Search Results (35)

Targeting the classification and evaluation of chemical flooding well groups in medium-thick sandstone reservoirs (single-layer thickness: 5–15 m), this study proposes a multi-level classification model based on decision trees. Through the comprehensive analysis of key static factors influencing chemical flooding efficiency, a four-tier classification index system was established, comprising: interlayer/baffle development frequency (Level 1), thickness-weighted permeability rush coefficient (Level 2), reservoir rhythm characteristics (Level 3), and pore-throat radius-based reservoir connectivity quality (Level 4) as its core components. The model innovatively transforms common reservoir physical parameters (porosity and permeability) into pore-throat radius parameters to enhance guidance for polymer molecular weight design, while employing a thickness-weighted permeability rush coefficient to simultaneously characterize heterogeneity impacts from both permeability and thickness variations. Unlike existing classification methods primarily designed for thin-interbedded reservoirs—which consider only connectivity or apply fuzzy mathematics-based normalization—this model specifically addresses medium-thick reservoirs’ unique challenges of interlayer development and intra-layer heterogeneity. Furthermore, its decision tree architecture clarifies classification logic and significantly reduces data preprocessing complexity. In terms of engineering practicality, the classification results are directly linked to well-group development bottlenecks, as validated in the J16 field application. By implementing customized chemical flooding formulations tailored to the study area, the production performance in the expansion zone achieved comprehensive improvement: daily oil output dropped from 332 tons to 243 tons, then recovered to 316 tons with sustained stabilization. Concurrently, recognizing that interlayer barriers were underdeveloped in certain well groups during production layer realignment, coupled with strong vertical heterogeneity posing polymer channeling risks, targeted profile modification and zonal injection were implemented prior to flooding conversion. This intervention elevated industrial replacement flooding production in the study area from 69 tons to 145 tons daily post-conversion. This framework provides a theoretical foundation for optimizing chemical flooding pilot well-group selection, scheme design, and dynamic adjustments, offering significant implications for enhancing oil recovery in medium-thick sandstone reservoirs through chemical flooding. Full article

Sensor selection in IoT-based smart healthcare systems is a complex fuzzy decision-making problem due to the presence of numerous uncertain and interdependent evaluation criteria. Traditional fuzzy multi-criteria decision-making (MCDM) approaches often assume independence among criteria and rely on aggregation operators that impose sharp transitions between preference levels. These assumptions can lead to decision outcomes with insufficient differentiation, limited discriminatory capacity, and potential issues in consistency and sensitivity. To overcome these limitations, this study proposes a novel fuzzy decision-making framework by integrating Quasi-D-Overlap functions into the fuzzy MARCOS (Measurement of Alternatives and Ranking According to Compromise Solution) method. Quasi-D-Overlap functions represent a generalized extension of classical overlap operators, capable of capturing partial overlaps and interdependencies among criteria while preserving essential mathematical properties such as associativity and boundedness. This integration enables a more intuitive, flexible, and semantically rich modeling of real-world fuzzy decision problems. In the context of real-time health monitoring, a case study is conducted using a hybrid edge–cloud architecture, involving sensor tasks such as heartrate monitoring and glucose level estimation. The results demonstrate that the proposed method provides greater stability, enhanced discrimination, and improved responsiveness to weight variations compared to traditional fuzzy MCDM techniques. Furthermore, it effectively supports decision-makers in identifying optimal sensor alternatives by balancing critical factors such as accuracy, energy consumption, latency, and error tolerance. Overall, the study fills a significant methodological gap in fuzzy MCDM literature and introduces a robust fuzzy aggregation strategy that facilitates interpretable, consistent, and reliable decision making in dynamic and uncertain healthcare environments. Full article

