of general fuzzy numbers is discussed. In addition, the triangular norm and triangular conorm operations (t-norm and t-conorm for short) of special discrete fuzzy numbers on countable sets are presented, and the properties of these two operators are proven. We also prove that these two operators satisfy the basic conditions for closure of operation and present some examples. Finally, the applications of special discrete fuzzy numbers on countable sets in image fusion and aggregation of subjective evaluation are proposed. Full article

An unmanned aerial vehicle (UAV)-integrated control system is a set of functionally independent subsystems of the ground and space segments interacting with each other under the conditions of the stochastic nature of the external environment. There is an approach to evaluating its effectiveness based on a generalized multiplicative criterion, which takes into account the features of this system to the maximum extent. It is proposed to single out two particular criteria that characterize the reliability of a UAV and the effectiveness of the control system in relation to it. At the same time, the generalized criterion is a multiplicative convolution based not on the triangular-norm (t-norm) of the particular criterion, but of its correspondence functions, which in a certain way reflect its significance. It is shown that in the particular case of linear dependence of the correspondence functions, the generalized criterion coincides with the classical multiplicative convolution in the form of product of event probabilities. The proposed approach with minimal changes can be adapted to assess the effectiveness of data management systems in heterogeneous networks, process control systems, projects, logistics, etc. Full article

This paper reveals some relations between fuzzy logic and quantum logic on partial residuated implications (PRIs) induced by partial t-norms as well as proposes partial residuated monoids (PRMs) and partial residuated lattices (PRLs) by defining partial adjoint pairs. First of all, we introduce the connection between lattice effect algebra and partial t-norms according to the concept of partial t-norms given by Borzooei, together with the proof that partial operation in any commutative quasiresiduated lattice is partial t-norm. Then, we offer the general form of PRI and the definition of partial fuzzy implication (PFI), give the condition that partial residuated implication is a fuzzy implication, and prove that each PRI is a PFI. Next, we propose PRLs, study their basic characteristics, discuss the correspondence between PRLs and lattice effect algebras (LEAs), and point out the relationship between LEAs and residuated partial algebras. In addition, like the definition of partial t-norms, we provide the notions of partial triangular conorms (partial t-conorms) and corresponding partial co-residuated lattices (PcRLs). Lastly, based on partial residuated lattices, we define well partial residuated lattices (wPRLs), study the filter of well partial residuated lattices, and then construct quotient structure of PRMs. Full article

To evaluate fuzzy information precisely, researchers and practitioners are apt to use linguistic variables to model vague or uncertain contexts in natural language. In this paper, some new operation laws for continuous linguistic terms using strict t-norms and t-conorms are defined. Significantly, these operation laws have some desirable properties and are closed on the restricted continuous linguistic term set. On the basis of these new linguistic operation laws, a series of triangular t-(co)norm-based linguistic generalized power geometric operators are developed. In order to consider the interactive influence and interrelationship of decision makers (DMs) and attributes, a decision-making trial and evaluation laboratory (DEMATEL)-based method for linguistic multiple attributes group decision making (MAGDM) is proposed. In the method, the weighting information for DMs and attributes are dependent on the initial direct-relation matrices among DMs and attributes, respectively. Finally, a numerical example is provided. In comparison with the existing methods, two aspects of the DEMATEL-based method for linguistic MAGDM in the work can be highlighted: the underlying operators for linguistic terms using strict t-norms and t-conorms that are closed on the set of the restricted continuous linguistic term set; and the techniques in determining the weighting information, with which the weighting information for DMs and attributes are determined by the interactive influence and interrelationship among DMs or attributes. Full article

Dombi t-norm (DTN) and t-conorm (TCN) are among the most effective triangular norms in fuzzy systems for aggregation purposes. The environment of interval-valued intuitionistic fuzzy (IVIF) set gives us precision in expressing uncertain information by using a membership grade (MG) and non-membership grade (NMG) in the form of closed subintervals of $\left[0, 1\right]$. The goal of this paper is to introduce DTN-based aggregation operators (AOs) for IVIF numbers (IVIFNs) and study their performance in the evaluation of the worth of energy recourses to be opted in Pakistan to deal with the energy crises situation. We first introduced some DTN and TCN-based operations for IVIFNs and developed two new AOs known as IVIF Dombi weighted averaging (IVIFDWA) and IVIF Dombi weighted geometric (IVIFDWG) operators. The validity and fitness of the proposed operators are tested. A case study is presented where the energy resources of Pakistan are discussed and the problem of the selection of sustainable energy resources in the context of Pakistan is investigated. The sensitivity analysis of the proposed IVIFDWA and IVIFDWG operators is studied and a comparative analysis of the current work with previous studies is established. Full article

