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Software reliability growth models (SRGMs) are widely used for predicting the reliability of software systems during testing and debugging. Selecting the most appropriate SRGM solutions is a multi-criteria decision-making (MCDM) problem that is very difficult when criteria are imprecise or ambiguous. The paper introduces a novel approach to SRGM selection which relies on q-rung orthopair fuzzy sets (q-ROFS) and the compromise ranking method of VIKOR. New q-rung orthopair fuzzy (q ROF) entropy and divergence measures are proposed for criteria weights assignment and to select superior SRGMs. The VIKOR method is then applied on the q-ROF decision matrix to identify the optimal compromise SRGM solution. This approach provides a systematic framework for handling subjective criteria and modeling uncertainty during SRGM selection. The proposed MCDM methodology is illustrated on the example of a case study involving four common SRGMs evaluated on the four different criteria. Results are demonstrated to be in line with the latest q-rung measures which provide more accurate results than the previous intuitionistic fuzzy methods. The q-ROF VIKOR approach provides the software teams with a more robust information base for the reliability growth decision-making process. At the end of this manuscript, we do the comparison of the proposed theory with certain prevailing concepts to reveal the dominance and supremacy of this work. Whereas yet there are some expected limitations of the proposed work for instance it can’t be helpful in the generalized structures of q-ROFS.

One of the best ways to handle the ambiguity and unpredictable nature of decision-making is through fuzzy logic, and one of the most recent developments in this area is the concept of spherical fuzzy sets. Since the squared total of membership, non-membership, and hesitation degrees should be between 0 and 1, and each degree should be defined in [0, 1], the hesitation of the decision-maker(s) about an attribute can be conveyed more thoroughly. The ambiguity of a fuzzy set is computed with the help of an entropy measure, and the available entropy measures for spherical fuzzy sets have various limitations. So, in this study, we suggest an innovative entropy measurement for spherical fuzzy sets and demonstrate its capacity to satisfy the axiomatic requirements. We compared the proposed entropy metric and all currently available spherical fuzzy entropy metrics, considering different factors, including attribute weight computation, linguistic hedges, and ambiguity computation. With the help of the proposed entropy metric, we introduce the Complex Proportional Assessment method for spherical fuzzy sets and illustrate it with a numerical example.

The inherent fuzziness of wetland ecosystems largely accounts for the spectral variability of wetland ecosystems in remote sensing images. In addition, a limited spatial resolution leads to the presence of many mixed pixels in middle-resolution multispectral remote sensing images. The existing methods that use a single center or a limited number of endmembers to represent land cover types cannot fully account for the spectral variability of land cover types; moreover, these methods use these limited representations to calculate the membership function (MF), leading to limited classification and mapping performance. To address spectral variability and mixed pixels, this study proposes a novel MF generation method, in which mixed pixels are treated as an auxiliary type, and the clustering and spectral characteristics are integrated to detect the cores of land cover types in spectral space. Then, the spectral diversity can be fully expressed by the core components of the land cover types. The membership values of mixed pixels are calculated from the core components via the sparse reconstruction method. The experiment shows that the proposed method has a substantial increase in classification accuracy over the existing methods.

AI-powered robots contain many sensors, such as vision devices like 2D/3D cameras, vibration sensors, proximity sensors, accelerometers, and other environmental sensors. These sensors enable real-time sensing data to be obtained and analyzed. Here, the discussion of robot selection AI-field. In this work, we aim to examine AI robotic systems based on a bipolar complex fuzzy soft set (BCFSS) with Power dombi aggregation operators (PDAO). Moreover, we aim to examine BCFS power dombi average AOs and BCFS power dombi geometric AOs. Three BCFS power dombi average (PDA) AOs are identified in this work, namely the BCFS power dombi weighted average (BCFSPDWA) AO, BCFS power dombi hybrid average (BCFSPDHA) AO and BCFS power dombi ordered weighted average (BCFSPDOWA) AO. Likewise, three types of BCFS power dombi geometric AOs have been identified, namely: BCFS power dombi weighted geometric (BCFSPDWG) AO, BCFS power dombi order-weighted geometric (BCFSPDOWG) AO and BCFS power dombi hybrid geometric (BCFSPDHG) AO. Subsequently, we will propose a numerical model for the proposed operators, as well as a multi-attribute decision-making (MADM) model that can be used to select the best robot in AI. Finally, we will compare the results of the numerical model with the prevailing outcomes in terms of supremacy and dominance.