Vehicle congestion and the environmental problems associated with the increasing vehicle fleet have led stakeholders to create solutions to these problems. Park-and-Ride (P&R) facilities are provided as a solution for public transportation to avoid increasing vehicular flow and using private vehicles. However, the optimal location of these facilities is still a challenge to be considered. Therefore, this article aims to present a systematic review of the mathematical models applied for P&R localization, using the PRISMA protocol to ensure a comprehensive analysis. A total of 44 articles between 2002 and 2025 were identified into four categories: decision support models, econometric models, optimization models, and other models. The review also examines the term distribution of urban contexts where the mathematical models are applied, distinguishing between Global North versus Global South urban contexts. The results showed the efficiency of mathematical models within the decision support models category due to their integration with multiple criteria. The econometric models analyze factors influencing user behavior, while the optimization models improve and optimize the efficiency of transport networks despite facing computational challenges. Finally, other models, such as multilevel programming and fuzzy logic, offer adaptive solutions for highly variable urban environments. The primary contribution of this study is its comprehensive application of the mathematical models used for the location of P&R facilities. This offers a systematic approach for anticipating future urban situations, developing supporting policies, and analyzing their effects. Full article

With the rapid advancement of the marine economy, conventional salvage equipment has become increasingly inadequate in meeting the operational demands of complex aquatic environments and deep-sea salvage operations. This study presents the preliminary design of a novel salvage catamaran and proposes a multi-level fuzzy comprehensive evaluation framework for hydrodynamic performance under multi-sea-state and multi-operational conditions. A hydrodynamic performance evaluation indicator system was established, integrating resistance and seakeeping criteria. Computational fluid dynamics (CFDs) simulations with overset grids were employed to calculate the resistance characteristics. Potential flow-theory-based analysis quantified motion responses under irregular waves. The framework effectively distinguishes performance variations across five sea states and two sets of loading conditions through composite scoring. Key findings demonstrate that wave-added resistance coefficients increase proportionally with a significant wave height (Hs) and spectral peak period (Tp), while payload variations predominantly influence heave amplitudes. A fuzzy mathematics-driven model assigned entropy–Analytic Hierarchy Process (AHP) hybrid weights, revealing operational trade-offs: Case1-Design achieved optimal seakeeping and resistance, whereas Case5-Light exhibited critical motion thresholds. Adaptive evaluation strategies were proposed, including dynamic weight adjustments for long/short-wave-dominated regions via sliding window entropy updates. This work advances the systematic evaluation of catamarans, offering a validated methodology for balancing hydrodynamic efficiency and operational safety in salvage operations. Full article

The construction of bridge pile foundations in karst regions faces significant risks, including karst collapse and ground subsidence caused by dewatering during excavation. Both karst collapse and shallow soil cavity subsidence are influenced by numerous factors, which significantly complicates the risk assessment of bridge pile foundation construction in these areas. This study proposes a risk assessment method for bridge pile foundation construction in karst regions based on the Fuzzy Analytic Hierarchy Process (FAHP). An evaluation index system for pile foundation construction risks was established through experimental research, expert surveys, and data analysis. Additionally, the concept of fuzzy mathematics was introduced to quantify the weights of the indicators, enabling the comprehensive assessment of multi-source risks. Experimental results from bridges across the project area demonstrate that this method exhibits a certain level of reliability in assessing the risks of bridge pile foundation construction in karst regions, with the evaluation results aligning well with actual conditions. Full article

This paper explores a multi-objective, multi-period integrated routing and scheduling problem under uncertain conditions for distributing relief to disaster areas. The goals are to minimize costs and maximize satisfaction levels. To achieve this, the proposed mathematical model aims to speed up the delivery of relief supplies to the most affected areas. Additionally, the demands and transportation times are represented using fuzzy numbers to more accurately reflect real-world conditions. The problem was formulated using a fuzzy multi-objective integer programming model. To solve it, a hybrid algorithm combining a multi-objective ant colony system and simulated annealing algorithm was proposed. This algorithm adopts two ant colonies to obtain a set of nondominated solutions (the Pareto set). Numerical analyses have been conducted to determine the optimal parameter values for the proposed algorithm and to evaluate the performance of both the model and the algorithm. Furthermore, the algorithm’s performance was compared with that of the multi-objective cat swarm optimization algorithm and multi-objective fitness-dependent optimizer algorithm. The numerical results demonstrate the computational efficiency of the proposed method. Full article

