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The study aimed to explore the influence of pre-oxidation oxygen concentration on the mass variation and microstructure of coal oxidation using TG and FTIR experiments. The objective was to comprehend the thermal effects and mechanisms of coal oxidation under distinct pre-oxidation conditions. Employing fuzzy mathematics and multiple linear regression equations, the study sought to elucidate the influence mechanism of pre-oxidation oxygen concentration on the thermal effect. The findings reveal that pre-oxidation did not alter the overall weight loss pattern during the spontaneous combustion process of coal, yet significantly accelerated the rate of weight loss. Furthermore, the dry cracking temperature experienced a notable advancement. Through FTIR experiments, it was observed that pre-oxidation activated the reactivity of C=O, -CH2-, and aromatic hydrocarbons, thus leading to more intense reactions. The key functional groups influencing the mass change were identified as aromatic hydrocarbons and hydrogen bonds. Notably, the pre-oxidation effect on the thermal impact was most pronounced when the pre-oxidation oxygen concentration reached 15%. [ABSTRACT FROM AUTHOR]

Gully erosion is one of the most severe forms of land degradation and poses a serious threat to regional food security, biodiversity, and human survival. However, there are few methods for the quantitative evaluation of gully activity, and the relationships between gully activity and influencing factors require further in-depth study. This study takes the Sunshui River Basin, as a case study. Based on field investigation, unmanned aerial vehicle (UAV) photography and remote sensing images, 71 typical gullies were identified. The vegetation coverage (VC), slope and main-branch gully ratio (MBGR) were used as evaluation indicators, and the gully activity was calculated using the fuzzy mathematics membership degree and then evaluated quantitatively. The factors influencing different active gullies were also analyzed. The results showed that (1) the fuzzy comprehensive evaluation method can be used to identify gully activity. Different levels of gully activity were defined based on the gully activity index. The active indices of stable gullies ranged from 0–0.25, those of semiactive gullies ranged from 0.25–0.75, and those of active gullies ranged from 0.75–1. (2) The activity indices of the 71 gullies ranged from 0.054 to 0.999, with an average value of 0.656. There are 31 active gullies, and 31 semiactive gullies. A total of 87.32% of the gullies in the study area were in the early or middle stage of gully development. Gully erosion was intense, which is consistent with the serious reality of soil erosion. (3) Gully activity was affected by multiple factors. It was significantly positively correlated with topographic relief (TR) (r = 0.64, P<0.01) and surface curvature (SC) (r = 0.51, P<0.01), while it was significantly negatively correlated with land use type (LUT) (r = -0.5, P<0.01). Surface roughness (SR) (r = 0.2, P<0.01) was positively correlated with gully activity; but not significantly. There was no significant correlation between aspect (As) and gully activity. The results of this study are helpful for quantitatively determining the level of gully activity and understanding the development process and mechanism controlling gullies, providing a reference for research on related regions and geomorphologic information. [ABSTRACT FROM AUTHOR]

In this paper, we use a t -measure derived from fuzzy logic to evaluate progress toward the 2030 Agenda for Sustainable Development adopted by the United Nations member states. In the first of this two-part series, we examined each of the Sustainable Development Goals individually. We now build a composite index score for 163 countries using the t -measure to examine their progress towards the Sustainable Development Goals as a whole, rank them, and examine the characteristics of highly performing and of poorly performing countries. We also study the impact of income category and region on progress towards the Goals. [ABSTRACT FROM AUTHOR]

We use a t -measure derived from fuzzy logic to evaluate progress toward the 2030 Agenda for Sustainable Development adopted by the United Nations Member States. In this first of a two-part series, we evaluate the 17 individual Sustainable Development Goals by applying the t -measure to a set of indicators. We examine the distribution and characteristics of the scores for each Goal and note trends over time, highlight outlier countries, and evaluate progress in each Goal area. In the second part, we will consider worldwide progress toward the Goals as a whole. [ABSTRACT FROM AUTHOR]

