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Multidimensional fuzzy sets (MFS) is a new extension of fuzzy sets on which the membership values of an element in the universe of discourse are increasingly ordered vectors on the set of real numbers in the interval [ 0 , 1 ]. This paper aims to investigate fuzzy negations on the set of increasingly ordered vectors on [ 0 , 1 ] , i.e. on L ∞ ([ 0 , 1 ]) , MFN in short, with respect to some partial order. In this paper we study partial orders, giving special attention to admissible orders on L n ([ 0 , 1 ]) and L ∞ ([ 0 , 1 ]). In addition, we study the possibility of existence of strong multidimensional fuzzy negations and some properties and methods to construct such operators. In particular, we define the ordinal sums of n-dimensional negations and ordinal sums of multidimensional fuzzy negations on a multidimensional product order. A multi-attribute group decision making algorithm is presented. [ABSTRACT FROM AUTHOR]

Picture fuzzy C-means clustering is a novel computational intelligence method that has some advantages over fuzzy clustering in pattern analysis and machine intelligence. However, picture fuzzy clustering is easily affected by noise and weighting exponent, which seriously limits its widespread application. To address this issue, this paper proposes a new robust possibilistic clustering method called "interval type-2 possibilistic picture C-means clustering with local information". This method combines interval type-2 fuzzy sets with possibilistic C-means clustering based on picture fuzzy sets, strengthening the noise resistance of picture fuzzy clustering. Firstly, this paper creatively extends an improved possibilistic clustering with double weighing exponents to picture fuzzy sets, solving the problem of consistency clustering in existing possibilistic picture clustering. Second, this paper originally introduces a new picture local information factor in possibilistic picture clustering and further enhances the anti-noise robustness of the method by using spatial possibilistic picture partition information. Finally, this paper skillfully extends this clustering method to interval type-2 fuzzy sets, which can handle more flexibly high-order uncertainties than type-1 clustering method. Experimental results indicate that this proposed method has better segmentation performance and stronger noise suppression ability compared with existing picture fuzzy clustering and interval type-2 fuzzy clustering. In summary, this work has made significant contributions to the development of picture fuzzy clustering theory and its applications. [ABSTRACT FROM AUTHOR]

Regarding the defects of Ruspini partition-based clustering in revealing the intrinsic correlation between classes, this paper proposes a series of generalized multiplicative fuzzy possibilistic product partition clustering algorithms. First, based on the existing concept of generalized multiplicative intuitionistic fuzzy sets, this paper introduces a new concept of generalized multiplicative fuzzy sets and further defines the corresponding multiplicative fuzzy partition. Then, based on the concept of multiplicative fuzzy partition, a novel generalized multiplicative fuzzy possibilistic product partition C-means (GMFPCM) clustering algorithm is presented, and its local convergence is strictly proved using Zangwill's theorem. Meanwhile, a robust Gaussian-base radial kernel based on the M-estimator is introduced into the GMFPCM algorithm to improve its robustness against noise and outliers in numerical data. Additionally, a multiplicative fuzzy possibilistic local information factor is constructed and embedded into the GMFPCM algorithm to strengthen its ability to suppress noise in images. Finally, the comparison with existing fuzzy possibilistic clustering algorithms in the literature confirms the competitiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

In the subjective evaluation process, the hesitant fuzzy set (HFS), as a convenient and robust presentation tool, cannot only suitably address the decision makers' (DMs') or experts' hesitant and uncertain issues but also can arise the dimension curse puzzle. Furthermore, the decision-making result is just derived according to the given objective and subjective information, without considering the DM's subjective evaluation and the environment's dynamic influence. Unlike the previous studies, this paper tries to address them from the deep learning viewpoint. To this end, we first define the non-equidimensional HFS (NHFS) and then introduce the equidimensional and classification characters into the NHFS to further develop the equidimensional HFS (EHFS) and the EHFS with the optimal classification result. Then, the equidimensional hesitant fuzzy-generative adversarial network (EHF-GAN) model is proposed to transform the hesitant fuzzy information from the non-equidimensional to the equidimensional form. The generalization and the convergence of the new model are proven to show the models' reasonability. In addition, the double-learning algorithm of the EHF-GAN model is designed, which can fuse the DMs' dynamic judgments and derive the optimal decision-making results. Lastly, this paper applies the proposed model and algorithm to an illustrative example of the new smart city enterprises and then shows their feasibility and effectiveness. [ABSTRACT FROM AUTHOR]