This paper deals with the austempering of ductile iron (ADI) and clarifies the influential austempering parameters during the production of ADI. During the austempering process, the heat treatment parameters can be varied, thus influencing the final microstructure and, of course, the mechanical properties of ADI. To appropriately conduct experiments and obtain good results, an experimental plan was developed using the Design Expert 13 software. Along with the heat treatment parameters, the influence of the copper content on the ADI toughness, tensile strength, and elongation was determined. The obtained results from this experiment were used to develop unique mathematical models which describe the influences of heat treatment and copper content on the observed mechanical properties of ADI samples. These mathematical models can be applied to predict the analysed mechanical properties of ADI in the dependence of heat treatment parameters and copper content in base ductile iron. For the multi response optimisation of toughness, tensile strength, and elongation, a hybrid grey-fuzzy technique was presented as a significant contribution to the enhancement of the analysed mechanical properties. Consequently, the copper content and heat treatment parameter levels that resulted in the maximal mechanical properties’ functions were defined. Full article

The research on the deep coalbed methane (CBM) in the Ordos Basin is mostly concentrated on the eastern margin of the basin. The geological resources of the Benxi Formation in the Yulin area, located in the central-eastern part, cover 15,000 × 10⁸ m³, indicating enormous resource potential. However, the characteristics of the reservoir distribution and the favorable areas are not yet clear. This research comprehensively performed data logging, coal rock experiments, and core observations to identify the geological characteristics of the #8 coal seam, using a multi-level fuzzy mathematics method to evaluate the favorable area. The results indicate the following: (1) The thickness of the #8 coal in the Yulin Block ranges from 2.20 m to 11.37 m, with depths of between 2285.72 m and 3282.98 m, and it is mainly underlain by mudstone; the gas content ranges from 9.74 m³/t to 23.38 m³/t, showing a northwest–low and southeast–high trend. The overall area contains low-permeability reservoirs, with a prevalence of primary structural coal. (2) A multi-level evaluation system for deep CBM was established, dividing the Yulin Block into three types of favorable areas. This block features a wide range of Type I favorable areas, concentrated in the central-eastern, northern, and southwestern parts; Type II areas are closely distributed around the edges of Type I areas. The subsequent development process should prioritize the central-eastern part of the study area. The evaluation system established provides a reference for selecting favorable areas for deep CBM and offers theoretical guidance for targeted exploration and development in the Yulin area. Full article

This research investigates the multi-response of both material removal rate (MRR) and surface roughness (Ra) for the wire electrical discharge machining (WEDM) of two stainless steel alloys: AISI 304 and AISI 316. Experimental results are utilized to compare the machining responses obtained for AISI 316 with those obtained for AISI 304, as previously reported in the literature. The experimental work is conducted through a full factorial experimental design of five running parameters with different levels: applied voltage, transverse feed, pulse-on/pulse-off times and current intensity. The machined workpieces are analyzed using an image processing technique in order to evaluate the size of cut slots to allow the calculation of the MRR. Followed by the characterization of the surface roughness along the side walls of the slots. Different mathematical regression techniques were developed to represent the multi-response of both materials using the MATLAB regression toolbox. It was found that WEDM process parameters have a fuzzy influence on the responses of both material models. This allowed for multi-objective optimization of the regression models using four different techniques: multi-objective genetic algorithm (MOGA), multi-objective pareto search algorithm (MOPSA), weighted value grey wolf optimizer (WVGWO) and osprey optimization algorithm (OOA). The optimization results reveal that the optimal WEDM parameters of each response are inconsistent to the others. Hence, the optimal results are considered a compromise between the best results of different responses. Noteworthily, the multi-objective pareto search algorithm outperformed the other candidates. Eventually, the optimal results of both materials share the high voltage, high transverse feed rate and low pulse-off time parameters; however, AISI 304 requires low pulse-on time and current intensity levels while AISI 316 optimal results entail higher pulse-on time and current levels. Full article