The concept of Fermatean fuzzy set offers a more comprehensive perspective on Pythagorean fuzzy sets, with greater potential for practical applications due to its broader scope compared to Pythagorean fuzzy sets. In contrast, distance measures serve as effective information measures in decision-making using deep learning methods. This research paper introduces a novel distance measure within the Fermatean fuzzy framework. This new distance measure exhibit enhanced performance indices compared to existing distance measures discussed in previous literature. The newly proposed distance operators based on Fermatean fuzzy sets offer a fresh approach by considering all three membership functions of Fermatean fuzzy sets, which differs from existing practices. This distance operator also incorporate all membership functions to prevent errors caused by exclusions, which have been observed in other distance operators. Several theorems are provided to validate the alignment of this new Fermatean fuzzy distance technique with properties expected of distance operators. The comparative analysis of the newly introduced Fermatean fuzzy distance measure with similar existing distance techniques is conducted through numerical comparison and also in relation to their applications, aiming to highlight the superiority of the proposed Pythagorean fuzzy distance techniques over the existing ones. The application of the proposed Fermatean fuzzy distance measure is demonstrated in scenarios involving pattern classification and bidirectional approximate reasoning.

This study’s major purpose is to highlight circular spherical fuzzy sets, that happens to be a prolongation of spherical fuzzy sets. The primary purpose of this research is to demonstrate the basic operations and theorems of circular spherical fuzzy structures (C-SFS), which give an effective way for dealing with data ambiguity. Aggregation operators (AOs) play a significant role in decision-making, particularly in situations where conflicting interests need to be taken into account. The Sugeno-Weber (SW) t-conorm and t-norm are employed in the C-SFS operating rules. The study describes in detail the fundamental operating criteria for C-SFS utilizing SW t-norms and t-conorms, as well as their crucial features. Furthermore, this research presents and fully investigates two novel operators, C-SFS Sugeno Weber weighted averaging (C-SFSWWA) and C-SFS Sugeno-Weber weighted geometric (C-SFSWWG), as well as their distinct applications and desired properties. A novel approach based on the C-SFSWWA and C-SFSWWG operators is suggested to address multiple attribute decision-making (MADM) problems utilizing C-SF information. A numerical example shows how this approach may be used to adapt a programming language for social media platform analytics, followed by a comparison study to highlight its advantages. The advised approach is successful, according to an investigation of authenticity and a comparison study. In reality, the recommended aggregation operators and decision-making approach are quite useful for decision analysis.

Complex T-spherical fuzzy set (CTSF) is the extended form of complex spherical fuzzy set (CSFs). CTSF can extract the maximum information from real-life phenomena with the help of a membership degree (MD), abstinence degree (AD), and non-membership degree (NMD). Due to this nature, CTSF can describe every human opinion’s phenomenon with less uncertainty. The major contribution of this article is to develop an interesting approach to aggregate the information in the form of the CTSFS. To do this, first, we develop the operational laws for CTSF values (CTSFVs) based on Frank’s operational laws. Then two types of aggregation operators (AOs), CTSF Frank weighted averaging (CTSFWA) and CTSF Frank weighted geometric (CTSFFWG) operators are introduced based on the Frank t-norm (FTNM). Further, some basic properties of the CTSFFWA and CTSFFWG operators are studied. The developed approach is also applied to the real-life problem of multi-attribute decision-making (MADM) where the soil fertility is assessed based on some factors affecting the soil fertility. The sensitivity of the developed approach is observed with the variation of the involved parameter graphically. The comparison of the developed approach is also studied and as well as graphed.

In this paper, a circular intuitionistic fuzzy set is implicated, which is the extension of a fuzzy set and an intuitionistic fuzzy set. The circular intuitionistic fuzzy set includes a radius for both membership and non-membership. After this, we describe the TODIM method for decision making, which can handle both quantitative and qualitative criteria, as well as imprecise and uncertain information. TODIM takes into account the decision-maker’s subjective preferences and attitudes towards the criteria while also considering the uncertainty and imprecision in the decision-making process. We define the algorithm of C-IF-TODIM approach for decisions making problem. The proposed method takes into account both the fuzziness and circularity of the decision-making problem, which come from the fact that the decision-maker’s preferences are subjective and that the criteria depend on each other. A case study of choosing materials for a cryogenic storage tank is used to test the proposed method, and the results are compared to those from other ways of making decisions. The results show that the proposed method makes decisions that are more accurate and reliable and that it can handle the uncertainty and complexity of choosing materials for cryogenic storage tanks well. After reviewing this paper, we can help make liquid nitrogen transportation safer and more reliable, which will cut down on the chance of accidents and financial losses. The proposed method can be applied to decision-making in other domains where circular intuitionistic fuzzy information is common.

The aim of this article is to implement the Generalized Modified Adomian Decomposition Method to compute the semi-numerical solution of the linear system of intuitionistic fuzzy initial value problems. Here, we consider the initial values as generalized trapezoidal intuitionistic fuzzy numbers. The technique is applied to brine tanks problem and coupled mass spring systems.Theoretically, different approaches to solving a system of generalized trapezoidal intuitionistic fuzzy differential equations are discussed in this study under the presumption that the coefficients of the system of the differential equations are associated to generalized trapezoidal intuitionistic fuzzy numbers. The approximate results are compared with exact solutions which shows good efficiency. The corresponding graphs at different levels of uncertainty show the example’s numerical outcomes. The graphical representations further demonstrate the effectiveness and accuracy of the proposed method in comparison to existing semi-numerical methods in the literature.

