Fuzzy Degree Research Articles

Multi-criteria decision making with Hamacher aggregation operators based on multi-polar fuzzy Z-numbers

Multi-polar fuzzy sets are crucial for capturing and representing diverse opinions or conflicting criteria in decision-making processes with greater flexibility and precision. While, Z-numbers are important for effectively modeling uncertainty by incorporating both the reliability of information and its degree of fuzziness, enhancing decision-making in uncertain environments. To date, no model in the literature exhibits the properties of multi-polar fuzzy sets and Z-numbers. In this article, we introduce a new concept of multi-polar fuzzy Z-number and Hamacher operations for multi-polar fuzzy Z-numbers. Based on the Hamacher operations, we propose aggregation operators for multi-polar fuzzy Z-numbers, namely, multi-polar fuzzy Z-number Hamacher weighted averaging operator, multi-polar fuzzy Z-number Hamacher ordered weighted averaging operator, multi-polar fuzzy Z-number Hamacher weighted geometric operator and multi-polar fuzzy Z-number Hamacher ordered weighted geometric operator. Additionally, we develop a decision-making model based on the proposed Hamacher aggregation operators. Further, we apply the proposed technique to a couple of case studies to check the validity and authenticity of the proposed methodology. Finally, we compare the outcomes of the study with several existing techniques to assess the accuracy of the proposed model.

Cross-PIC: A cross-scale in-context learning network for 3D multibeam point cloud segmentation of submarine pipelines

The multibeam sonar has become a powerful tool for undersea pipeline detection, which can obtain high quality three-dimensional point cloud data. However, the identification accuracy of current pipeline algorithms remains low because of insufficient utilization of context features. Therefore, this paper proposes an improved context-learning point cloud segmentation network, named Cross-scale Point-In-Context (Cross-PIC), to identify submarine pipelines. Cross-PIC designs the sampling module Balanced-FPS to improve the equalization sampling. Meanwhile, Cross-PIC constructs different scale coding architecture based on context learning, which includes Auxiliary line and Baseline for multi-scale feature encoding. Finally, the Refine Module is designed to realize cross-scale coded feature fusion to output segmentation results. Experiments with different fuzzy degrees show that Cross-PIC also significantly outperforms the original Point-In-Context network with less training data. Cross-PIC also achieves better results than other networks based on point, voxel, and dynamic graph convolution.

Measuring integrated accessibility for sustainable mobility: a fuzzy set approach case study

Sustainable transportation is vital to climate justice and social equity. Despite the efforts to achieve sustainability, there is still a lack of adequate measurement that integrates land use and transportation systems, which can be barriers to planning implementation. With methodological improvements in fuzzy theory application, this study develops an integrated index to measure the sustainability of multimodal accessibility. We do so by defining a fuzziness degree based on the different trip purposes and modes of transportation with a case study in Isfahan, Iran. Sustainable accessibility indicators were developed for walking, biking, and public transportation to represent the performance of each transportation system, considering the integration with land-use patterns. We analyze transportation modes and the accessibility to five main urban activities, including employment opportunities, education, healthcare, shopping, and recreation services, based on the travel distances, followed by a statistical integration method with Principal Components Analysis (PCA) for each travel mode. The outcome provides insights for urban planners and transportation planners to effectively evaluate the degree of integration between transportation and land-use systems and contribute to enhancing sustainable accessibility.

Fuzzy centrality measures in social network analysis: Theory and application in a university department collaboration network

The motivation behind this research stems from the inherent complexity and vagueness in human social interactions, which traditional Social Network Analysis (SNA) approaches often fail to capture adequately. Conventional SNA methods typically represent relationships as binary or weighted ties, thereby losing the subtle nuances and inherent uncertainty in real-world social connections. The need to preserve the vagueness of social relations and provide a more accurate representation of these relationships motivates the introduction of a fuzzy-based approach to SNA. This paper proposes a novel framework for Fuzzy Social Network Analysis (FSNA), which extends traditional SNA to accommodate the vagueness of relationships. The proposed method redefines the ties between nodes as fuzzy numbers rather than crisp values and introduces a comprehensive set of fuzzy centrality indices, including fuzzy degree centrality, fuzzy betweenness centrality, and fuzzy closeness centrality, among others. These indices are designed to measure the importance and influence of nodes within a network while preserving the uncertainty in the relationships between them. The applicability of the proposed framework is demonstrated through a case study involving a university department's collaboration network, where relationships between faculty members are analyzed using data collected via a fascinating mouse-tracking technique.

