Evaluation of Industrial IoT Service Providers with TOPSIS Based on Circular Intuitionistic Fuzzy Sets

Industrial Internet of Things(IIoT)service providers have become increasingly important in the manufacturing industry due to their ability to gather and process vast amounts of data from connected devices,enabling manufacturers to improve operational efficiency,reduce costs,and enhance product quality.These platforms provide manufacturers with real-time visibility into their production processes and supply chains,allowing them to optimize operations and make informed decisions.In addition,IIoT service providers can help manufacturers create new revenue streams through the development of innovative products and services and enable them to leverage the benefits of emerging technologies such as Artificial Intelligence(AI)and machine learning.Overall,the implementation of IIoT platforms in the manufacturing industry is crucial for companies seeking to remain competitive and meet the ever-increasing demands of customers in the digital age.In this study,the evaluation criteria to be considered in the selection of IIoT service provider in small andmedium-sized(SME)manufacturing enterprises will be determined and IIoT service providers alternatives will be evaluated using the technique for order preference by similarity to an ideal solution(TOPSIS)method based on circular intuitionistic fuzzy sets.Based on the assessments conducted in accordance with the literature review and expert consultations,a set of 8 selection criteria has been established.These criteria encompass industry expertise,customer support,flexibility and scalability,security,cost-effectiveness,reliability,data analytics,as well as compatibility and usability.Upon evaluating these criteria,it was observed that the security criterion holds the highest significance,succeeded by cost-effectiveness,data analytics,flexibility and scalability,reliability,and customer support criteria,in descending order of importance.Following the evaluation of seven distinct alternatives against these criteria,it was deduced that the A6 alternative,a German service provider,emerged as the most favorable option.The identical issue was addressed utilizing sensitivity analysis alongside various multi-criteria decision-making(MCDM)methods,and after comprehensive evaluation,the outcomes were assessed.Spearman’s correlation coefficient was computed to ascertain the association between the rankings derived from solving the problem using diverse MCDM methods.

Complex Decision Modeling Framework with Fairly Operators and Quaternion Numbers under Intuitionistic Fuzzy Rough Context

The main goal of informal computing is to overcome the limitations of hypersensitivity to defects and uncertainty while maintaining a balance between high accuracy,accessibility,and cost-effectiveness.This paper investigates the potential applications of intuitionistic fuzzy sets(IFS)with rough sets in the context of sparse data.When it comes to capture uncertain information emanating fromboth upper and lower approximations,these intuitionistic fuzzy rough numbers(IFRNs)are superior to intuitionistic fuzzy sets and pythagorean fuzzy sets,respectively.We use rough sets in conjunction with IFSs to develop several fairly aggregation operators and analyze their underlying properties.We present numerous impartial laws that incorporate the idea of proportionate dispersion in order to ensure that the membership and non-membership activities of IFRNs are treated equally within these principles.These operations lead to the development of the intuitionistic fuzzy rough weighted fairly aggregation operator(IFRWFA)and intuitionistic fuzzy rough ordered weighted fairly aggregation operator(IFRFOWA).These operators successfully adjust to membership and non-membership categories with fairness and subtlety.We highlight the unique qualities of these suggested aggregation operators and investigate their use in the multiattribute decision-making field.We use the intuitionistic fuzzy rough environment’s architecture to create a novel strategy in situation involving several decision-makers and non-weighted data.Additionally,we developed a novel technique by combining the IFSs with quaternion numbers.We establish a unique connection between alternatives and qualities by using intuitionistic fuzzy quaternion numbers(IFQNs).With the help of this framework,we can simulate uncertainty in real-world situations and address a number of decision-making problems.Using the examples we have released,we offer a sophisticated and systematically constructed illustrative scenario that is intricately woven with the complexity ofmedical evaluation in order to thoroughly assess the relevance and efficacy of the suggested methodology.

Analysis of Landscape Vitality of Historical and Cultural Blocks Based on AHPFuzzy Comprehensive Evaluation Method:A Case Study of Daopashi Street in Anqing City

Historical and cultural blocks are witnesses of history and inheritors of culture. As one of the main spaces for outdoor interaction in historical and cultural blocks, the improvement of its vitality is of great significance for the improvement of residential environment and the better inheritance of history and culture. Taking Daopashi Street in Anqing City as an example, an evaluation model of landscape spatial vitality of historical and cultural blocks was constructed from three aspects of viewing function, store status and service facilities, and analytic hierarchy process was used to determine the index weight and vaguely evaluate the landscape spatial vitality of historical and cultural blocks. The results show that through the comparison of weight, architectural style(0.317), the practicability of service facilities(0.168) and plant landscape(0.165) had a significant impact on the landscape spatial vitality of historical and cultural blocks,and the landscape spatial vitality of historical and cultural blocks in Daopashi Street in Anqing City was at a good level.