Aiming at the problem that the existing aggregation operators only consider the weight of the data itself or the weight of the data position when aggregating data, a group decision information fusion model based on the combinatorial ordered weighted average operator is proposed, which considers the incompleteness, uncertainty and plurality of the decision information, and effectively improves the accuracy of group consensus. In this paper, an interval intuitionistic fuzzy combinatorically weighted average operator is proposed, which embodies the weight of the set data itself and the weight of data position, and can adjust the importance of the two weights in the operator through parameters, and prove that the operator has the properties of boundedness, monotonicity, idempotency and permutation invariance. Secondly, a position weight solving model of interval intuitionistic fuzzy combinatorial ordered weighted average operator is established, and the position weight is solved with the help of cross-entropy and Orness measures. Finally, a group decision information fusion process based on IVIFCOWA operators is designed, and the decision maker weight information is obtained according to the decision matrix, and the comprehensive decision matrix is obtained by fusion of IVIFCOWA operators, and then the mean similarity is obtained. Through specific case analysis, it is proved that the proposed operator can make full use of the decision data, and can better reach group consensus after data fusion than the existing operator.

Since there are many kinds of automobile instruments and the industrial environment is usually complex, automatic instrument detection during automobile production test becomes a challenging task. This article presents an automobile pointer instrument detection method based on prior information and fuzzy sets. The proposed method consists of two frameworks built around a pointer meter prior information model (PMPIM). The first one targets PMPIM construction to obtain the required prior information. With this purpose, a pointer-free template is obtained from a template generation algorithm and pointer positions are mapped into an energy function for optimization, using an energy function-based pointer positioning algorithm. The energy function is defined based on the distance between the crisp and fuzzy sets. The second framework targets PMPIM utilization to detect pointer meters during production test. A fuzzy-based image enhancement method is proposed to enhance test images and the template simultaneously. A prior information and energy function-based pointer positioning algorithm is also proposed to locate pointers in test images. Finally, the indicator value (the value the pointer points to) is calculated according to the positions of the pointer and scale marks. Experimental results show that the proposed method achieves better generalization and robustness than existing state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Adaptive imagesteganography embeds secret messages into areas of cover images with complex features, including rich edges and complex textures. In this article, an adaptive image steganography technique based on the edge and complex texture areas of images is proposed, by comprehensively considering three rules in the design of image steganography. First, the embedding area is composed of the edge and complex texture areas of images, according to the complexity-first rule. Edge detection is realized by an improved fuzzy enhancement function, optimized by the grey wolf optimizer to detect both the weak and strong edges. Second, the minimum average classification error rate is used to assess the choice of the complex texture areas. Third, under the spreading rule, two different average filters and one KerBohme filter are used to design the cost function in the embedding areas. Finally, confidential information is adaptively embedded through syndrome-trellis codes. Experimental results show that the proposed algorithm outperforms seven classical adaptive image steganography algorithms on two steganalytic feature sets. The performance improvement is particularly significant when the payload is large. [ABSTRACT FROM AUTHOR]

In several practical decision procedures, it is not accessible to denote assessments by a single crisp number due to a lack of information. However, representing information by an interval number within [0, 1] is a more credible approach. In multi-criteria decision making (MCDM) such an interval number can significantly catch information. In addition, the combination of soft sets with interval-valued q-rung orthopair fuzzy sets can be viewed as interval-valued q-rung orthopair fuzzy soft sets (IVq-ROFSs). It can be a reliable tool to cope with uncertainties. Usually, aggregation operators are functional in MCDM techniques; therefore, aggregation operators on IVq-ROFSs can significantly aggregate pieces of information in intervals with IVq-ROFSs. In this paper, we investigated some crucial properties of interval valued q-rung orthopair fuzzy soft sets (IVq-ROFSSs) and expressed a different representation of IVq-ROFSS in the form of IVq-ROFS number. Based on this representation, we investigated IVq-ROF weighted averaging, IVq-ROF weighted geometric operators and given their basic properties. Moreover, we consider interactions between non-memberships and memberships of different interval-valued q-rung orthopair fuzzy values and defined IVq-ROF weighted interaction averaging, IVq-ROF weighted interaction geometric aggregation operators in IVq-ROFS environments. A decision-making process is given, and an illustration is provided by tackling application in automation company evaluation.

This article is about a criterion based on credibility complex fuzzy set (CCFS) to study the prevailing substitution boxes (S-box) and learn their properties to find out their suitability in image encryption applications. Also these criterion has its own properties which is discussed in detailed and on the basis of these properties we have to find the best optimal results and decide the suitability of an S-box to image encryption applications. S-box is the only components which produces the confusion in the every block cipher in the formation of image encryption. So, for this first we have to convert the matrix having color image using the nonlinear components and also using the proposed algebraic structure of credibility complex fuzzy set to find the best S-box for image encryption based on its criterion. The analyses show that the readings of GRAY S-box is very good for image data.