Estimation of Reservoir Storage Capacity Using the Gould-Dincer Formula with the Aid of Possibility Theory

This paper presents a method for estimating reservoir storage capacity using the Gould–Dincer normal formula (G-DN), enhanced by the possibility theory. The G-DN equation is valuable for regional studies of reservoir reliability, particularly under climate change scenarios, using regional statistics. However, because the G-DN formula deals with measured data, it introduces a degree of uncertainty and fuzziness that traditional probability theory struggles to address. Possibility theory, an extension of fuzzy set theory, offers a suitable framework for managing this uncertainty and fuzziness. In this study, the G-DN formula is adapted to incorporate fuzzy logic, and the possibilistic nature of reservoir capacity is translated into a probabilistic framework using α-cuts from the possibility theory. These α-cuts approximate probability confidence intervals with high confidence. Applying the proposed methodology, in the present crisp case with the storage capacity D = 0.75, the value of the capacity C was found to be 1271×106 m3, and that for D = 0.5 was 634.5×106 m3. On the other hand, in the fuzzy case using the possibility theory, the value of the capacity for D = 0.75 is the internal [315,5679]×106 m3 and for D = 0.5 the value is interval [158,2839]×106 m3, with a probability of ≥95% and a risk level of α = 5% for both cases. The proposed approach could be used as a robust tool in the toolkit of engineers working on irrigation, drainage, and water resource projects, supporting informed and effective engineering decisions.

Constructing a Hybrid Algorithm to Model the Physical and Chemical Inspection Station Data of the Shatt Al-Arab Waters*

The aim of this paper is to find a hybrid method between of statistical methods that deal with non-linear high-dimensions. The data often suffer from complexity and overlap problems in their mathematical functions. It is difficult to delineate or accurately determine the effect of each variable on the other, accordingly it was constructing a hybrid model between the KPCA and FCM methods. The KPCA method aims to address the problem of high-dimensional nonlinear data and reduce it by finding a kernel matrix that depends primarily on the smoothing parameter matrix that was estimated using the ROT method. Then, the FCM was adopted to obtain the clusters. This proposal was applied to the water sector in Basrah Governorate through a study of (8) stations for physical and chemical examination through (15) variables for the years (2019, 2020, 2021) and data were collected on a monthly basis. Through the application of this methodology, the paper was able to determine (7) Basic variables, which are (TH, Na, Cl, TDS, No3, EC, O_G). As for the stations, the overlapping stations between the clusters were identified, which are (SH1, SH2, SH3, SH4, E20, T34), as for the best degree of fuzziness it was (3.6) and the best number of clusters is (k = 3).

Fuzzy Fractional Brownian Motion: Review and Extension

In traditional finance, option prices are typically calculated using crisp sets of variables. However, as reported in the literature novel, these parameters possess a degree of fuzziness or uncertainty. This allows participants to estimate option prices based on their risk preferences and beliefs, considering a range of possible values for the parameters. This paper presents a comprehensive review of existing work on fuzzy fractional Brownian motion and proposes an extension in the context of financial option pricing. In this paper, we define a unified framework combining fractional Brownian motion with fuzzy processes, creating a joint product measure space that captures both randomness and fuzziness. The approach allows for the consideration of individual risk preferences and beliefs about parameter uncertainties. By extending Merton’s jump-diffusion model to include fuzzy fractional Brownian motion, this paper addresses the modelling needs of hybrid systems with uncertain variables. The proposed model, which includes fuzzy Poisson processes and fuzzy volatility, demonstrates advantageous properties such as long-range dependence and self-similarity, providing a robust tool for modelling financial markets. By incorporating fuzzy numbers and the belief degree, this approach provides a more flexible framework for practitioners to make their investment decisions.