Operation State of theWind Turbine Pitch System Based on Fuzzy Comprehensive Evaluation

To ensure wind turbine(WT)safe operations and improve the utilization rate of wind energy,effective evaluation of the operation state of the pitch system is critical.Therefore,a new method was proposed to evaluate the operation state of the pitch system of WT based on fuzzy comprehensive evaluation.Firstly,based on SCADA data,the working state of the pitch system under rated power state and power state of WT were analyzed.Secondly,through the analysis of characteristic parameters and physical mechanism of the pitch system,the consistency principle of characteristic parameters,the stability principle of power under rated state,and the stability principle of blade angle underpowered state were obtained.Next,based on the aforementioned principles,the evaluation indexes were established,and the fuzzy comprehensive evaluation method was used to establish the operation state evaluation model of the pitch system under rated power state and under power state of the WT.Finally,an example was provided to verify the effectiveness of the method.The evaluation model established in this study can be used as a technical reference for the online monitoring of WT pitch systems to ensure the safe and stable operation of WTs.

Evaluation of Water Resources Carrying Capacity in Gansu Section of Yellow River Basin Based on Fuzzy Comprehensive Evaluation Model

As a basic natural resource and strategic economic resource,the development and utilization of water resources is an important issue related to the national economy and people's livelihood.How to scientifically evaluate the water resources carrying capacity is the premise to improve the regional water resources carrying capacity and ensure the regional water security.The Gansu section of the Yellow River basin is an important water conservation and recharge area.Whether the water resources in this area can ensure the normal operation of the ecosystem and whether it can carry the sustainable development of social economy is the key to realize the high-quality development of the Yellow River basin.In this study,from the three dimensions of water consumption per capita,water consumption of 10000 yuan GDP and ecological water use rate,by constructing the evaluation index system and index grading standard of water resources carrying capacity,the fuzzy comprehensive evaluation model was used to evaluate the water resources carrying capacity of Gansu section of the Yellow River Basin,in order to provide theoretical decision-making basis for the comprehensive development,utilization and planning management of water resources in Gansu section of the Yellow River basin and even the whole basin,and help the high-quality development of the Yellow River basin.

Multi-attribute decision making method for air target threat evaluation based on intuitionistic fuzzy sets

The function of the air target threat evaluation （TE） is the foundation for weapons allocation and senor resources management within the surface air defense. The multi-attribute evaluation methodology is utilized to address the issue of the TE in which the tactic features of the detected target are treated as evaluation attributes. Meanwhile, the intuitionistic fuzzy set （IFS） is employed to deal with information uncertainty in the TE process. Furthermore, on the basis of the entropy weight and inclusion-comparison probability, a hybrid TE method is developed. In order to accommodate the demands of naturalistic decision making, the proposed method allows air defense commanders to express their intuitive opinions besides incorporating into the threat features of the detected target. An illustrative example is provided to indicate the feasibility and advantage of the proposed method.

Application of Fuzzy Comprehensive Evaluation Method Based on Entropy Weight Theory in Evaluation of Salt Tolerance of Cotton

[Objective] The aim was to propose a new entropy weight fuzzy compre- hensive evaluation method for assessing cotton salt tolerance, realizing the objective, accurate and comprehensive evaluation of salt tolerance of cotton. [Method] A sand culture experiment under salt stress of 150 mmol/L of NaCI was designed. The in- dicator weight was determined with the entropy weight fuzzy comprehensive evalu- ation method, based on the salt injury index of indicators. The salt tolerance of cotton was evaluated comprehensively. [Result] At the germination stage, the entropy and weight of salt injury index of germination energy, vigor index, hypocotyl length and fresh weight were highest, followed by germination rate and germination index, and of root length were lowest. At the seedling stage, the entropy and weight of salt injury index of plasma membrane permeability, root vigor and leaf expansion rate were highest, followed by plant height and net photosynthetic rate, and of shoot dry weight and root dry weight were lowest. The salt tolerance of cotton differed a- mong growth stages and cultivars. Among the 11 cultivars, CCRI-44 and CCRI-75 were steadily salt-tolerant at both germination and seedling stages; CCRI-17, Sumi- an 22, Sumian 15 and Dexiamianl had a stable moderate salt tolerance; while Sumian 12 and Simian 3 were steadily salt-sensitive. [Conclusion] The evaluated result was objective and exact, which indicated that this method could be used in comprehensive evaluation of salt tolerance of cotton.