In this article, a new method of option pricing in the form of fuzzy number is established based on fuzzy number binary tree model. Firstly,by using the operation rules of fuzzy number addition and number multiplication in cut set form, the fuzzy number binary tree model is equivalently transformed into two families of classical binary tree models which change with the level value, and some properties of the two binary tree model families are obtained, which are related to solve the problem of fuzzy option pricing. Then, based on the results obtained by us, the concepts of fuzzy set option price and fuzzy number option price are defined, and a sufficient condition is obtained for fuzzy set option price to be fuzzy number option price in the fuzzy number binary tree model. And then, for the convenience of practical application, the concepts of fold line fuzzy set and fuzzy number option price are introduced, a sufficient condition for fold line fuzzy set option price to be fold line fuzzy number option price is obtained, and a specific solution method of the fold line set and the fold line fuzzy number option pricing are set up. At last, two specific examples are given to show how to solve the fold line set and the fold line fuzzy number option price. [ABSTRACT FROM AUTHOR]

This article proposes an optimal indirect approach of constraint-following control for fuzzy mechanical systems. The system contains (possibly fast) time-varying uncertainty that lies in a fuzzy set. It aims at an optimal controller for the system to render bounded constraint-following error such that it can stay within a predetermined bound at all time and be sufficiently small eventually. First, for deterministic performance, the original system is transformed into a constructed system. A deterministic (not the usual IF-THEN rules-based) robust control is then designed for the constructed system to render it to be uniformly bounded and uniformly ultimately bounded, regardless of the uncertainty. Second, for optimal performance, a performance index, including the average fuzzy system performance and control effort, is proposed based on the fuzzy information. An optimal design problem associated with the control gain is then formulated and solved by minimizing the performance index. Finally, it is proved when the constructed system renders uniform boundedness and uniform ultimate boundedness, the original system achieves the desired performance of bounded constraint following. [ABSTRACT FROM AUTHOR]

Rule-based fuzzy models play a dominant role in fuzzy modeling and come with extensive applications in the system modeling area. Due to the presence of system modeling error, it is impossible to construct a model that fits exactly the experimental evidence and, at the same time, exhibits high generalization capabilities. To alleviate these problems, in this study, we elaborate on a realization of granular outputs for rule-based fuzzy models with the aim of effectively quantifying the associated modeling errors. Through analyzing the characteristics of modeling errors, an error model is constructed to characterize deviations among the estimated outputs and the expected ones. The resulting granular model comes into play as an aggregation of the regression model and the error model. Information granularity plays a central role in the construction of granular outputs (intervals). The quality of the produced interval estimates is quantified in terms of the coverage and specificity criteria. The optimal allocation of information granularity is determined through a combined index involving these two criteria pertinent to the evaluation of interval outputs. A series of experimental studies is provided to demonstrate the effectiveness of the proposed approach and show its superiority over the traditional statistical-based method. [ABSTRACT FROM AUTHOR]

Fuzzy sets and fuzzy rough sets are widely applied in data analysis, data mining, and decision-making. So far, the common method is to use rough approximate operators to induce aggregation functions when fuzzy rough sets are used for multicriteria decision-making (MCDM). However, they are parametric linear and the corresponding weights are additive measures. In this article, we give a novel method for MCDM based on fuzzy covering rough sets by using the nonadditive measure [i.e., fuzzy measure (FM)] and the nonlinear integral [i.e., Choquet integral (ChI)]. First, two nonadditive measures are presented by fuzzy covering lower and upper approximation operators, respectively. Moreover, both of them are FMs which are called $\beta$ -neighborhood approximation measures. Second, two types of ChIs with respect to $\beta$ -neighborhood approximation measures are constructed. A novel method, which considers the association, is presented to solve the problem of MCDM under the fuzzy covering rough set model. Third, a new approach based on $\beta$ -neighborhood approximation measures is proposed for attribute reductions in a fuzzy $\beta$ -covering information table. This approach of attribute reductions is used in MCDM. Finally, both new methods above are compared with other methods through some numerical examples and UCI datasets, respectively. [ABSTRACT FROM AUTHOR]

Pythagorean fuzzy set (PFS) is a significant soft computing tool for tackling embedded fuzziness in decision-making. Many computing methods have been studied to facilitate the application of PFS in modeling practical problems, among which the concept of correlation coefficient is very important. This article proposes some novel methods of computing correlation between PFSs via the three characteristic parameters of PFS by incorporating the ideas of Pythagorean fuzzy deviation, variance, and covariance. These novel methods evaluate the magnitude of relationship, show the potency of correlation between the PFSs, and also indicate whether the PFSs are related in either negative or positive sense. The proposed techniques are substantiated together with some theoretical results and numerically validated to be superior in terms of reliability and accuracy compared to some similar existing techniques. Decision-making processes involving pattern recognition and career placement problems are determined using the proposed techniques. [ABSTRACT FROM AUTHOR]