From Fuzzy to Mobile Fuzzy

From Fuzzy to Mobile Fuzzy

Developing an Adaptive Neuro-Fuzzy Inference System for Performance Evaluation of Pavement Construction Projects

This study employs an adaptive neuro-fuzzy inference system (ANFIS) to identify critical success factors (CSFs) crucial for the success of pavement construction projects. Challenges such as construction cost delays, budget overruns, disputes, claims, and productivity losses underscore the need for effective project management in pavement projects. In contemporary construction management, additional performance criteria play a vital role in influencing the performance and success of pavement projects during construction operations. This research contributes to the existing body of knowledge by comprehensively identifying a multidimensional set of critical success performance factors that impact pavement and utility project management. A rigorous literature review and consultations with pavement experts identified sixty CSFs, categorized into seven groups. The relative importance of each element and group is determined through the input of 287 pavement construction specialists who participated in an online questionnaire. Subsequently, the collected data undergo thorough checks for normality, dependability, and independence before undergoing analysis using the relative importance index (RII). An ANFIS is developed to quantitatively model critical success factors and assess the implementation performance of construction operations management (COM) in the construction industry, considering aspects such as clustering input/output datasets, fuzziness degree, and optimizing five Gaussian membership functions. The study confirms the significance of three primary CSFs (financial, bureaucratic, and governmental) and communication-related variables through a qualitative structural and behavioral validation process, specifically k-fold cross-validation. The outcomes of this research hold practical implications for the management and assessment of overall performance indices in pavement construction projects. The ANFIS model, validated through robust testing methodologies, provides a valuable tool for industry professionals seeking to enhance the success and efficiency of pavement construction endeavors.

Compromise optimum allocation in neutrosophic multi-character survey under stratified random sampling using neutrosophic fuzzy programming

Survey sampling has wide range of applications in social and scientific investigation to draw inference about the unknown parameter of interest. In complex surveys, the sample information about the study variable cannot be expressed by a precise number under uncertain environment due fuzziness and indeterminacy. Therefore, this information is expressed by neutrosophic numbers rather than the classical numbers. The neutrosophic statistics, which is generalization of classical statistics, deals with the neutrosophic data that has some degree of indeterminacy and fuzziness. In this study, we investigate the compromise optimum allocation problem for estimating the population means of the neutrosophic study variables in a multi-character stratified random sampling under uncertain per unit measurement cost. We proposed the intuitionistic fuzzy cost function, modeling the fuzzy uncertainty in stratum per unit measurement cost. The compromise optimum allocation problem is formulated as a multi-objective intuitionistic fuzzy optimization problem. The solution methodology is suggested using neutrosophic fuzzy programming and intuitionistic fuzzy programming approaches. A numerical study includes the means estimation of atmospheric variables is presented to explore the real-life application, explain the mathematical formulation, and efficiency comparison with some existing methods. The results show that the suggested methods produce more precise estimates with less utilization of survey resources as compared to some existing methods. The Python is used for statistical analysis, graphical designing and numerical optimization problems are solved using GAMS.

A Systematic Overview of Fuzzy Extended Entity Relationship (Fuzzy EER) Model Using Practical Examples

Most real-world data are vague and imprecise, so traditional relational databases cannot represent, integrate, and manage them effectively. In this research, we gave an overview of the application of fuzzy logic to the conceptual modeling facet of database design, which is an enhancement of the Extended Entity Relationship (EER) model. This is done to give a clearer picture of how imprecise and vague data are represented and managed, especially in multiple-criteria decision-making database systems. To achieve this, an overview of fuzzy attributes, fuzzy values in the attributes, notation for fuzzy representations, fuzzy degree in each value of an attribute, fuzzy degree in a set of values of different attributes, fuzzy degree with its own meaning and fuzzy degree to the model was carried out with practical examples.