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This paper presents the establishment of a sensory evaluation system for purple sweet potato rice steamed sponge cake (PSPRSSC) utilizing fuzzy mathematics. Initially, eight key sensory evaluation indices were identified through expert consultations. These indices were subsequently prioritized using fuzzy binary comparison, resulting in the following order: aroma, taste, crust color, elasticity, viscosity, chewiness, hardness, and brightness. The corresponding weight values assigned to each index were 23%, 18%, 16%, 13%, 12%, 8%, 6%, and 4%, respectively. Notably, aroma was found to have a more significant impact than visual attributes in the sensory evaluation of PSPRSSC. Based on this prioritization, comprehensive sensory evaluation criteria for PSPRSSC were formulated. Verification tests confirmed the efficacy of the proposed evaluation system. This study provides critical data and theoretical support for the sensory quality assessment of PSPRSSC, thereby facilitating its industrialization and enhancing its market viability. [ABSTRACT FROM AUTHOR]

In this study, trapezoidal-type inequalities in fuzzy settings have been investigated. The theory of fuzzy analysis has been discussed in detail. The integration by parts formula of analysis of fuzzy mathematics has been employed to establish an equality. Trapezoidal-type inequality for functions with values in the fuzzy number-valued space is proven by applying the proven equality together with the properties of a metric defined on the set of fuzzy number-valued space and Höler's inequality. The results proved in this research provide generalizations of the results from earlier existing results in the field of mathematical inequalities. An example is designed by defining a function that has values in fuzzy number-valued space and validated the results numerically using the software Mathematica (latest v. 14.1). The p-levels of the defined fuzzy number-valued mapping have been shown graphically for different values of p ∈ 0 , 1 . [ABSTRACT FROM AUTHOR]

Copyright of China Condiment is the property of China Condiment and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Tunnel excavation breaks the original groundwater balance, leading to groundwater loss, wastage of water resources, and damage to the local ecological environment. The focus is on effectively predicting the impact of unexcavated tunnels on the groundwater environment and using this prediction to guide construction. This study established an evaluation system by analyzing factors such as natural geography, engineering geology and hydrogeology at the tunnel site. The sensitivity evaluation model of groundwater environment affected by tunnel excavation was established by combining the Analytic Hierarchy Process (AHP) and fuzzy mathematics. The tunnel site was evaluated based on the Wanshishan tunnel on the southern extension of Xiamen rail line 3. Given that previous research primarily provided an overall assessment of the environmental impact of tunnels, while the impact on the groundwater environment varied due to different regional geological conditions and special features such as fault fracture zones, this study evaluated different mileage sections along the tunnel excavation route based on surrounding rock grades. The study found that, for section K5 + 540, the comprehensive evaluation index was 2. 864 8, indicating a sensitivity level between average and moderately strong. Overall, the groundwater environment of the whole tunnel site was categorized into four levels: moderately Validation through field geophysical exploration and other assessment models confirmed the reliability and rationality of the findings, providing a valuable reference for the design of water control and drainage schemes in engineering projects. [ABSTRACT FROM AUTHOR]

This paper introduced a new definition of rough fuzzy sets based on a fuzzy ideal l defined on a fuzzy approximation space (X, R). This definition considered the degree r ∈ [0, 1] in defining the after sets and the before sets of the arbitrary fuzzy relation R on the finite set of objects X. It is shown that this new type of roughness is a generalization to many of previous definitions in the fuzzy case and also in the ordinary case. As an application, it is given a rough fuzzy‐connected set notion depending on some degree r ∈ [0, 1]. [ABSTRACT FROM AUTHOR]

Many modern technological objects in practice are characterized by the uncertainty of the initial information necessary for their management. Recently, one of the pressing scientific and practical problems is the development of new optimization methods for controlling the operating modes of such objects in a fuzzy environment. In this regard, the objective of this study is to develop methods of multi-criteria optimization in a fuzzy environment by modifying the simplex method and various optimality principles based on fuzzy mathematics methods. The methodology of the proposed study is based on a hybrid approach, which consists of the integrated use and modification of simplex methods and optimization methods with various optimality principles for working in a fuzzy environment. The main results are as follows: a simplex method of multi-criteria optimization of immeasurable criteria (here, we are talking about the impossibility of physical measurements of criteria, the values of which are estimated by decision maker); a theorem on the convergence of the solution sequence obtained using the proposed method to the minimum value of the criteria; a heuristic method based on a modification for fuzziness and a combination of the maximin and Pareto optimality principles, which allows effectively solving multi-criteria optimization problems in a fuzzy environment. The heuristic method proposed will be used to solve a real production problem—optimization of the technological process of benzene production. [ABSTRACT FROM AUTHOR]