Mathematical expression retrieval is an essential component of mathematical information retrieval. Current mathematical expression retrieval research primarily targets single modalities, particularly text, which can lead to the loss of structural information. On the other hand, multimodal research has demonstrated promising outcomes across different domains, and mathematical expressions in image format are adept at preserving their structural characteristics. So we propose a multi-modal retrieval model for mathematical expressions based on ConvNeXt and HFS to address the limitations of single-modal retrieval. For the image modal, mathematical expression retrieval is based on the similarity of image features and symbol-level features of the expression, where image features of the expression image are extracted by ConvNeXt, while symbol-level features are obtained by the Symbol Level Features Extraction (SLFE) module. For the text modal, the Formula Description Structure (FDS) is employed to analyze expressions and extract their attributes. Additionally, the application of the Hesitant Fuzzy Set (HFS) theory facilitates the computation of hesitant fuzzy similarity between mathematical queries and candidate expressions. Finally, Reciprocal Rank Fusion (RRF) is employed to integrate rankings from image modal and text modal retrieval, yielding the ultimate retrieval list. The experiment was conducted on the publicly accessible ArXiv dataset (containing 592,345 mathematical expressions) and the NTCIR-mair-wikipedia-corpus (NTCIR) dataset.The MAP@10 values for the multimodal RRF fusion approach are recorded as 0.774. These substantiate the efficacy of the multi-modal mathematical expression retrieval approach based on ConvNeXt and HFS. Full article

Rock burst is a multifaceted phenomenon that involves various intricate factors. A precise evaluation of its risk encounters numerous challenges. To address this issue, the present paper proposed a multilevel fuzzy comprehensive evaluation model based on the Analytic Hierarchy Process–Fuzzy Comprehensive Evaluation (AHP-FCE) method. Three primary influencing factors and twelve secondary influencing factors that impact the rock burst risk were identified. The mechanisms by which each influencing factor affects the rock burst were analyzed and the membership degree for each factor was calculated accordingly. The weight of each influencing factor was determined through the AHP. To obtain a quantitative evaluation result, the evaluation model was calculated using the second-order fuzzy mathematics calculation method. The application of the model was demonstrated on the 310 working face of the Tingnan Coal Mine, and the evaluation results were consistent with those achieved through the use of the comprehensive index method and the probability index method. All of the results exhibited consistent alignment with the actual circumstances. The verification process confirmed the scientific, effective, and practical nature of the model. Full article

The Molodtsov-initiated soft set theory plays an important role as a powerful mathematical tool for handling uncertainty. As an extension of the soft set, the fuzzy soft set can be seen to be more generic and flexible than utilizing the soft set only that fails to represent problem parameters fuzziness. Through this progress, the fuzzy soft set theory cannot deal with decision-making problems involving multi-attribute sets, bipolarity, or some effective considered parameters. Therefore, the goal of this article is to adapt effectiveness and bipolarity concepts with the multi-fuzzy soft set of order n. One can see that this approach generates a novel, extended, effective decision-making environment that is more applicable than any previously introduced one. In addition, types, concepts, and operations of effective bipolar-valued multi-fuzzy soft sets of dimension n are provided, each with an example. Furthermore, properties like absorption, associative, distributive, commutative, and De Morgan’s laws of those new sets are investigated. Moreover, a decision-making methodology under effective bipolar-valued multi-fuzzy soft settings is established. This technique facilitates reaching the final decision that this student is qualified to take a certain education level, or this patient is suffering from a certain disease, etc. In addition, a case study represented in a medical diagnosis example is discussed in detail to make the proposed algorithm clearer. Applying matrix techniques in this example as well as using MATLAB^®, not only makes it easier and faster in doing calculations, but also gives more accurate, optimal, and effective decisions. Finally, the sensitivity analysis, as well as a comparison with the existing methods, are conducted in detail and are summarized in a chart to show the difference between them and the current one. Full article