This paper presents a novel approach for predicting and explaining instances of Information Disorder. The paper reports two significant findings: i) the use of structures of opposition to describe relationships between instances of Information Disorder, and ii) the development of an explainable prediction method that combines Fuzzy Rough Sets and TOPSIS with these structures. The findings have the potential to assist analysts and decision-makers in gaining a deeper understanding of the phenomenon of Information Disorder. The results are based on real data and demonstrate promising applications for future research. [ABSTRACT FROM AUTHOR]

This paper shows that a bipolar-valued fuzzy set and a special interval-valued fuzzy set, whose cut-off point of left and right ends of the interval-valued membership is λ (0 < λ < 1) , are identical from a mathematical point of view. All results on bipolar-valued fuzzy sets can be obtained by corresponding results of interval-valued fuzzy sets or fuzzy sets. This paper does not completely reject bipolar-valued fuzzy sets, but points the way for such research. [ABSTRACT FROM AUTHOR]

• Criteria system construction for selecting GRID suppliers. • Introduction of novel fuzzy sets (SVZs, SVZPRs) combining Z-numbers and CST. • Improved efficiency of S-BWM through SVZPR extension. • Development of TOPSIS with SVZs combining TOPSIS and CST. • Enhancement of decision reliability through PageRank integration in SMCDM. Firms need a reliable decision-making framework to select suppliers who are Green, Resilient, and embrace Inclusive Development (GRID). However, GRID supplier selection is challenged by events that are uncertain and often dependent. Such events affect supplier rankings in a fuzzy decision environment. This paper builds a GRID-based criteria system and applies an enhanced Best Worst Method (BWM) and Technique for Order Preferencing using the Similarity to the Ideal Solution (TOPSIS), with Scenario-Varying Z-numbers (SVZs) and reversed PageRank. The decision criteria are extracted from the literature and confirmed by expert judgement. The SVZs and SVZ Preference Relations (SVZPRs) are developed by combining the Concept of Stratification Theory (CST) with Z-numbers, to reflect the impact of Dependent Uncertain Events (DUEs). Reverse PageRank is then used to find the occurrence probability of the scenarios due to DUEs. BWM is applied in an SVZPR environment to obtain the weights of the decision criteria. TOPSIS, incorporating SVZs, is used to rank the suppliers. An example is used to highlight the enhanced BWM-TOPSIS, to find the priority ranking of the GRID weights. Comparative and sensitivity analyses are conducted to validate the proposed method. [ABSTRACT FROM AUTHOR]

Among the multi-source data clustering tasks, there is a kind of frequently encountered tasks where only one of the multi-source datasets is available for sake of privacy and other reasons. The only available dataset is called local dataset, and the other are called external datasets. The horizontal collaborative fuzzy clustering (HCFC) model is a typical one that can deal with such clustering tasks. In HCFC, each external dataset is used through the knowledge mined from it rather than itself. The knowledge expressed as a knowledge partition matrix is fused into the clustering process of the local dataset. Reviewing the existing HCFC models, we can find three issues that need improvement. Firstly, the existing HCFC models quantify the collaboration contribution of each external knowledge by a hyperparameter at dataset-level, and moreover, do not distinguish the collaboration contributions of objects in the same external dataset. This may lead to counterintuitive clustering results. Focused on this issue, this paper proposes an enhanced HCFC (EHCFC) algorithm that extends the collaboration from dataset-level to object-level, and assigns different weights to objects based on the information amount provided by objects. Through EHCFC, a more flexible collaboration and a more intuitive clustering result can be reached. Secondly, the collaboration mechanisms of the existing HCFC models require that the dimensionalities of the partition matrices of external datasets and local dataset are the same, which makes the HCFC algorithms unable to work in many real situations. Focused on this limitation, a knowledge adaption mechanism based on relative entropy and spectral clustering is proposed resulting in a further refined EHCFC-KA algorithm, i.e., EHCFC with knowledge adaption. The proposed knowledge adaption mechanism makes both the HCFC algorithms and the EHCFC algorithm effective and successful in more application scenarios. Finally, we define two indexes in terms of consistency (the consistency of the clustering result with external knowledge) to evaluate the performance of collaborative clustering. Experiments on synthetic datasets and UCI public datasets demonstrate that the proposed EHCFC and EHCFC-KA algorithms outperform the existing HCFC algorithms and achieve significantly better intuitive collaborative clustering performance. [ABSTRACT FROM AUTHOR]