Different remote sensing image applications require different quality remote sensing images, and selecting the best quality remote sensing image from multiple remote sensing images with similar quality directly determines the application effect of the image. According to the different applications of remote sensing images, the Rough Set Theory, Fuzzy Set Theory and Back Propagation Neural Network theory (BP Neural Network) are used to establish a remote sensing image quality evaluation model. Combining the basic influencing factors of remote sensing image quality and the influencing factors of specific applications as evaluation indicators, the remote sensing image quality evaluation model is imported, and the best quality remote sensing images are selected in specific applications for remote sensing images of special quality. Finally, this paper proves the feasibility of the model in the selection of the best image quality for specific applications of three different experiments.

Due to the spectral diversity of objects within the same classes and the spectral similarity between different classes, classical fuzzy classification methods perform poorly in multispectral remote sensing image classification. The basic reason is that they often use a single spectral curve to represent a land cover type while ignoring spectral diversity characteristics. To solve this issue, this article proposes a novel multicenter supervised fuzzy classification (MCSFC) method for modeling spectral diversity in multispectral remote sensing data. Images are first split into clusters with similar sizes or volumes, namely, granularities, by a hierarchical clustering process. Second, the granularities are labeled by training samples. As a result, the centers of the granularities corresponding to one type of sample can represent the spectral diversity within one class and, thus, are treated as the multiple centers of a land cover type. The membership degree of each unlabeled sample belonging to any land cover type is determined by the shortest distance to the centers of each type, and the spectral diversity is considered in this stage. A comparison reveals that the proposed method clearly improves the classification performance of various single-center fuzzy semisupervised clustering (FSSC) methods. Two case studies indicate that the granularity volume parameter notably affects the classification performance, and the overall accuracy (OA) decreases with increasing granularity volume. [ABSTRACT FROM AUTHOR]

Fuzzy systems have good modeling capabilities in several data science scenarios and can provide human-explainable intelligence models with explainability and interpretability. To obtain a human-explainable data intelligence model for decision making, in this article, we investigate explainable fuzzy-theoretic utility mining on multisequences. Meanwhile, a more normative formulation of the problem of fuzzy utility mining on sequences is formulated. By exploring fuzzy set theory for utility mining, we propose a novel method termed pattern growth fuzzy utility mining (PGFUM) for mining fuzzy high-utility sequences with linguistic meaning. In the case of sequence data, PGFUM reflects the fuzzy quantity and utility regions of sequences. To improve the efficiency and feasibility of PGFUM, we develop two compressed data structures with explainable fuzziness. Furthermore, one existing and two new upper bounds on the explainable fuzzy utility of candidates are adopted in three proposed pruning strategies to substantially reduce the search space and, thus, expedite the mining process. It is demonstrated that PGFUM achieves not only human-explainable mining results that contain the original nature of revealable intelligibility, but also high efficiency in terms of runtime and memory cost. [ABSTRACT FROM AUTHOR]

Uncertainty measurement (UM) can offer new visual angle for data analysis. A fuzzy set-valued information system (FSVIS) indicates an information system (IS) where its information values are fuzzy sets. This article investigates UM for fuzzy set-valued data based on Chebyshev distance. First, the distance between information values is founded in a given subsystem. After that, the tolerance relation induced by this subsystem is obtained by means of this distance. Moreover, the information structure of this subsystem is proposed. Next, the uncertainty of a FSVIS are measured. Eventually, to show the feasibility of the proposed measures, effectiveness analysis is carried out from a statistical view. The obtained outcomes may be helpful for comprehending the nature of uncertainty in a FSVIS.

The identification of interactions between single-nucleotide polymorphisms (SNP-SNP interactions) is crucial for determining human genetic disease susceptibility. With rapid technological advancements, multiobjective multifactor dimensionality reduction (MOMDR) measurements have achieved high detection success rates. However, the classification of high- or low-risk groups is central to MOMDR and has yet to be extensively studied. To address limitations in binary classification, we propose an improved fuzzy sigmoid (FS) approach that uses membership degrees in MOMDR, thus denoting it as FSMOMDR. For determining the interval of membership, our improved FS approach assesses the distance between the ith multifactor class and outcome (cases and controls). Thus, the improved FS approach enables MOMDR algorithms to determine the membership degrees of high- and low-risk groups in each multifactor class because the two-element set is extended to a specified membership interval. Moreover, the improved FS approach can handle uncertain information, which thus enables the effective detection of the m -locus combinations with similar distributions. FSMOMDR measurements can also distinguish similar frequencies among genotype combinations, thus enabling the detection of more significant SNP-SNP interactions. On the basis of the classification accuracy rate of MOMDR and results obtained from the analysis of several test data sets, we determined FSMOMDR to be superior to other MDR-based methods with respect to detection success rate. The results indicate that binary and fuzzy classifications involving MOMDR can provide insight into uncertainty in risk classification. Thus, FSMOMDR could successfully detect SNP-SNP interactions in coronary artery disease in a large data set obtained from the Wellcome Trust Case Control Consortium. We could successfully reduce uncertain information in MDR and thus suggest that membership based on the improved sigmoid function can be used to identify SNP-SNP interactions as well as obtain content knowledge.