Not-from-concentrate (NFC) juice effectively retains the original characteristics of the fruit. Despite the various health benefits of Goji berries, reports on the processing technology and quality changes of NFC goji juice are lacking. We optimised the processing technology of NFC goji juice. Employing fuzzy mathematics evaluation combined with response surface methodology based on single-factor experiments, the physicochemical, nutritional, and microbiological indicators of the juice were determined. Gas chromatography-ion mobility spectroscopy was used to analyse changes in volatile compounds before and after processing. The optimal processing parameters were: times for homogenisation, ultrasonication, and sterilisation of 2 min, 3 min, and 85 s, respectively, and sterilisation temperature of 102 °C. The resulting product had a sensory evaluation score of 85.5 and a rich, pleasant taste. The ratio of total soluble solids to titratable acidity and turbidity were 12.8 and 1420 NTU, respectively. Post-processing, the contents of β-carotene, polysaccharides, and betaine increased by 57.3%, 26.7%, and 31.5%, respectively. Microbiological indicators met Chinese national limits for food pollutants and microorganisms. The total relative content of volatile substances in NFC goji juice decreased by 19.86% after processing. This study provides a theoretical reference for the intensive processing and development of high-value goji berries. [ABSTRACT FROM AUTHOR]

In this paper, we use two approaches to define the concept of fuzzy nominal sets: classic and universal algebraic. We see that the fuzzy nominal sets obtained using the universal algebraic approach (so-called fuzzy nominal sets) are within finitely supported mathematics, whereas the fuzzy nominal sets derived using the classical approach (so-called fuzzy nominal ν supp -sets) are within ordinary mathematics and each fuzzy nominal set can be considered as a fuzzy nominal ν supp -set. We also go over the presheaf representation of fuzzy nominal sets and some other properties of these various types of fuzzy nominal sets. [ABSTRACT FROM AUTHOR]

Based on the mining technical conditions of the orebody in the north area deep in Xishan area of Sanshandao Gold Mine, this study aims to optimize the stope structural parameters for the upward approach cut-and-fill mining method. 10 preliminary stope structural parameters were selected and analyzed using ABAQUS software for numerical simulation. These simulation results were further optimized using fuzzy mathematics. Through comprehensive comparison and analysis, Scheme 2 is recommended for the structural parameters of the stope in the SL06154 panel of the north area deep in Xishan area of Sanshandao Gold Mine. The scheme involves a first-step stope width of 8 m, a second-step stope width of 6 m, and a stope height of 4.5 m, with an alternate mining approach for the orebody in the north area deep in Xishan area of Sanshandao Gold Mine. [ABSTRACT FROM AUTHOR]

The homotopy permutation approach is used in this article to solve the fractional-order biological population model (FOBPM). The fractional derivative is defined using the Atangana-Baleanu operator (ABO). The suggested technique provides of several solutions for FOBPM. The HPM technique is regarded as one of the finest analytical processes for solving fractional-order, nonlinear PDEs, notably the FOBPM, Since it requires fewer computations and has a greater rate of convergence than other analytical approaches. [ABSTRACT FROM AUTHOR]

In this paper, we study neutrosophic hesitant fuzzy ideal. We introduce the notions of neutrosophic hesitant fuzzy primary ideal, neutrosophic hesitant fuzzy semiprimary ideal of a ring and discussion of some important theorems and results. [ABSTRACT FROM AUTHOR]

In this work, we introduce a different interpretation of the notion of a partial fuzzy metric, which we refer to as a partial fuzzy co-metric. We define a partial fuzzy co-metric from a t-conorm and compare it with partial fuzzy metric, in contrast to the conventional approach to the theory of partial fuzzy metric spaces, which is based on the use of a t-norm. Here, we limit the scope of our analysis to Sedghi's definition of partial fuzzy metrics. Additionally, we proposed and compared the ideas of strong partial fuzzy co-metric spaces and strong partial fuzzy metric spaces. We also presented a few examples of these novel ideas. [ABSTRACT FROM AUTHOR]