This paper proposes a variable-type hierarchical fuzzy system (VTHFS) with high accuracy and strong interpretability. An improved rear-part direct-connected structure is used in the VTHFS, which eliminates the intermediate variables of the hierarchical fuzzy system (HFS). A new feature sorting method is proposed to find suitable input variables for each layer of subsystems of VTHFS. Under the proposed topology structure, layer by layer training of VTHFS can be achieved by changing the expected output of each layer, thereby reducing residual errors layer by layer and improving the prediction accuracy of VTHFS. Three fuzzy set distribution constraints are used in parameter optimization of VTHFS to improve the interpretability, including integrity, distinguishability, and footprint of uncertainty. The type of fuzzy set is automatically adjusted according to the uncertainty characteristics of input data measured by fuzziness, which further enhances the semantic interpretability of the VTHFS and solves the problem of requiring prior knowledge to define the fuzzy set type in existing research. Finally, the proposed VTHFS is tested on the regression data sets in the real world. Experimental results demonstrate the effectiveness of the feature sorting method and the fuzzy set type adjustment method. Through a large number of quantitative indicators, it can be confirmed that VTHFS has stronger interpretability and higher prediction accuracy compared to other fuzzy systems. [ABSTRACT FROM AUTHOR]

A rule-based system is a widely used artificial intelligence system that employs a set of rules to make decisions. The belief rule-based (BRB) classification system is an extension of fuzzy rule-based (FRB) system that handles uncertainty and imprecision in classification tasks by incorporating Dempster-Shafer evidence theory and fuzzy set theory. However, the BRB classification system suffers from the combinatorial explosion and high time complexity problems. To solve these issues, the fuzzy unordered rule induction algorithm (FURIA) is introduced into the BRB classification systems to design a novel BRB classification system in this paper. FURIA is computationally less complex and has superior classification performance. The proposed system outperforms BRB classification systems in terms of classification performance and significantly reduces the number of rules and conditions. Furthermore, the proposed system offers a more effective solution than FURIA. To evaluate the validity and superiority of the proposed system, we conduct two classification experiments, comparing it with five traditional classifiers and seven rule-based systems, respectively, in terms of classification performance and interpretability. [ABSTRACT FROM AUTHOR]

Evidential likelihood-based inference is a new approach to statistical inference in which the relative likelihood function is interpreted as a possibility distribution. By expressing new data as a function of the parameter and a random variable with known probability distribution, one then defines a random fuzzy set and an associated predictive belief function representing uncertain knowledge about future observations. In this paper, this approach is applied to binomial and multinomial regression. In the binomial case, the predictive belief function can be computed by numerically integrating the possibility distribution of the posterior probability. In the multinomial case, the solution is obtained by a combination of constrained nonlinear optimization and Monte Carlo simulation. In both cases, computations can be considerably simplified using a normal approximation to the relative likelihood. Numerical experiments show that decision rules based on predictive belief functions make it possible to reach lower error rates for different rejection rates, as compared to decisions based on posterior probabilities. [ABSTRACT FROM AUTHOR]

Multi-label feature selection based on fuzzy rough sets, as a key step of multi-label data preprocessing, has been widely concerned by scholars in recent years. Most of the existing multi-label feature selection algorithms directly treat labels as logical labels and use a single distance metric to describe similarity. However, the variability of label descriptions and the limitations of a single distance measure should not be overlooked. In this paper, we propose a fuzzy rough set model with metric learning and label enhancement. Specifically, we use a kernel membership label enhancement algorithm based on JS divergence to convert logical labels into numerical labels, which not only reflects the importance of different labels, but also takes into account the differences in label distribution. In addition, a multi-metric learning algorithm is proposed for multi-label learning, in which the metric distance function under the label space and feature space can be learned autonomously. Then, based on the proposed model, we propose a novel multi-label feature selection algorithm based on metric learning and fuzzy rough sets. On this basis, a fast multi-label feature selection algorithm is further designed to improve the computational efficiency. In the experiments, compared with other nine algorithms on real-world datasets, the results show the superiority of the proposed algorithm. [ABSTRACT FROM AUTHOR]