Spectral purification improves monitoring accuracy of the comprehensive growth evaluation index for film-mulched winter wheat

In order to further improve the utility of unmanned aerial vehicle(UAV)remote-sensing for quickly and accurately monitoring the growth of winter wheat under film mulching, this study examined the treatments of ridge mulching,ridge–furrow full mulching, and flat cropping full mulching in winter wheat.Based on the fuzzy comprehensive evaluation (FCE) method, four agronomic parameters (leaf area index, above-ground biomass, plant height, and leaf chlorophyll content) were used to calculate the comprehensive growth evaluation index (CGEI) of the winter wheat, and 14 visible and near-infrared spectral indices were calculated using spectral purification technology to process the remote-sensing image data of winter wheat obtained by multispectral UAV.Four machine learning algorithms, partial least squares, support vector machines, random forests, and artificial neural network networks(ANN), were used to build the winter wheat growth monitoring model under film mulching, and accuracy evaluation and mapping of the spatial and temporal distribution of winter wheat growth status were carried out.The results showed that the CGEI of winter wheat under film mulching constructed using the FCE method could objectively and comprehensively evaluate the crop growth status.The accuracy of remote-sensing inversion of the CGEI based on the ANN model was higher than for the individual agronomic parameters, with a coefficient of determination of 0.75,a root mean square error of 8.40, and a mean absolute value error of 6.53.Spectral purification could eliminate the interference of background effects caused by mulching and soil, effectively improving the accuracy of the remotesensing inversion of winter wheat under film mulching, with the best inversion effect achieved on the ridge–furrow full mulching area after spectral purification.The results of this study provide a theoretical reference for the use of UAV remote-sensing to monitor the growth status of winter wheat with film mulching.

On similarity measures of interval-valued intuitionistic fuzzy sets and their application to pattern recognitions

The concept of the degree of similarity between interval-valued intuitionistic fuzzy sets （IVIFSs） is introduced, and some distance measures between IVIFSs are defined based on the Hamming distance, the normalized Hamming distance, the weighted Hamming distance, the Euclidean distance, the normalized Euclidean distance, and the weighted Euclidean distance, etc. Then, by combining the Hausdorff metric with the Hamming distance, the Euclidean distance and their weighted versions, two other similarity measures between IVIFSs, i. e., the weighted Hamming distance based on the Hausdorff metric and the weighted Euclidean distance based on the Hausdorff metric, are defined, and then some of their properties are studied. Finally, based on these distance measures, some similarity measures between IVIFSs are defined, and the similarity measures are applied to pattern recognitions with interval-valued intuitionistic fuzzy information.

A Modified Comprehensive Evaluation System of Groundwater Pollution Based on Fuzzy Set Theory

A modified comprehensive evaluation system of groundwater pollution based on Fuzzy set theory is introduced.In this evaluation system,a five-degree membership function and a comprehensive weight function are built by combining Delphi method with double weight method.By studying a typical engineering project,the features and advantages of the modified evaluation system are analyzed by comparing to the popular simple comparison method.This indicates that the weighted average model is applicable in the situation that the content of every evaluation factor is even and the evaluation aim is to externalize the contribution of every evaluation factor in groundwater environmental quality.

Application of Fuzzy Comprehensive Evaluation Method Based on Entropy Weight to Evaluate Pond Water Quality

[Objective] This study was to provide references for the evaluation of water quality in aquaculture ponds by evaluating the pond water quality using fuzzy comprehensive evaluation method based on entropy weight. [Method] The fuzzy compre- hensive evaluation method based on entropy weight was used to evaluate the water quality in the ponds with Ukraine scale carp （Cyprinus carpio） as the main cultivated fish. The average size of the fish was 71.4 g/ind, and totally three groups of pond were set with the population density of 6 000, 9 000, 12 000 ind/hm2. [Result] According to the GB3838-2002 Environmental Quality Standards for Surface Water of China, the water quality of 6 000 ind/hm2 group was Grade I, and the water quality of 9 000 and 12 000 ind/hm2 were Grade V. [Conclusion] With the increasing of feeding density, the pond water quality would worsen, however, there is no difference on water quality between 9 000 and 12 000 ind/hm2 groups.