Data mining is a critical technology for extracting valuable knowledge from databases. It has been used in many fields, like retail, finance, biology, etc. In computational intelligence, fuzzy logic has been applied in many intelligent systems widely because it is simple and similar to human inference. Fuzzy utility mining combines utility mining and fuzzy logic for getting linguistic utility knowledge. In this paper, we study a more challenging, complicated, but practical topic called temporal fuzzy utility data mining, which considers the temporal periods in transactions, purchased amounts, item profits, and understandable linguistic terms as important factors. Although an Apriori-based algorithm was proposed previously, its execution was not efficient. We thus use a modified tree structure based on the classical frequent-pattern tree to improve its performance. A tree-based mining algorithm is also proposed to mine temporal fuzzy utility itemsets from quantitative transactional databases. The tree structure is built to keep all temporal fuzzy utility 1-itemsets in a database. All the high temporal fuzzy utility itemsets in a database can be obtained by traversing the tree-based structure. The proposed algorithm gets the final results through two phases. In the first phase, a procedure like FP-Growth is used to find the candidate itemsets. In the second phase, the temporal fuzzy utility database is scanned to decide whether the candidate itemsets are desired. Experimental results show that the proposed algorithm is superior to the existing algorithm for temporal fuzzy utility mining in terms of processing time and used memory.

Temporal fault trees (TFTs), an extension of classical Boolean fault trees, can model time-dependent failure behaviour of dynamic systems. The methodologies used for quantitative analysis of TFTs include algebraic solutions, Petri nets (PN), and Bayesian networks (BN). In these approaches, precise failure data of components are usually used to calculate the probability of the top event of a TFT. However, it can be problematic to obtain these precise data due to the imprecise and incomplete information about the components of a system. In this paper, we propose a framework that combines intuitionistic fuzzy set theory and expert elicitation to enable quantitative analysis of TFTs of dynamic systems with uncertain data. Experts' opinions are taken into account to compute the failure probability of the basic events of the TFT as intuitionistic fuzzy numbers. Subsequently, for the algebraic approach, the intuitionistic fuzzy operators for the logic gates of TFT are defined to quantify the TFT. On the other hand, for the quantification of TFTs via PN and BN-based approaches, the intuitionistic fuzzy numbers are defuzzified to be used in these approaches. As a result, the framework can be used with all the currently available TFT analysis approaches. The effectiveness of the proposed framework is illustrated via application to a practical system and through a comparison of the results of each approach.

Zadeh's extension principle (ZEP) is a fundamental concept in fuzzy set (FS) theory that enables crisp mathematical operation on FSs. A well-known shortcoming of ZEP is that the height of the output FS is determined by the lowest height of the input FSs. In this article, we introduce a generalized extension principle (GEP) that eliminates this weakness and provides flexibility and control over how membership values are mapped from input to output. Furthermore, we provide a computationally efficient point-based FS representation. In light of our new definition, we discuss two approaches to perform aggregation of FSs using the Choquet integral. The resultant integrals generalize prior work and lay a foundation for future extensions. Last, we demonstrate the extended integrals via a combination of synthetic and real-world examples. [ABSTRACT FROM AUTHOR]

This paper proposes a hesitant bipolar-valued neutrosophic set (HBVNS) based on the combination of bipolar neutrosophic sets and hesitant fuzzy sets. The proposed set generalizes the notions of fuzzy set, intuitionistic fuzzy set, hesitant fuzzy set, single-valued neutrosophic set, single-valued neutrosophic hesitant fuzzy set, bipolar fuzzy set and bipolar neutrosophic set. Further, we define the basic operational laws, union, intersection and complement for hesitant bipolar-valued neutrosophic elements (HBVNEs) and study its associated properties. Some relevant examples are also given to provide a better understanding of the proposed concept. Two aggregation operators are developed based on HBVNS which are the hesitant bipolar-valued neutrosophic weighted averaging (HBVNWA) and the hesitant bipolar-valued neutrosophic weighted geometric (HBVNWG). A decision making method is developed based on new sets and the proposed HBVNWA and HBVNWG operators. Finally, an illustrative example is given to show the applicability of the proposed decision making method. A comparative analysis with the existing methods is also provided.