The criterion fuzzy concept refers to a fuzzy set that represents the decision-maker's subjective preference for each criterion within the universe of criteria. Addressing the challenge of ranking all alternatives based on a given criterion fuzzy concept is a novel research direction in the field of fuzzy multi-criteria ranking issues. This paper proposes a three-phase approach for multi-criteria ranking in fuzzy environments, which combines the criterion fuzzy concept and three-way decision thinking. The proposed approach not only analyzes the decision-making characteristics of all alternatives but also facilitates their ranking. During the first phase, a qualitative classification method based on the criterion fuzzy concept and ideal solutions is defined, which divides all alternatives into three independent decision sub-regions. During the second phase, by analyzing the priority relationships among the alternatives within every sub-region, three local ranking rules for alternatives are proposed to determine the ranking of alternatives in each classification region. During the third phase, the semantic relations among three classification regions are considered to give an overall ranking of all alternatives. Finally, combined with two existing quantitative ranking indicators, multiple data sets are employed to verify the feasibility and superiority of the proposed three-phase multi-criteria ranking approach. [ABSTRACT FROM AUTHOR]

Overlap functions, which can be characterized as a type of non-associative binary aggregation operators, have emerged as one of the most extensively utilized aggregation operators in numerous applications, including image processing, information fusion, and classification problems. At the same time, fuzzy rough sets have also been widely used in these fields due to their excellent ability to handle continuous and uncertain information. However, the variable precision fuzzy rough set model based on overlap functions and its applications have not been fully studied. For instance, some basic properties are invalid and there is a lack of practical applications. In this paper, both overlap functions and precision parameters are introduced into the fuzzy rough sets, namely the overlap function-based variable precision fuzzy rough set (OVPFRS), which is then used in the practical problem of tumor classification. First, considering the existing overlap function-based rough set models, the OVPFRS model is established, and some underlying properties of this model are explored. Second, on the basis of the proposed model, a method for attribute reduction is developed. Finally, the new method is applied to the classification of tumor data from the real world. Through experimentation and comparison with other attribute reduction methods, it has been demonstrated that our model is flexible and the algorithm is viable and effective. [ABSTRACT FROM AUTHOR]

The concept of bipolar-valued fuzzy set was introduced by Zhang. Can we discuss three-way decisions based on bipolar-valued fuzzy sets over three-way decision spaces? In response to this problem, firstly, the paper discusses partially orders on truth values of bipolar-valued fuzzy sets and three-way decision spaces on this basis. Secondly, this paper presents construction method of decision evaluation functions based on bipolar-valued fuzzy sets over three-way decision spaces. Thirdly, this paper makes three-way decisions based on bipolar-valued fuzzy sets over three-way decision spaces and uses an example on an evaluation problem of credit card applicants to illustrate some notions of the (semi-, quasi-)three-way decision spaces and benefits of constructing methods from semi-(quasi-)decision evaluation functions to decision evaluation functions. Finally, the conclusions are summed up. [ABSTRACT FROM AUTHOR]

As one of the most promising classification approaches, association classification (AC) integrates data classification and association discovery techniques for generating a compact set of classification association rules. Recently, the fuzzy set and evidence theories are successively applied into AC in order to improve the classification performance in terms of accuracy and interpretability. However, from the perspectives of applicability and universality, there still exists two important issues in the current AC framework. On one hand, several key parameters, such as the number of fused rules in classification and the minimum support threshold in association discovery, are difficult to be accurately predefined in practice. On the other hand, the fixed grid-based fuzzy partition is not benefit to adapt for those datasets with large number of features. In this paper, an association rule-based adaptive fuzzy-evidential classification framework (AR-AFEC) is developed for overcoming the above limitations. To do so, an optimal rule fusion strategy and a dynamic minimum support threshold setting scheme are proposed for adaptively learning the parameters during classification and association mining respectively. In addition, an entropy-based trapezoidal fuzzy partition technique is proposed to adaptively obtain the fuzzy sets defined on each continuous feature domain. Experiments on 26 benchmark datasets and a human activity recognition application demonstrate that the proposal can achieve better accuracy than some state-of-the-art rule-based classification approaches, using less rules with more general structure. [ABSTRACT FROM AUTHOR]