Construction of Tourist Satisfaction Degree Evaluation Model in Western Tourist Area by Performance Prism and Fuzzy Comprehensive Evaluation Method——with Lijiang in Yunnan Province as the Study Case

Starting from the utilization and protection of local knowledge, with the performance prism as the framework, the evaluation index system of tourist satisfaction degree was established. The weight was determined by using AHP method. Finally, the investigating result was judged with fuzzy comprehensive evaluation method, the evaluation model of tourist satisfaction degree in western tourist area was built, and the case study was carried out. With Lijiang in Yunnan Province as example, according to AHP method, five dimensions weight of the performance prism, various KPI weight and consistency were obtained, fuzzy evaluation on tourist satisfaction degree was conducted. The results showed that the overall was satisfactory, but there were still some problems. Aiming at the utilization and protection of local knowledge, some corresponding countermeasures were put forward which will benefit for further development of tourism in Lijiang of Yunnan Province.

基于AHP-Fuzzy法的海南热带海洋文化景观资源综合评价

海南热带海洋文化景观资源评价,有助于全面了解热带海洋文化景观资源的全貌,文章运用AHP层次分析法和Fuzzy模糊综合评价法来评价海南热带海洋文化景观,从景观自身价值、景观开发潜力、景观开发条件三个方面构建了海南热带海洋文化景观资源综合评价模型,运用层次分析法确定各指标的权重,得出景观自身价值的比重比较大。以两大类九小类的海南热带海洋文化景观为对象进行了模糊评价,验证了评价模型的可行性,根据得出的结论提出相应的对策建议。

An evaluation method of contribution rate based on fuzzy Bayesian networks for equipment system-of-systems architecture

The contribution rate of equipment system-of-systems architecture(ESoSA)is an important index to evaluate the equipment update,development,and architecture optimization.Since the traditional ESoSA contribution rate evaluation method does not make full use of the fuzzy information and uncertain information in the equipment system-of-systems(ESoS),and the Bayesian network is an effective tool to solve the uncertain information,a new ESoSA contribution rate evaluation method based on the fuzzy Bayesian network(FBN)is proposed.Firstly,based on the operation loop theory,an ESoSA is constructed considering three aspects:reconnaissance equipment,decision equipment,and strike equipment.Next,the fuzzy set theory is introduced to construct the FBN of ESoSA to deal with fuzzy information and uncertain information.Furthermore,the fuzzy importance index of the root node of the FBN is used to calculate the contribution rate of the ESoSA,and the ESoSA contribution rate evaluation model based on the root node fuzzy importance is established.Finally,the feasibility and rationality of this method are validated via an empirical case study of aviation ESoSA.Compared with traditional methods,the evaluation method based on FBN takes various failure states of equipment into consideration,is free of acquiring accurate probability of traditional equipment failure,and models the uncertainty of the relationship between equipment.The proposed method not only supplements and improves the ESoSA contribution rate assessment method,but also broadens the application scope of the Bayesian network.

Business Blockchain Suitability Determinants: Decision-Making through an Intuitionistic Fuzzy Method

Blockchain is one of the innovative and disruptive technologies that has a wide range of applications in multiple industries beyond cryptocurrency.The widespread adoption of blockchain technology in various industries has shown its potential to solve challenging business problems,as well as the possibility to create new business models which can increase a firm’s competitiveness.Due to the novelty of the technology,whereby many companies are still exploring potential use cases,and considering the complexity of blockchain technology,which may require huge changes to a company’s existing systems and processes,it is important for companies to carefully evaluate suitable use cases and determine if blockchain technology is the best solution for their specific needs.This research aims to provide an evaluation framework that determines the important dimensions of blockchain suitability assessment by identifying the key determinants of suitable use cases in a business context.In this paper,a novel approach that utilizes both qualitative(Delphi method)and quantitative(fuzzy set theory)methods has been proposed to objectively account for the uncertainty associated with data collection and the vagueness of subjective judgments.This work started by scanning available literature to identify major suitability dimensions and collected a range of criteria,indicators,and factors that had been previously identified for related purposes.Expert opinions were then gathered using a questionnaire to rank the importance and relevance of these elements to suitability decisions.Subsequently,the data were analyzed and we proceeded to integrate multi-criteria group decision-making(MCGDM)and intuitionistic fuzzy set(IFS)theory.The findings demonstrated a high level of agreement among experts,with the model being extremely sensitive to variances in expert assessments.Furthermore,the results helped to refine and select the most relevant suitability determinants under three important dimensions:functional suitability of the use case,organizational applicability,and ecosystem readiness.