Within the scope of this research, the fuzzy‐analytical hierarchy process (F‐AHP) method is applied to assess the waste management approaches adopted by various hospitals in the city of Gwalior, India. Fuzzy‐AHP, as an alternative to traditional AHP, accommodates uncertainty and imprecision, offering a decision‐making method that is more adaptable and realistic. The F‐AHP methodology, delineated in a seven‐step process, incorporates pairwise comparisons, fuzzy mathematics, and linguistic variables to compute fuzzy weights for waste management criteria, encompassing physical, biological, social, and economic aspects. Hospital 1, with a weight value of 0.406 and strict adherence to the Bio‐medical Waste Management (Amendment), 2018 rules and regulations of the Government of India, emerges as the most promising sustainability hospital based on the F‐AHP analysis findings. Conversely, Hospital 5 exhibits the poorest waste management practices among the surveyed hospitals, earning the lowest possible ranking. While the proposed F‐AHP method provides valuable insights, the study is limited to a specific geographic area (Gwalior) and potential variations based on environmental factors. Additionally, the practical implications extend beyond the general emphasis on continuous monitoring to include specific actions for hospitals to enhance their waste management systems. [ABSTRACT FROM AUTHOR]

The performance evaluation involves a variety of composite factors, and most factors are subjectively determined by the people, so the fuzziness of this evaluation is inevitable. This paper firstly focuses on this issue based on the dynamic influence of digital twin technology input for different kinds of digital twin technology activities. Then this paper carries out a detailed analysis and research on the main core and criterion of digital twin technology. Thirdly this paper puts forward the following suggestions so as to give full play to the role of digital twin technology input of three different kinds in activities. Lastly this paper constructs a novel quantifiable weight model of performance evaluation by applying fuzzy mathematics theory. The calculation results indicate that this model can keep an eye on the evolution rule of digital twin technology to timely change the system are the optimal plans and measures based on weight analysis, and their weights are 0.336, 0.334 and 0.330 respectively, and the rationality of quantifiable weight behavior has a significant impact on the technology development. [ABSTRACT FROM AUTHOR]

Since the early 21st century, within fuzzy mathematics, there has been a stream of research in the field of option pricing that introduces vagueness in the parameters governing the movement of the underlying asset price through fuzzy numbers (FNs). This approach is commonly known as fuzzy random option pricing (FROP). In discrete time, most contributions use the binomial groundwork with up-and-down moves proposed by Cox, Ross, and Rubinstein (CRR), which introduces epistemic uncertainty associated with volatility through FNs. Thus, the present work falls within this stream of literature and contributes to the literature in three ways. First, analytical developments allow for the introduction of uncertainty with intuitionistic fuzzy numbers (IFNs), which are a generalization of FNs. Therefore, we can introduce bipolar uncertainty in parameter modelling. Second, a methodology is proposed that allows for adjusting the volatility with which the option is valued through an IFN. This approach is based on the existing developments in the literature on adjusting statistical parameters with possibility distributions via historical data. Third, we introduce into the debate on fuzzy random binomial option pricing the analytical framework that should be used in modelling upwards and downwards moves. In this sense, binomial modelling is usually employed to value path-dependent options that cannot be directly evaluated with the Black–Scholes–Merton (BSM) model. Thus, one way to assess the suitability of binomial moves for valuing a particular option is to approximate the results of the BSM in a European option with the same characteristics as the option of interest. In this study, we compared the moves proposed by Renddleman and Bartter (RB) with CRR. We have observed that, depending on the moneyness degree of the option and, without a doubt, on options traded at the money, RB modelling offers greater convergence to BSM prices than does CRR modelling. [ABSTRACT FROM AUTHOR]

Copyright of Systems Engineering & Electronics is the property of Journal of Systems Engineering & Electronics Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Integrated Intelligent Energy is the property of Editorial Department of Integrated Intelligent Energy and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of China Condiment is the property of China Condiment and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Accurately and quickly identifying harmful driving behaviors is of great research significance. This article introduces a multi class Adaboost algorithm for accurately and quickly identifying harmful driving behaviors on urban roads. This method first carefully collects data related to bad driving behavior on road sections. Then, the optical flow method is used to capture images of driving behavior, and the TV-L1 optical flow method is used to refine the images to improve clarity. Finally, the CART decision tree serves as the cornerstone for constructing a rigorously trained weak classifier, strategically combining multiple individual weak classifiers to form a robust strong classifier. This powerful classifier is supported by the Adaboost algorithm and can provide detailed classification of bad driving behavior. To ensure a holistic assessment, fuzzy mathematics is deployed to discern behavioral risks, thereby facilitating the correlated identification of adverse driving patterns. Experiment results verifies the efficacy of our approach, with recognition time dwindling to a mere 1.9 seconds and the accuracy of correlated recognition soaring to an impressive 99.8%. [ABSTRACT FROM AUTHOR]