In some multi-attribute decision-making (MADM) models studying attributes’ interactive phenomena is very important for the minimizing decision risks. Usually, the Choquet integral type aggregations are considered in such problems. However, the Choquet integral aggregations do not consider all attributes’ interactions; therefore, in many cases, when these interactions are revealed in less degree, they do not perceive these interactions and their utility in MADM problems is less useful. For the decision of this problem, we create the Choquet integral-based new aggregation operators’ family which considers all pair interactions between attributes. The problem under the discrimination q-rung picture linguistic and q-rung orthopair fuzzy environments is considered. Construction of a 2-order additive fuzzy measure (TOAFM) involves pair interaction indices and importance values of attributes of a MADM model. Based on the attributes’ pair interactions for the identification of associated probabilities of a 2-order additive fuzzy measure, the Shapley entropy maximum principle is used. The associated probabilities q-rung picture linguistic weighted averaging (APs-q-RPLWA) and the associated probabilities q-rung picture linguistic weighted geometric (APs-q-RPLWG) aggregation operators are constructed with respect to TOAFM. For an uncertainty pole of experts’ evaluations on attributes regarding the possible alternatives, the associated probabilities of a fuzzy measure are used. The second pole of experts’ evaluations as arguments of the aggregation operators by discrimination q-rung picture linguistic values is presented. Discrimination q-rung picture linguistic evaluations specify the attribute’s dominant, neutral and non-dominant impacts on the selection of concrete alternative from all alternatives. Constructed operators consider the all relatedness between attributes in any consonant attribute structure. Main properties on the rightness of extensions are showed: APs-q-RPLWA and APs-q-RPLWG operators match with q-rung picture linguistic Choquet integral averaging and geometric operators for the lower and upper capacities of order two. The conjugation among the constructed operators is also considered. Connections between the new operators and the compositions of dual triangular norms $\left(T_p,S_p^q\right)$ and $(T_{\min },S_{\max })$ are also constructed. Constructed operators are used in evaluation of a selection reliability index (SRI) of candidate service centers in the facility location selection problem, when small degree interactions are observed between attributes. In example MADM, the difference in optimal solutions is observed between the Choquet integral aggregation operators and their new extensions. The difference, however, is due to the need to use indices of all interactions between attributes. Full article

In mathematics, distance and similarity are known as dual concepts. However, the concept of similarity is interpreted as fuzzy similarity or T-equivalence relation, where T is a triangular norm (t-norm in brief), when we discuss a fuzzy environment. Dealing with multi-polarity in practical examples with fuzzy data leadsus to introduce a new concept called m-polar $\mathbf{T}$-equivalence relations based on a finitely multivalued t-norm $\mathbf{T}$, and to study the metric behavior of such relations. First, we study the new operators including the m-polar triangular norm $\mathbf{T}$ and conorm $\mathbf{S}$ as well as m-polar implication $\mathbf{I}$ and m-polar negation $\mathbf{N}$, acting on the Cartesian product of $[0,1]$m-times.Then, using the m-polar negations $\mathbf{N}$, we provide a method to construct a new type of metric spaces, called m-polar $\mathbf{S}$-pseudo-ultrametric, from the m-polar $\mathbf{T}$-equivalences, and reciprocally for constructing m-polar $\mathbf{T}$-equivalences based on the m-polar $\mathbf{S}$-pseudo-ultrametrics. Finally, the link between fuzzy graphs and m-polar $\mathbf{S}$-pseudo-ultrametrics is considered. An algorithm is designed to plot a fuzzy graph based on the m-polar ${\mathbf{S}}_L$-pseudo-ultrametric, where ${\mathbf{S}}_L$ is the m-polar Lukasiewicz t-conorm, and is illustrated by a numerical example which verifies our method. Full article