A Novel Incremental Attribute Reduction Algorithm Based on Intuitionistic Fuzzy Partition Distance

Attribute reduction,also known as feature selection,for decision information systems is one of the most pivotal issues in machine learning and data mining.Approaches based on the rough set theory and some extensions were proved to be efficient for dealing with the problemof attribute reduction.Unfortunately,the intuitionistic fuzzy sets based methods have not received much interest,while these methods are well-known as a very powerful approach to noisy decision tables,i.e.,data tables with the low initial classification accuracy.Therefore,this paper provides a novel incremental attribute reductionmethod to dealmore effectivelywith noisy decision tables,especially for highdimensional ones.In particular,we define a new reduct and then design an original attribute reduction method based on the distance measure between two intuitionistic fuzzy partitions.It should be noted that the intuitionistic fuzzypartitiondistance iswell-knownas aneffectivemeasure todetermine important attributes.More interestingly,an incremental formula is also developed to quickly compute the intuitionistic fuzzy partition distance in case when the decision table increases in the number of objects.This formula is then applied to construct an incremental attribute reduction algorithm for handling such dynamic tables.Besides,some experiments are conducted on real datasets to show that our method is far superior to the fuzzy rough set based methods in terms of the size of reduct and the classification accuracy.

Fuzzy Comprehensive Evaluation Model for Water Resources Carrying Capacity in Tarim River Basin,Xinjiang,China

This paper explores the method of comprehensive evaluation of water resources carrying capacity and sets up an evaluation model applying the fuzzy comprehensive evaluation method. Based on the data of nature,society,economics and water resources of the Tarim River Basin in 2002,we evaluated the water resources carrying capacity of the basin by means of the model. The results show that the comprehensive grades are 0.438 and 0.454 for Aksu and Kashi prefectures respectively,where the current water resources exploitation and utilization has reached a relative high degree and there is only a very limited water carrying capacity,0.620 for Kizilsu Kirgiz Autonomous Prefecture,where water resources carrying capacity is much higher,and in between for Hotan Prefecture and Bayingolin Mongo-lian Autonomous Prefecture. As a whole,the comprehensive grade of the Tarim River Basin is 0.508 and the current water resources exploitation and utilization has reached a relative high degree. Thus,we suggest that the integrated management of the water resources in the basin should be strengthened in order to utilize water resources scientifically and sustainably.

Risk analysis of extended reach wells in the Liuhua Oilfield,South China Sea,based on comprehensive fuzzy evaluation method

Drilling engineering has great uncertainty and it always involves huge investment and high risk. Risk analysis of extended reach drilling （ERD） is very important to prevent complex failures and to improve drilling efficiency. Nowadays there are few reports on how to analyze quantitatively the drilling risk for extended reach wells （ERWs）. Based on the fuzzy set theory, a comprehensive fuzzy evaluation model for analyzing risks of ERD is proposed in this paper. Well B6ERW07 is a planned 8,000-meter ERW with a high ratio of horizontal displacement （HD） to vertical depth （VD） in the Liuhua Oilfield, the South China Sea, China. On the basis of the evaluation model developed in this study, the risk for drilling Well B6ERW07 was evaluated before drilling. The evaluation result shows that the success rate of drilling this well is predicted to be 51.9%, providing important rational and scientific information for the decisionmakers.

A novel similarity measure between intuitionistic fuzzy sets based on the mid points of transformed triangular fuzzy numbers with applications to pattern recognition and medical diagnosis

Similarity measure is an essential tool to compare and determine the degree of similarity between intuitionistic fuzzy sets (IFSs). In this paper, a new similarity measure between intuitionistic fuzzy sets based on the mid points of transformed triangular fuzzy numbers is proposed. The proposed similarity measure provides reasonable results not only for the sets available in the literature but also gives very reasonable results, especially for fuzzy sets as well as for most intuitionistic fuzzy sets. To provide supportive evidence, the proposed similarity measure is tested on certain sets available in literature and is also applied to pattern recognition and medical diagnosis problems. It is observed that the proposed similarity measure provides a very intuitive quantification.