Assembly sequence planning is a critical facet of product design and manufacturing, influencing assembly effectiveness and product tolerances. Ineffectual sequences can hamper product quality and development efficiency. This study introduces a matrix-based evaluation function and an enhanced pollination algorithm for optimal assembly sequence determination. This approach accounts for various assembly factors and links the evaluation matrix to fuzzy mathematics through expert decision-making methods. The algorithm is tailored to assembly sequences, with defined rules for judgment, operation, assignment and repair. It incorporates Levy flights for broader search exploration and an adaptive mutation factor for refined local search. The hybrid algorithm, combining genetic algorithm principles, is employed for sequence planning and analysis. Comparative simulations highlight the hybrid algorithm's robust global search and convergence capabilities. This research offers practical significance in enhancing assembly performance and overall product reliability within the product development cycle. [ABSTRACT FROM AUTHOR]

The created SDE-Framework combines neutronosophic logic and fuzzy mathematics in a novel method, aiming at facilitating more informed decision outcomes in computational systems and information technology management. This method hopes to aid in determining strategic solutions by controlling the expected sophistication and ambiguity in these two technologically dynamic industries. Neutronosophic logic divides data into three components: truth, indeterminacy, and falsity, build an exhaustive technique for addressing contradiction and indeterminacy. This significantly increases the method by enabling a more complete exploration of potential options with ambiguous and inadequate data. Second, the fuzzy mathematics gives a valuable contribution. It offers a refined method for managing the levels of probability and certainty through membership features, resulting in more exact and flexible evaluations. By the usage of such compared sophisticated mathematics concepts, SDEFramework addresses potential decision-making scenarios by letting the computer formulates do the judgements for the determinable and in determinable explicit data. The subsequent crucial parameters are adopted to tolerance values: validity and responsibility, falseness foreach, indeterminacy magnitude to each, and truth value. This guarantees its combination of complexity supportive rand reading of actual surroundings. [ABSTRACT FROM AUTHOR]

Copyright of China Condiment is the property of China Condiment and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of China Condiment is the property of China Condiment and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The paper makes a comparative transient study of an infinite server queue with catastrophes and repair under fuzzy environment using two fuzzy methods– one is through lenient alpha-cuts mathematics and other one is through L-R mathematics. The study has been made by modelling a university campus with free Wi-Fi facility to the persons within the campus at any time. The model has numerical parameters and the model is based on the queueing system described by Bura1 . Average number of persons within the campus (at any time) has been computed and compared by the two methods mentioned above. [ABSTRACT FROM AUTHOR]

In Present time, the utility of the theory of reliability and lifetesting analysis attracting many workers and theory is well established in engineering and medical sciences. Now, as the area of applicability of life testing is enlarging day by day, the variety of situations and their related data are also growing up. So, it seems not logical that this variety of data can be dealt with only two or three types of the above life testing models. It seems desirable to develop more and more realistic life testing models to deal with the variety of life testing data so that the proper inferences concerning with the reliability and other aspects can be drawn with more precision. It has been observed that in a number of situations the application of the models discussed so far can be made only after imposing a number of assumptions. So, there is a requirement of a relatively larger family of life time models, so that proper justification can be done with the daya analysis. In the present paper, an attempt has been made to develop a new life-testing model to enlarge the family of life testing models. [ABSTRACT FROM AUTHOR]