Deep learning-based recommendations have demonstrated impressive performance in improving recommendation accuracy. However, such approaches mainly utilize implicit feedback to predict user preferences and neglect the adverse impact of explicit preference noise, which affects the robustness and reliability of model training. To consider the reliability of both rating input and output, we propose a novel joint deep neural recommendation framework that incorporates rating reliability derived solely from ratings to provide reliable recommendations for active users. Firstly, we introduce a noise detection method based on intuitionistic fuzzy sets to identify incorrect ratings from the perspective of fuzzy preferences and label them to generate a binary rating reliability matrix. Subsequently, we propose a joint deep neural framework that integrates rating reliability to simultaneously capture the high-order features of users and items, yielding predictions with their corresponding reliability probabilities. Finally, to achieve a balance between accuracy and reliability for recommendations, we design a reliability threshold selection strategy based on K-means clustering to find an appropriate threshold. Experimental results on three widely used datasets show that our model achieves an average improvement of 9.4% and 8.0% in the metrics Recall and NDCG, respectively, compared with the closest competitor. This paper provides new insights for integrating rating reliability into a deep neural network to enhance the performance of recommender systems. [ABSTRACT FROM AUTHOR]

Rough set theory is a well-known mathematical framework that can deal with inconsistent data by providing lower and upper approximations of concepts. A prominent property of these approximations is their granular representation: that is, they can be written as unions of simple sets, called granules. The latter can be identified with "if..., then..." rules, which form the backbone of rough set rule induction. Alternatively, this property of granular representability can be defined as being free from inconsistencies, i.e. there are no elements within the set that are indiscernible to elements outside the set. It has been shown previously that this property can be maintained for various fuzzy rough set models, including those based on ordered weighted average (OWA) operators. In this paper, we will focus on some instances of the general class of fuzzy quantifier-based fuzzy rough sets (FQFRS). In these models, the lower and upper approximations are evaluated using binary and unary fuzzy quantifiers, respectively. One of the main targets of this study is to examine the granular representation of different models of FQFRS. The main findings reveal that Choquet-based fuzzy rough sets can be represented granularly under the same conditions as OWA-based fuzzy rough sets, whereas Sugeno-based FRS can always be represented granularly. Additionally, we provide counterexamples for the granular representability of other FQFRS models, and show that despite this, these approaches still demonstrate effectiveness in mitigating inconsistencies in real-life datasets. This observation highlights the potential of these models for resolving data inconsistencies and managing noise. [ABSTRACT FROM AUTHOR]

• A PF-WPA-CRITIC-MARCOS framework is reported to select the preferential sustainable food supplier for resilient cities. • A hierarchical model of criteria for sustainable food supplier selection is constructed. • The deviation between input data and the interactive criteria is considered in selecting sustainable food suppliers. • A numerical case of the food supply chain is illustrated to test the proposed model. Sustainable food supplier selection (SFSS) can be handled as an uncertain decision-making issue. The Pythagorean fuzzy set (PFS), a type of non-standard fuzzy set, offers an expanded description space for articulating fuzzy and uncertain data. Accordingly, this paper proposes a Pythagorean fuzzy synthetic decision method-based selection framework for solving the SFSS problem within a subjective context. Then, the weighted distance measures for the PFS are introduced to derive the importance degrees of the experts, which can provide a more objective decision result. Then, an information fusion method with a PFS-weighted power average (WPA) operator is introduced to form a group decision matrix competent to accommodate the deviation effect. Next, an extended PF-measurement of alternatives and ranking according to compromise solution (MARCOS) method integrating PF-criteria importance through inter-criteria correlation (CRITIC) is presented to calculate the priority of each supplier, which can capture the inter-correlations between criteria. Finally, a numerical example of SFSS is implemented to show the application of the proposed synthetic decision approach. Subsequently, the sensitivity analysis of distance parameters and comparison analysis among different SFSS approaches were conducted to test the rationality and advantages of the proposed framework for resolving the SFSS problem. The results show that the reported method can provide a practical way to resolve the SFSS problems with uncertain data. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new distance measure between picture fuzzy sets (PFSs) to overcome the drawbacks of the existing distance measures between PFSs. We also propose a weight-determination method to determine attributes' weights using the proposed distance measure between PFSs. We also propose a novel multi-attribute decision-making (MADM) method on the basis of the proposed distance measure between PFSs and the modified combined compromise solution (CoCoSo) method. The proposed MADM method can overcome the drawbacks of the existing MADM methods based on PFSs. It gives us a very useful way for MADM in picture fuzzy environments. [ABSTRACT FROM AUTHOR]