Entropy for q-rung linear diophantine fuzzy hypersoft set with its application in MADM

A notable advancement in fuzzy set theory is the q-rung linear diophantine fuzzy set. The soft set theory was expanded into the hypersoft set theory. By combining both the q-rung linear diophantine fuzzy set and hypersoft set, this study describes the notion of q-rung linear diophantine fuzzy hypersoft set that can handle multi sub-attributed q-rung linear diophantine fuzzy situations in the real world. Furthermore, some of its algebraic operations such as union, intersection and complement are described in this study. In addtion, the entropy measure of the q-rung linear diophantine fuzzy hypersoft set is established as it is helpful in determining the degree of fuzziness of q-rung linear diophantine fuzzy hypersoft sets. A multi-attribute decision making algorithm based on suggested entropy is presented in this study along with a numerical example of selecting a suitable wastewater treatment technology to demonstrate the effectiveness of the proposed algorithm in real-life situations. A comparative study was undertaken that describes the validity, robustness and superiority of the proposed algorithm and notions by discussing the advantages and drawbacks of existing theories and algorithms. Overall, this study describes a novel fuzzy extension that prevails over the existing ones and contributes to the real world with a valid real-life multi-attribute decision making algorithm that can cover many real-world problems that are unable to be addressed by the existing methodology.

Privacy-Preserving Face Recognition Method Based on Randomization and Local Feature Learning.

Personal privacy protection has been extensively investigated. The privacy protection of face recognition applications combines face privacy protection with face recognition. Traditional face privacy-protection methods encrypt or perturb facial images for protection. However, the original facial images or parameters need to be restored during recognition. In this paper, it is found that faces can still be recognized correctly when only some of the high-order and local feature information from faces is retained, while the rest of the information is fuzzed. Based on this, a privacy-preserving face recognition method combining random convolution and self-learning batch normalization is proposed. This method generates a privacy-preserved scrambled facial image and an image fuzzy degree that is close to an encryption of the image. The server directly recognizes the scrambled facial image, and the recognition accuracy is equivalent to that of the normal facial image. The method ensures the revocability and irreversibility of the privacy preserving of faces at the same time. In this experiment, the proposed method is tested on the LFW, Celeba, and self-collected face datasets. On the three datasets, the proposed method outperforms the existing face privacy-preserving recognition methods in terms of face visual information elimination and recognition accuracy. The recognition accuracy is >99%, and the visual information elimination is close to an encryption effect.

The fuzzy degree of nondensifiability and applications

We introduce the notion of fuzzy degree of nondensifiability (FDND for short) as a non-negative real number that measures the Hausdorff distance between a bounded set of a fuzzy metric space and its closest Peano continuum. The FDND allows us to analyze the precompact subsets of a fuzzy metric space. In fact, we present a characterization of the family of precompact and arc-connected subsets in terms of the FDND, namely, those subsets whose FDND is equal to zero, provided that the fuzzy metric space be of stationary type. As an application of our results, we prove a variant of the Sadovskiĭ fixed point theorem based on the FDND, which generalizes that of Schauder in fuzzy Banach spaces. Likewise, we present an example where the FDND method is applicable but the one based on measures of noncompactness is not.

Quantum Euler angles and agency-dependent space-time

Abstract Quantum gravity is expected to introduce quantum aspects into the description of reference frames. Here we begin exploring how quantum gravity induced deformations of classical symmetries could modify the transformation laws among reference frames in an effective regime. We invoke the quantum group SUq(2) as a description of deformed spatial rotations and interpret states of a representation of its algebra as describing the relative orientation between two reference frames. This leads to a quantization of one of the Euler angles and to an aspect of agency dependence: space is reconstructed as a collection of fuzzy points, exclusive to each agent, which depends on their choice of reference frame. Each agent can choose only one direction in which points can be sharp, while points in all other directions become fuzzy in a way that depends on this choice. Two agents making different choices will thus observe the same points with different degrees of fuzziness.

Fuzzy based self-similarity weight estimation in non-local means for gray-scale image de-noising

Image de-noising in imaging systems is one of the most demanding issues that have been addressed in this work. Non-local mean filtering is gaining traction as a convincing method for image de-noising. Nevertheless, the performance of the traditional non-local mean filter is diminished by the computational expense of its weighted averaging process. In the proposed method, the similarity between the two patches of the image subspace is used to find the best weight for each pixel using a fuzzy inference algorithm. By using the similarity of non-local neighborhood pixels as an input antecedent in the input fuzzy set and the degree of weights as a consequent in the output fuzzy set, the fuzzy inference system which consists of IF-THEN rules, implication, and aggregation is employed. Eventually, de-fuzzification helps to measure how similar the pixels are to their non-local neighborhoods and estimates the fuzzy degrees of weight. Experiments on a variety of speckled noisy gray-scale images from standard and real public datasets demonstrate the improved performance of this fuzzy-based self-similar weight approximation in non-local mean filtering when compared to state-of-the-art image de-noising methods and sophisticated non-local mean methods in terms of standard evaluation metrics. Additionally, the suggested technique works satisfactorily when tested on actual speckled synthetic aperture radar images.