In this paper, comparative study of the steady state retrial system investigated by Han et al.¹ under fuzzy and Intuitionistic fuzzy number has been made by us. The retrial system has negative arrivals, and breakdown with delayed repair. Studies have been made by constructing a tele-medicine consultation model with numerical parameters satisfying the stability condition for the steady state system as proposed in the original model. Triangular fuzzy and triangular intuitionistic fuzzy mathematics are our tools. To validate the stability condition, a ranking method (for fuzzy number) and a magnitude method (for intuitionistic fuzzy number) have been used. Various system probabilities together with multitude of performance measures, under both the environment, have been evaluated. We have supported the important effectiveness measures by relevant graphs. [ABSTRACT FROM AUTHOR]

The authors in this paper aim to introduce and study the concepts of half-soft β open sets. Furthermore, the properties of half-soft β separated and half-soft β connected sets are introduced and discussed with suitable examples. Finally, the half-soft β continuous function is defined and studied. [ABSTRACT FROM AUTHOR]

Process scheduling algorithms make multiprogramming more productive by optimizing the utilization of the CPU. It is a very crucial task of scheduling algorithms that the CPU should not ideal if processes are in ready queue. We developed a unique algorithm for improving the process execution in real-time systems by utilizing the modified round robin (RR) algorithm variations that utilizes the use of the degree of multiprogramming. The developed algorithm removes the issue of starvation as compared with traditional priority scheduling algorithms. We also proposed an intuitionistic fuzzy inference system based MMFNP model to calculate the new priority that plays a key role for the execution of urgent tasks. Maximum value of New Priority represents the uppermost priority. The proposed algorithm increases the throughput of the system and reduces the average response time, average waiting time and average turnaround time. For the performance evaluation of the suggested algorithm, we also compared the results with RR algorithm and priority-based RR algorithm. [ABSTRACT FROM AUTHOR]

Abstract Background Urban ecological health is crucial for the long-term sustainable development of watershed. Accurately evaluating the health level of the ecological environment helps to develop reasonable strategies for ecological environment restoration and resource management. This paper constructed a comprehensive evaluation index system based on the Pressure-State-Response (PSR) framework and evaluated the ecological health of eleven administrative regions in the Wei River Basin (WRB), northwest China in 1980, 2000, and 2020 using an evaluation model established by fuzzy mathematics. Further, obstacle degrees were used to quantify the contribution of pressure, state, and response modules, as well as individual indicators to ecological health. Results The comprehensive evaluation system constructed based on the PSR framework could effectively reflect the ecological health conditions of different regions in the WRB. During the study period, the ecological health went through a process of first deterioration and then improvement. By 2020, the ecological health of seven administrative regions reached healthy levels. The state module was the main obstacle module of the PSR framework to the ecological health of the most regions. The population density (P1), patch density of construction land (S5), comprehensive elasticity index (S8), soil erosion index (R1), and per capital GDP (R3) were the most crucial individual indicators affecting the ecological health. For different cities, the main obstacle factors varied. In economically developed cities, the limiting effect of P1 was more significant, while in economically underdeveloped cities, the limiting effect of R3 was stronger. Conclusions In response to the special natural environment and socio-economic conditions of arid and semi-arid areas in the WRB, an ecological health evaluation index system suitable for the characteristics of the basin was constructed. The results indicated that, to improve the levels of urban ecological health, it is necessary to restore the natural ecological environment and control population size while accelerating economic construction. Our results can provide scientific support for the ecological health evaluation and protection of the WRB and even the arid and semi-arid areas in northwest China.

Background: Urban ecological health is crucial for the long-term sustainable development of watershed. Accurately evaluating the health level of the ecological environment helps to develop reasonable strategies for ecological environment restoration and resource management. This paper constructed a comprehensive evaluation index system based on the Pressure-State-Response (PSR) framework and evaluated the ecological health of eleven administrative regions in the Wei River Basin (WRB), northwest China in 1980, 2000, and 2020 using an evaluation model established by fuzzy mathematics. Further, obstacle degrees were used to quantify the contribution of pressure, state, and response modules, as well as individual indicators to ecological health. Results: The comprehensive evaluation system constructed based on the PSR framework could effectively reflect the ecological health conditions of different regions in the WRB. During the study period, the ecological health went through a process of first deterioration and then improvement. By 2020, the ecological health of seven administrative regions reached healthy levels. The state module was the main obstacle module of the PSR framework to the ecological health of the most regions. The population density (P1), patch density of construction land (S5), comprehensive elasticity index (S8), soil erosion index (R1), and per capital GDP (R3) were the most crucial individual indicators affecting the ecological health. For different cities, the main obstacle factors varied. In economically developed cities, the limiting effect of P1 was more significant, while in economically underdeveloped cities, the limiting effect of R3 was stronger. Conclusions: In response to the special natural environment and socio-economic conditions of arid and semi-arid areas in the WRB, an ecological health evaluation index system suitable for the characteristics of the basin was constructed. The results indicated that, to improve the levels of urban ecological health, it is necessary to restore the natural ecological environment and control population size while accelerating economic construction. Our results can provide scientific support for the ecological health evaluation and protection of the WRB and even the arid and semi-arid areas in northwest China. [ABSTRACT FROM AUTHOR]