A variety of fuzzy sets, especially Pythagorean fuzzy sets (PFSs), are commonly utilized to describe the ambiguity of information in three-way decision (3WD) models. PFSs can handle fuzzy information well but ignore the description of stochastic information. To address this issue, in this paper, we attempt to construct a novel three-way multiattribute decision model by combining 3WD with constrained Pythagorean fuzzy sets (CPFSs) which can measure the reliability of PFSs. Firstly, we introduce the concept of constrained Pythagorean fuzzy information systems (CPFISs). Comprehensive positive and negative similarities of objects are given in a CPFIS by introducing normalization, score function, comparison rules, and positive and negative ideal solutions. Secondly, by comprehensive positive and negative similarities, novel formulas for calculating comprehensive relative utility function values are obtained and an objective method for estimating conditional probabilities is presented in the absence of decision attributes. Based on the above knowledge, we establish a similarity-based three-way multiattribute decision model in a CPFIS. Furthermore, we conduct a case analysis of appendicitis to realize the application of our proposed model and several comparative analyses to demonstrate the effectiveness and superiority of our model. Finally, the good performance of the new model is verified through experimental analyses. [ABSTRACT FROM AUTHOR]

Innovative, Resilient, and Green Supplier Selection (IRGSS) is an emerging need often viewed as a complex multi-criteria decision-making problem. However, overly stringent restrictions on the assessed values, such as q-rung ortho -pair hesitant fuzzy uncertain linguistic sets, and dependent uncertainty events affecting criterion weights threaten the decision's reliability. Thus, LPHFS-SPFUCOM-MULTIMOORA is proposed to address these challenges. First, the paper proposes novel Linguistic Polytopic Hesitant Fuzzy sets (LPHFSs), which assume the sum of the q th power of the three types of memberships is not greater than 1 and relax the constraints on the assessed values. Second, the Full Consistency Method (FUCOM) is improved to find weights by integrating the Concept of Stratification Theory (CST) and PageRank, named SPFUCOM. CST depicts the occurrence process of uncertain events and PageRank finds their occurrence probabilities considering dependency. Third, the multiplicative Multi-objective Optimization by Ratio Analysis (MULTIMOORA) is novelly applied with SPFUCOM and LPHFSs to rank suppliers. Finally, a case from an electric vehicle manufacturer is studied to illustrate the applicability of the proposed method. Through sensitivity and comparative analyses, the rationality and advantages of the proposed method are verified. This study can provide insights for managers to solve the IRGSS problem. [ABSTRACT FROM AUTHOR]

The loss function plays an important role in deep learning models as it determines the model convergence behavior and performance. In semantic segmentation, many methods utilize pixel-wise (e.g. cross-entropy) and region-wise (e.g. dice) losses while boundary-wise loss is underexplored. It is known that one of the key aims of semantic segmentation is to precisely delineate objects' boundaries. Hence, it is essential to design a loss function that measures the errors around objects' boundaries. Fuzzy rough sets are constituted by the fuzzy equivalence relation, which is commonly used to measure the difference between two sets. In this paper, the lower approximation of fuzzy rough sets is proposed to construct the boundary-wise loss in deep learning models for the first time. The experiments with various segmentation models and datasets have verified that the proposed fuzzy rough sets loss is superior to other boundary-wise losses in terms of segmentation accuracy and time complexity. Compared with the commonly used pixel-wise and region-wise losses, the proposed boundary-wise loss performs similarly in dice coefficient, pixel-wise accuracy, but has a better performance in Hausdorff distance and symmetric surface distance. It indicates that the proposed loss provides a better guidance for segmentation models in producing more accurate shapes of the target objects. Code is available online at Github: https://github.com/qiaolin1992/Boundary-Loss. [ABSTRACT FROM AUTHOR]