The max-Łukasiewicz algebra describes fuzzy systems working in discrete time which are based on two binary operations: the maximum and the Łukasiewicz triangular norm. The behavior of such a system in time depends on the solvability of the corresponding bounded parametric max-linear system. The aim of this study is to describe an algorithm recognizing for which values of the parameter the given bounded parametric max-linear system has a solution—represented by an appropriate state of the fuzzy system in consideration. Necessary and sufficient conditions of the solvability have been found and a polynomial recognition algorithm has been described. The correctness of the algorithm has been verified. The presented polynomial algorithm consists of three parts depending on the entries of the transition matrix and the required state vector. The results are illustrated by numerical examples. The presented results can be also applied in the study of the max-Łukasiewicz systems with interval coefficients. Furthermore, Łukasiewicz arithmetical conjunction can be used in various types of models, for example, in cash-flow system. Full article

Biometrics is a scientific technology to recognize a person using their physical, behavior or chemical attributes. Biometrics is nowadays widely being used in several daily applications ranging from smart device user authentication to border crossing. A system that uses a single source of biometric information (e.g., single fingerprint) to recognize people is known as unimodal or unibiometrics system. Whereas, the system that consolidates data from multiple biometric sources of information (e.g., face and fingerprint) is called multimodal or multibiometrics system. Multibiometrics systems can alleviate the error rates and some inherent weaknesses of unibiometrics systems. Therefore, we present, in this study, a novel score level fusion-based scheme for multibiometric user recognition system. The proposed framework is hinged on Asymmetric Aggregation Operators (Asym-AOs). In particular, Asym-AOs are estimated via the generator functions of triangular norms (t-norms). The extensive set of experiments using seven publicly available benchmark databases, namely, National Institute of Standards and Technology (NIST)-Face, NIST-Multimodal, IIT Delhi Palmprint V1, IIT Delhi Ear, Hong Kong PolyU Contactless Hand Dorsal Images, Mobile Biometry (MOBIO) face, and Visible light mobile Ocular Biometric (VISOB) iPhone Day Light Ocular Mobile databases have been reported to show efficacy of the proposed scheme. The experimental results demonstrate that Asym-AOs based score fusion schemes not only are able to increase authentication rates compared to existing score level fusion methods (e.g., min, max, t-norms, symmetric-sum) but also is computationally fast. Full article

Neutrosophic triangular norms (t-norms) and their residuated lattices are not only the main research object of neutrosophic set theory, but also the core content of neutrosophic logic. Neutrosophic implications are important operators of neutrosophic logic. Neutrosophic residual implications based on neutrosophic t-norms can be applied to the fields of neutrosophic inference and neutrosophic control. In this paper, neutrosophic t-norms, neutrosophic residual implications, and the residuated lattices derived from neutrosophic t-norms are investigated deeply. First of all, the lattice and its corresponding system are proved to be a complete lattice and a De Morgan algebra, respectively. Second, the notions of neutrosophic t-norms are introduced on the complete lattice discussed earlier. The basic concepts and typical examples of representable and non-representable neutrosophic t-norms are obtained. Naturally, De Morgan neutrosophic triples are defined for the duality of neutrosophic t-norms and neutrosophic t-conorms with respect to neutrosophic negators. Third, neutrosophic residual implications generated from neutrosophic t-norms and their basic properties are investigated. Furthermore, residual neutrosophic t-norms are proved to be infinitely ∨-distributive, and then some important properties possessed by neutrosophic residual implications are given. Finally, a method for producing neutrosophic t-norms from neutrosophic implications is presented, and the residuated lattices are constructed on the basis of neutrosophic t-norms and neutrosophic residual implications. Full article

In this paper, a new concept of the triangular neutrosophic cubic fuzzy numbers (TNCFNs), their score and accuracy functions are introduced. Based on TNCFNs, some new Einstein aggregation operators, such as the triangular neutrosophic cubic fuzzy Einstein weighted averaging (TNCFEWA), triangular neutrosophic cubic fuzzy Einstein ordered weighted averaging (TNCFEOWA) and triangular neutrosophic cubic fuzzy Einstein hybrid weighted averaging (TNCFEHWA) operators are developed. Furthermore, their application to multiple-attribute decision-making with triangular neutrosophic cubic fuzzy (TNCF) information is discussed. Finally, a practical example is given to verify the developed approach and to demonstrate its practicality and effectiveness. Full article