Nodal invulnerability has broad application prospects because of its emphasis on the differences between buses. Due to their long-term exposure, transmission lines are inevitably susceptible to damage caused by physical attacks or extreme weather. Therefore, restoring nodal invulnerability through a remedial approach or the introduction of mobile generators (MGs) is pivotal for resisting subsequent damage after a system is attacked. However, the research devoted to this field is limited. In order to fill the gap, this study conducts research on the configuration of MGs considering power generation balance to recover nodal invulnerability. First, a defender–attacker–defender (DAD) model is established, corresponding to the bi-objective robust optimization problem. The upper-level model is formulated to obtain the optimal compromise configuration scheme, the uncertainties of the attacked lines are elucidated in the middle level, and the nodal N − k security criterion utilized for measuring nodal invulnerability cooperates in the lower level. Then, a modified column-and-constraint generation (C&CG) algorithm is developed to incorporate fuzzy mathematics into the solution framework. In addition, the nodal invulnerability settings are optimized under limited resources. Numerical experiments are executed on the IEEE 24-bus system to verify the effectiveness and rationality of the proposed method. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Food Safety & Quality is the property of Journal of Food Safety & Quality Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper, for fuzzy metric spaces we will attempt to demonstrate some novel fixed-point theorems that is common. To support our findings with evidence, we employ the concept of compatibility. The previous review found several useful mutual fixedpoint theorems for metric and fuzzy metric spaces. Our results greatly expand and strengthen these theorems. Reconsideration of fuzzy metric spaces is done by this study so that fuzzy scalars are utilized to construct fuzzy metric spaces rather than real numbers or fuzzy numbers. In contrast to the preceding work, which defined fuzzy metric spaces using fuzzy or real numbers, this definition uses fuzzy numbers. It has been demonstrated that any complete regular metric space can, under certain conditions, complete fuzzy metric space are given. In addition, we provide evidence that the fuzzy metric spaces generate fuzzy topology that is specified in this study and is consistent with previously presented fuzzy topologies. In the coming years, these findings will pave the way for additional research into imperfect optimization and pattern recognition. [ABSTRACT FROM AUTHOR]

Pingliang City has a complex topography and diverse soil types. To realize the improvement of soil according to local conditions and the reasonable and sustainable use of soil resources, an evaluation of soil quality in Pingliang City was carried out, based on the soil distribution situation in Pingliang City, adopting a method combining fuzzy mathematics and cluster analysis of the main evaluation factors, such as soil organic matter, topsoil depth, soil erosion intensity, soil moisture regime, effective soil thickness, soil texture, soil profile structure, soil nutrient status and topographical parts, to carry out a comprehensive evaluation. A comprehensive evaluation of soil quality was conducted in seven counties under the jurisdiction of Pingliang City, and the evaluation results were compared and analyzed against the national standard, "Cultivated land quality grade", to provide a basis for the selection of scientific soil improvement methods. The results of the arable land quality grades indicate that the quality of farmland in Pingliang City is divided into three to ten grades, and the average quality grade of farmland is 6.83, which is in the middle–lower level, and the overall grade distribution shows the characteristics of low in the middle and high in the east and west. The results of fuzzy mathematics combined with cluster analysis indicated the following trends in soil quality for the 12 soil genera: Chuan black gunny soil > yellow moist soil > sandy soil > silt soil > mulching helilu soil> loessal soil> loamy soil > slope loessal soil > arenosol > tillage leaching gray cinnamon soil > calcareous gray cinnamon soil > red clay soil. The results of the combination of fuzzy mathematics and clustering were significantly correlated with the results of the evaluation of the soil quality of arable land; the correlation coefficient was 0.884. This indicates that the method can accurately and objectively review the advantages and disadvantages of arable land soil and can be effectively applied to the evaluation of the soil quality of agricultural soils in other regions. It is a complement to the existing evaluation of the soil quality of arable land and at the same time provides a reference for the improvement of soil quality in agricultural regions. [ABSTRACT FROM AUTHOR]