The knowledge measure or uncertainty measure for constructing interval-valued intuitionistic fuzzy sets has attracted much attention. However, many uncertainty measures are measured by the entropy of interval-valued intuitionistic fuzzy sets, which cannot adequately reflect the knowledge of interval-valued intuitionistic fuzzy sets. In this paper, we not only extend the axiomatic definition of the knowledge measure of the interval-valued intuitionistic fuzzy set to a more general level but also establish a new knowledge measure function complying with the distance function combined with the technique for order preference by similarity to ideal solution (TOPSIS). Further, we investigate the properties of the proposed knowledge measure based on mathematical analysis and numerical examples. In addition, we create the entropy function by calculating the distance from the interval-valued fuzzy set to the most fuzzy point and prove that it satisfies the axiomatic definition. Finally, the proposed entropy is applied to the multi-attribute group decision-making problem with interval-valued intuitionistic fuzzy information. Experimental results demonstrate the effectiveness and practicability of the proposed entropy measure. Full article

The linear Diophantine fuzzy set notion is the main foundation of the interactive method of tackling nonlinear fractional programming problems that is presented in this research. When the decision maker (DM) defines the degree $\alpha$ of $\alpha$ level sets, the max-min problem is solved in this interactive technique using Zimmermann’s min operator method. By using the updating technique of degree $\alpha$, we can solve DM from the set of $\alpha$-cut optimal solutions based on the membership function and non-membership function. Fuzzy numbers based on $\alpha$-cut analysis bestowing the degree $\alpha$ given by DM can first be used to classify fuzzy Diophantine inside the coefficients. After this, a crisp multi-objective non-linear fractional programming problem (MONLFPP) is created from a Diophantine fuzzy nonlinear programming problem (DFNLFPP). Additionally, the MONLFPP can be reduced to a single-objective nonlinear programming problem (NLPP) using the idea of fuzzy mathematical programming, which can then be solved using any suitable NLPP algorithm. The suggested approach is demonstrated using a numerical example. Full article

In order to simulate the flight state of the helicopter effectively, it is necessary to trim the helicopter during the forward flight in a wind tunnel test. Previously, due to the lack of an internal-control closed loop in the test rig, the helicopter-wind-tunnel-test trimming was carried out manually, with low test efficiency, unstable data quality, and high labor intensity. With the continuous development of computer technology and automatic control technology, the helicopter-wind-tunnel-test trimming technology has been developing in the direction of automation and intelligence. The helicopter wind tunnel test automatic trimming system is a typical multi-input–multi-output (MIMO), strongly coupled, and complex nonlinear system, involving data acquisition and a processing system, rotor control system, tail-supported mechanism control system, wind-tunnel-speed pressure control system, and other subsystems, which is difficult to describe with an accurate mathematical model. Therefore, in order to meet the needs of a 3 m diameter rotor model aerodynamic performance evaluation and noise characteristics research wind tunnel test, an error feedback variable step automatic trimming algorithm is proposed based on the fuzzy-control principle to realize automatic trimming of aerodynamic loads of rotor model in the forward flight state. To verify the effectiveness and reliability of the trimming strategy, a series of wind tunnel tests on a 3 m diameter scaled rotor model of a helicopter were conducted in the FL-17 aeroacoustics wind tunnel of China Aerodynamics Research and Development Center (CARDC) based on the Φ3m tail-supported helicopter rotor model wind tunnel test rig. The wind tunnel test’s results show that the proposed automatic trimming algorithm has the characteristics of fast trimming speed and high efficiency, which can realize the automatic trimming of rotor model aerodynamic loads under different test states in the wind tunnel test effectively and reliably and greatly improve the intelligence level of helicopter wind tunnel test. Full article