Computing crisp bisimulations for fuzzy structures

We present an efficient algorithm for computing the partition corresponding to the greatest crisp bisimulation of a given finite fuzzy labeled graph. Its complexity is of order O((mlog⁡l+n)log⁡n), where n, m and l are the number of vertices, the number of nonzero edges and the number of different fuzzy degrees of edges of the input graph, respectively. We also study a similar problem for the setting with counting successors, which corresponds to the case with qualified number restrictions in description logics and graded modalities in modal logics. In particular, we provide an efficient algorithm with the complexity O((mlog⁡m+n)log⁡n) for the considered problem in that setting.

Fuzzy Degree and Intuitionistic Fuzzy Degree for Chemical Hyperstructures

The notion of hyperstructures first introduced by Marty in 1934 as a generalization of algebraic structures. Next, by associating fuzzy sets, Corsini introduced new notion in hyperstructures, that is fuzzy hyperstructures. After fuzzy hyperstructures introduced by Corsini, Cristea introduced the notion of intuitionistic fuzzy hyperstructures as a generalization of fuzzy hyperstructures. In 2023, Violeta-Fotea related the notion of fuzzy hyperstructures with genetic inheritance. Inspired by this research, this paper aims to find relation between fuzzy and intuitionistic fuzzy hyperstructures with chemical hyperstructures, that is to finding the fuzzy degree and intuitionistic fuzzy degree on chemical hyperstructures such as redox reactions, electrochemical cells, equilibrium reactions, and acid rain reactions.

Extended DEMATEL method with intuitionistic fuzzy information: A case of electric vehicles.

The Decision-Making Trial and Laboratory (DEMATEL) methodology excels in the analysis of interdependent factors within complex systems, with correlation data typically presented in crisp values. Nevertheless, the judgments made by decision-makers often possess a degree of fuzziness and uncertainty, rendering the sole reliance on precise values inadequate for representing real-world scenarios. To address this issue, our study extends the DEMATEL approach to more effectively and efficiently handle intuitionistic fuzzy information, which denotes the factor correlation information from decision-makers in the form of intuitionistic fuzzy terms. The paper aggregates the intuitionistic fuzzy correlation information from each decision-maker, employing operators designed for managing intuitionistic fuzzy numbers. The significance and categorization of factors are determined through intuitionistic fuzzy matrix operations. Additionally, a causal and effect diagram is constructed to elucidate the distinct roles of these factors. Finally, this study illustrates the applicability of our proposed method with a real-world case in the context of electric vehicles (EVs). The study's results identify four cause factors and six effect factors within EV battery technology. The identification and categorization of these factors will assist EV companies in implementing targeted measures to foster the advancement of the battery technology.

Application of high-dimensional multi-objective differential evolutionary algorithm based on global ordering to heat supply pipe network resistance identification

The distribution of resistance coefficients of heat supply pipe networks is the key data guiding the hydraulic balance adjustment of heat networks. Since the heat supply pipe network is composed of many pipe segments and the resistance coefficient of each pipe segment is different during heat supply operation, the identification of the resistance coefficient of the heat supply pipe network is an optimization problem with multiple objective functions. In this paper, a high-dimensional multi-objective differential evolutionary algorithm based on global sorting is developed as a method to identify the resistance coefficients of the heat network and the multi-objective algorithm is applied to the resistance identification of the heat network, and the computational process of resistance identification is improved. The fuzzy mathematical method is applied to the process of resistance identification, and a set of optimal solution sets are generated through the identification of each pipe segment and the optimal solutions are selected from the optimal solution sets based on the fuzzy degree of subordination to solve the problem of determining the optimal solutions. The problem of determining the optimal solution is solved. The results show that compared with the single-objective algorithm, the high-dimensional multi-objective differential evolutionary algorithm based on global sorting produces a uniform and concentrated optimal solution set, and the optimal solution accuracy is higher.