The object of this study is a large class of mathematical programming problems under conditions of uncertainty of initial data. The formulated object generates a subclass of problems of rational distribution of a limited resource under conditions of initial data described in terms of fuzzy mathematics. The conventional, standardly used method for solving such problems is based on optimization on average. To obtain such a solution, it is sufficient to replace all fuzzy initial data with their modal values in the analytical description of the mathematical model of the corresponding problem. To solve the resulting deterministic problem, one can use known methods of mathematical programming. However, the results of such a solution can be used in practice if the carriers of fuzzy parameters are specified compactly, that is, the intervals of possible values of fuzzy parameters of the problem are small. Otherwise, the implementation of this solution may lead to unpredictably large losses. Other alternative approaches are based on the use of insufficiently informative estimates of the best or worst possible values of fuzzy parameters of the problem. These circumstances make the statement of the problem and the objective of the study relevant: devising a method for solving the problem of rational distribution of a limited resource under conditions of fuzzy initial data. To solve the stated problem of rational distribution of a limited resource, a productive idea of constructing the proposed general optimization method under conditions of uncertainty of the initial data has been constructively implemented. In this case, the initial problem is reduced to a clear problem of optimizing a complex criterion constructed on the basis of the objective function of the initial problem and a set of membership functions of its fuzzy parameters. An example of solving the problem has been considered, leading to a solution that is better than that obtained on the basis of the modal values of the fuzzy parameters of the problem. [ABSTRACT FROM AUTHOR]

This paper considers objects that affect the social security of the country. The complexity of such objects makes the development of computer systems in sociological research a difficult algorithmic task because of information uncertainty. Human thinking is based on inaccurate, approximate data, the analysis of which makes it possible to formulate clear decisions. In practice, there are usually no precise mathematical models that describe social objects. In such cases, it is advisable to use fuzzy mathematics as a tool for solving this problem. The main advantage of this approach compared to other artificial intelligence methods is the ability to interpret the results obtained. To assess the level of social well-being of the population, we used the mathematical apparatus of fuzzy set theory and fuzzy inference. The study is based on the OECD Better Life Index, which was developed by the Organization for Economic Cooperation and Development (OECD) to help countries assess and improve the quality of life of their citizens. In the course of the study, a fuzzy inference system was built to measure the social well-being of the population based on the indicators of the OECD Better Life Index. Since determining the level of social well-being is a complex task, a hierarchical structure with two main groups of social well-being indicators was constructed to simplify it. The resultant system evaluates each social indicator included in the OECD’s Better Life Index. Using the fuzzy inference model built, it was possible to assess the social well-being of the country’s population in a simple and transparent way in comparison with the OECD member countries. The results of the study make it possible to understand which indicators of social well-being of the country’s population are desirable or need to be improved in the future. [ABSTRACT FROM AUTHOR]

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Copyright of China Condiment is the property of China Condiment and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Food & Fermentation Industries is the property of Food & Fermentation Industries and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Rough Set (RS) is a relatively new technique for making imprecise and uncertain decisions. It is an emerging area of ambiguous mathematics associated with fuzzy set theory. In comparison with fuzzy sets and other theories, RS has more advantages. Unlike statistics, evidence theory, and fuzzy set theory, RS theory does not require any additional or preliminary information about data. RS theory deals with approximating arbitrary subsets of the universe using two subsets namely lower and upper approximation. The advantage of RS is that rough approximations can be expanded into fuzzy environments which aids in solving a wide variety of realtime problems. The goal of this study is to focus on Rough Fuzzy Prime Ideals (RFPI) in ring structure and explain specific aspects of its upper and lower approximations. Furthermore, Rough Fuzzy Ideal (RFI) and RFPI notions and characteristics are described. [ABSTRACT FROM AUTHOR]