Being a pair of dual concepts, the normalized distance and similarity measures are important tools for decision-making and pattern recognition under the intuitionistic fuzzy set framework. In this paper, we first construct some counterexamples to illustrate that two existing similarity measures do not meet the axiomatic definition of intuitionistic fuzzy similarity measures. We then show that (1) these two measures cannot effectively distinguish some intuitionistic fuzzy values (IFVs); (2) except for the endpoints, there exist infinitely many pairs of IFVs, where the maximum distance "1" can be achieved under these two distances, leading to counter-intuitive results. To overcome these drawbacks, we introduce the concept of strict intuitionistic fuzzy distance measure (SIFDisM) and strict intuitionistic fuzzy similarity measure (SIFSimM), and propose an improved intuitionistic fuzzy distance measure based on Jensen-Shannon divergence. Moreover, we prove that (1) it is a SIFDisM; (2) its dual similarity measure is a SIFSimM; (3) its induced entropy is an intuitionistic fuzzy entropy. Comparative analysis and numerical examples demonstrate that our proposed distance measure is superior to the existing ones. In particular, our proposed distance measure can better distinguish and rank intuitionistic fuzzy sets. [ABSTRACT FROM AUTHOR]

This study introduces the Complex T-Spherical Fuzzy Soft Set (CTSFSS), a novel and practical model for representing two-dimensional ambiguous information. This is achieved by integrating the Complex T-Spherical Fuzzy Set (CTSFS) with the Soft Set (SS). The development of the CTSFSS theory is motivated by the absence of neutral membership in complex q-rung orthopair fuzzy soft sets and the limitations of Traditional Spherical Fuzzy Soft Sets (TSFSS) in capturing two-dimensional data. Data storage and processing in the modern technological landscape necessitate sophisticated algorithmic computations and robust representation of information. To this end, computational systems predominantly rely on a binary system structured on two fundamental states: 0 (off) and 1 (on). Moreover, the significance of energy resources and computer-aided tools is underscored in this domain, especially considering the potential impact of quantum computing and advances in energy resources on the evolution of digital technology. In addressing these complexities, we propose Complex T-Spherical Fuzzy Soft Relations (CTSFSRs), formulated through the Cartesian product of two CTSFSSs. These relations are adept at handling complex and uncertain data in real-world scenarios. We define and categorize various types of CTSFSRs, followed by an in-depth analysis of their outcomes. Additionally, this paper introduces innovative visualization techniques based on CTSFSRs, tailored for decision-making processes involving energy resources and quantum computing applications. The efficacy and applicability of these proposed methodologies are substantiated through comparative analysis with existing models. [ABSTRACT FROM AUTHOR]

In this paper, we systematically study the algebraic structures of the spaces L ([ 0 , 1 ]) , encompassing all closed subintervals of [ 0 , 1 ] , under the generated admissible orders. We first prove that the admissible order on L ([ 0 , 1 ]) generated by a non-degenerate matrix must be the form of two weighted averaging operators. As a corollary, we deduce that each admissible order on L ([ 0 , 1 ]) generated by a non-degenerate matrix and the standard order ≤ on [ 0 , 1 ] are not isomorphic. Furthermore, we show that each admissible order on L ([ 0 , 1 ]) derived from two continuous mappings and the standard order ≤ on [ 0 , 1 ] are not isomorphic, partially answering a conjecture proposed by Santana et al. (2020) [38]. Besides, we prove that L ([ 0 , 1 ]) is a complete lattice under the admissible order generated by two continuous mappings. This is the first result regarding the completeness of L ([ 0 , 1 ]). Finally, we apply the admissible orders to solve a minimal path problem within the context of interval-valued fuzzy weighted graph. The above results theoretically refine the study of the classification, non-isomorphism, and completeness of admissible orders, while expanding the scope of interval-valued fuzzy sets in practical applications. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new similarity measure (SM) between picture fuzzy sets (PFSs). The proposed SM between PFSs can overcome the drawbacks of the existing SMs between PFSs. We also propose a weight-determination approach based on the proposed SM between PFSs to determine attributes' weights in picture fuzzy environments. We also propose a new multi-attribute decision-making (MADM) approach based on the proposed SM between PFSs and the Measurement of Alternatives and Ranking according to Compromise Solution (MARCOS) method for MADM with picture fuzzy information. The proposed MADM approach can overcome the shortcomings of the existing MADM approaches based on PFSs. It provides us a very useful approach for MADM in picture fuzzy settings. [ABSTRACT FROM AUTHOR]