We develop a novel mathematical tool known as complex multi-fuzzy soft set (CMFSS) which has the ability to handle uncertainties, imprecision, and vagueness of information that are inherent in the data by considering the amplitude and phase terms of the complex numbers simultaneously. This CMFSS constitutes of a hybrid structure of multi-fuzzy set and soft set which are defined in a complex setting. The structure is flexible as it allows for a greater range of values for the membership function by extending them to the unit circle in a complex plane through modification of the multi-fuzzy soft set by the inclusion of an additional term called the phase term in order to take into account of the periodic nature of the data. Accordingly, the novelty of this paper lies in the complex multi-membership functions which consider more range of values while handling the uncertainty of the periodic data. In this paper, the concept of complex multi-fuzzy soft set is introduced. We then define its basic operations of complement, union and intersection and study some related properties, with supporting proofs. Subsequently, by means of level soft sets, we present an algorithm to solve a CMFSSs decision making problem, to illustrate the effectiveness and practicality of the proposed concept. Finally, we introduce axiomatic definitions of entropy and similarity measure for CMFSSs, and some formulas have also been put forward to calculate them. Numerical examples are given to demonstrate that the proposed entropy measure for CMFSSs is an important concept for measuring uncertainty in the information/data. Furthermore, some theorems are proposed showing how the entropy of CMFSS can be found from the similarity measure of CMFSS.

Decision support is a vital function in electronic commerce (e-commerce). The purpose of this paper is to construct a review-based decision support model for items comparison in e-commerce. The proposed model uses probability multivalued neutrosophic linguistic numbers (PMVNLNs) to characterize online reviews. It overcomes the limitation of existing models by considering neutral information and hesitancy in text reviews. The fuzzy characterization of reviews (i.e., PMVNLN) can reflect similarities and differences in positive (negative) information. In addition, the model considers consumers’ bounded rational behaviors by combining the regret theory with an outranking method. We empirically compare the proposed model with models in http://PConline.com and four existing models with data from http://PConline.com. The performance of these models in terms of accuracy is measured by the total relative difference metric. Results indicate the good performance of the proposed model. Our model is a promising option for e-commerce to provide consumers with good decision support service. [ABSTRACT FROM AUTHOR]

How to capture distinctive features from facial images when there are large variations in illumination, poses, and expressions is important for the face recognition problems. This paper introduces a novel algorithm called fuzzy linear regression discriminant projection (FLRDP) for face recognition. The proposed algorithm FLRDP seeks to generate an efficient subspace for the LRC method and could effectively handle variations between facial images. To be specific, FLRDP first computes the gradual membership degrees of each sample to corresponding classes, and then incorporates such membership degree information into the construction of the fuzzy between-class and within-class reconstruction errors. Finally, the criterion function is derived via maximizing the ratio of the fuzzy between-class reconstruction error to the fuzzy within-class reconstruction error. Experimental results carried out on the ORL, CMU PIE, and FERET face databases show the superiority of our proposed method over other state-of-the-art algorithms.

The key issue of multi-sensor image fusion is how to accurately extract and fuse the high-quality pixels or coefficients of source images. Nevertheless, the so-called high-quality is an uncertain or fuzzy definition, which is very suitable for fuzzy theory to address this problem. By the integration of stationary wavelet transform (SWT) and fuzzy sets, this paper proposes a new multi-focus image fusion scheme, which can merge the important features of different source images into a fused image. First, the source images are decomposed by SWT to get a set of sub-images with different detailed features. Second, the Gaussian membership function (GMF) is utilized to get the fuzzy sets of sub-images data. Third, the local spatial frequency (LSF) is employed to extract the local features of the sub-images by the generated fuzzy sets. At last, the fusion rule is designed based on consistency verification to fuse the sub-images according to the LSF of fuzzy sets, and then inverse SWT (ISWT) is implemented to reconstruct the fused image. The experimental and contrastive results of different image sets show that the proposed method is an effective multi-focus image fusion scheme which can achieve better fusion effect than other methods.

The robust control design problem for uncertain dynamical systems is considered in this study. The uncertainty is time varying (possibly fast) and bounded, and the bound lies within a prescribed fuzzy set (hence the fuzzy dynamical system). We design the robust control in two steps. First, we propose a class of robust controls based on tunable parameters, which is in deterministic form and not conventionally IF–THEN fuzzy rule based. It is shown that these controls are able to guarantee deterministic system performance, namely uniform boundedness and ultimate uniform boundedness. Second, we seek the optima of tunable parameters in the control by formulating a two-player Nash game, which is based on two performance indexes (i.e., the cost functions). It is shown that the Nash equilibrium (i.e., the optima of tunable parameters) always exists. The procedure of obtaining the Nash equilibrium is provided. Under the proposed control, the system performance is both deterministically guaranteed and fuzzily optimized from the Nash game perspective. The effectiveness of the control design is illustrated by the simulation control of a unicycle robot. [ABSTRACT FROM AUTHOR]