As a vital theoretical research of three-way decision (3WD), three-way decision space (3WDS) further enriches the theory on 3WD and enhances its application. In 3WDS, decision evaluation function (DEF) is an indispensable component and plays a crucial role in practical decision problems. But, a large number of valuable functions are the semi-decision evaluation functions (S-DEFs). For this problem, Hu gave many S-DEFs and presented a transformation method from S-DEFs to DEFs. Since then, it has led to a research hotspot that is the introduction of the usual aggregation functions (AFs) into the transformation method of Hu's form. This paper focuses on the new form of transformation methods from semi-three-way decision spaces (S-3WDSs) to 3WDSs and their applications. Firstly, we present a new form of transformation method with parameter σ from S-DEFs to DEFs. And, we verify both theoretically and experimentally that this introduced parameter σ provides a valid window to dynamically adjust 3WDSs by changing the parameter σ , respectively. Notably, this new form of transformation method covers all existing 3WDSs transformation methods except the representable uninorms-based methods. Secondly, we give a more general function named with F -function, which can be introduced to these construction methods in the same way as usual AFs. This enables decision-makers to select more suitable functions for solving practical problems. Thirdly, based on the new form, usual AFs and F -functions, we present some new construction methods of S-DEFs (resp. DEFs) related to fuzzy sets, interval-valued fuzzy sets and random sets. Finally, to make up for the application of the theory of 3WDSs in complex datasets, we select 7 complex datasets for experimenting and conduct comparative and sensitivity analysis to test the viability and efficacy of our methods. Notably, we also give an algorithm to calculate the thresholds α and β , which can adjust the optimal thresholds α and β according to different 3WDSs. [ABSTRACT FROM AUTHOR]

In this paper, a new interval-valued intuitionistic fuzzy-based algorithm is proposed to enhance low-light images. In this proposed algorithm, the low-light image is first changed to the fuzzy image by normal fuzzification. Then the above is converted to an intuitionistic fuzzy image and further to the interval-valued intuitionistic fuzzy image. After applying contrast limited adaptive histogram equalization, we derive the required image. In the experimental part, the proposed algorithm is compared with other existing algorithms including histogram equalization, contrast limited adaptive histogram equalization, histogram specification, dehazing, fractional order image enhancement, intuitionistic fuzzy, and interval-valued intuitionistic fuzzy. In terms of overall visual quality and performance metrics, the results showed that the proposed technique surpasses other current methods including entropy, absolute mean brightness error, and contrast improvement index. [ABSTRACT FROM AUTHOR]

Current machine learning algorithms encounter challenges such as missing labels and high dimensionality. Feature selection serves as an effective dimensionality reduction technique, enhancing the efficiency and accuracy of subsequent machine learning tasks by eliminating irrelevant and redundant features. Given the difficulty in obtaining fully labeled data, partially labeled data has become a crucial target for machine learning models to address. The related family is an efficient, rough set-based feature selection approach; however, it cannot be applied to semi-supervised learning tasks. Consequently, this paper introduces a semi-supervised feature selection method based on a fuzzy related family for partially labeled data. At first, the fuzzy label values of unlabeled samples are calculated based on fuzzy similarity relationships by establishing a novel fuzzy covering system. Subsequently, a fuzzy related family is constructed by a consistent fuzzy set. Then a semi-supervised feature selection algorithm, referred to as the Semi-supervised Fuzzy Related Family (SFRF), is developed using the established feature significance measurement. Compared to existing semi-supervised feature selection algorithms, SFRF considerably enhances feature selection efficiency while preserving classification accuracy. Specifically, the average reduction efficiency across twelve datasets increased by up to 109 times. [ABSTRACT FROM AUTHOR]