Z-number is a new framework of fuzzy sets that combines with constraint and reliability. Managing the uncertainty of Z-number is an important issue in the fuzzy decision making of Z-number based. In this paper, we first develop a new uncertainty measure of fuzzy set considering the influence of fuzziness measure and the range (or cardinality) of the fuzzy set. Some properties of the developed uncertainty measure of the fuzzy set are presented. We then propose and discuss method of measuring the uncertainty of Z-number. Examples are used to illustrate the effectiveness of the proposed methodologies. [ABSTRACT FROM AUTHOR]

Most of the community detection methods require the global information of the original network to be available, however, it is often expensive (even no way) to obtain the global information of the network in many real-world networks. So, the local community detection, only based on the local information, becomes especially important. The local community is the community in the network to which a given starting node belongs. Some local community detection methods have been proposed. However, these methods did not consider the characteristics of the local community during the local community formation. In this paper, we analyze the formation of the local community and propose two local community detection algorithms based on the dynamic membership function. Each of the algorithms is divided into three stages: 1) the initial stage, 2) the middle stage, and 3) the closing stage. At the initial stage, we design a dynamical membership function to detect local community and nodes with the greatest neighborhood intersect rate could be added to the local community. At the middle stage, we design another dynamical membership function, and the goal of this stage is to make the connection of the node in the local community closest. At the closing stage, the third dynamical membership function is provided, and the local community is further improved by collecting some nodes that should not be omitted. We test our algorithms on several synthetic datasets and real datasets; the results show that the local communities detected by our method are closer to the real local communities. [ABSTRACT FROM AUTHOR]

Skeletonization offers a compact representation of an object while preserving important topological and geometrical features. Literature on skeletonization of binary objects is quite mature. However, challenges involved with skeletonization of fuzzy objects are mostly unanswered. This paper presents a new theory and algorithm of skeletonization for fuzzy objects, evaluates its performance, and demonstrates its applications. A formulation of fuzzy grassfire propagation is introduced; its relationships with fuzzy distance functions, level sets, and geodesics are discussed; and several new theoretical results are presented in the continuous space. A notion of collision-impact of fire-fronts at skeletal points is introduced, and its role in filtering noisy skeletal points is demonstrated. A fuzzy object skeletonization algorithm is developed using new notions of surface- and curve-skeletal voxels, digital collision-impact, filtering of noisy skeletal voxels, and continuity of skeletal surfaces. A skeletal noise pruning algorithm is presented using branch-level significance. Accuracy and robustness of the new algorithm are examined on computer-generated phantoms and micro- and conventional CT imaging of trabecular bone specimens. An application of fuzzy object skeletonization to compute structure-width at a low image resolution is demonstrated, and its ability to predict bone strength is examined. Finally, the performance of the new fuzzy object skeletonization algorithm is compared with two binary object skeletonization methods. [ABSTRACT FROM AUTHOR]

MicroRNAs (miRNAs) are known as an important indicator of cancers. The presence of cancer can be detected by identifying the responsible miRNAs. A fuzzy-rough entropy measure (FREM) is developed which can rank the miRNAs and thereby identify the relevant ones. FREM is used to determine the relevance of a miRNA in terms of separability between normal and cancer classes. While computing the FREM for a miRNA, fuzziness takes care of the overlapping between normal and cancer expressions, whereas rough lower approximation determines their class sizes. MiRNAs are sorted according to the highest relevance (i.e., the capability of class separation) and a percentage among them is selected from the top ranked ones. FREM is also used to determine the redundancy between two miRNAs and the redundant ones are removed from the selected set, as per the necessity. A histogram based patient selection method is also developed which can help to reduce the number of patients to be dealt during the computation of FREM, while compromising very little with the performance of the selected miRNAs for most of the data sets. The superiority of the FREM as compared to some existing methods is demonstrated extensively on six data sets in terms of sensitivity, specificity, and $F$ score. While for these data sets the $F$ score of the miRNAs selected by our method varies from 0.70 to 0.91 using SVM, those results vary from 0.37 to 0.90 for some other methods. Moreover, all the selected miRNAs corroborate with the findings of biological investigations or pathway analysis tools. The source code of FREM is available at http://www.jayanta.droppages.com/FREM.html. [ABSTRACT FROM PUBLISHER]

In this study, we compared the amplitude and the duration of $P$ and $T$ waves of sport horses before a training program with after a training program. Waves are transformed to the entropies by the same methods of Şengönül et al., “The entropy of the waves $P$ and $T$ in electrocardiogram and some comments,” Int. J. Math. Model. Comput., vol. 6, pp. 159–173, 2016. We have benefitted from the definition of fuzzy sets and have assigned an entropy for each $P$ and $T$ waves of sport horses. Then, we have calculated Cesàro entropies for each wave in a particular segment for ten beats. In addition, the graphical representations are obtained for healthy and diseased horses by formalization from the paper “The entropy of the waves $P$ and $T$ in electrocardiogram and some comments,” by Şengönül et al. [ABSTRACT FROM PUBLISHER]