Analysis of TOPSIS techniques based on bipolar complex fuzzy N-soft setting and their applications in decision-making problems

A novel model termed a bipolar complex fuzzy N-soft set(BCFN-SS)is initiated for tackling information that involves positive and negative aspects,the second dimension,and parameterised grading simultaneously.The theory of BCFN-SS is the generalisation of two various theories,that is,bipolar complex fuzzy(BCF)and N-SS.The invented model of BCFN-SS helps decision-makers to cope with the genuine-life dilemmas containing BCF information along with parameterised grading at the same time.Further,various algebraic operations,including the usual type of union,intersection,complements,and a few others types,are invented.Certain primary operational laws for BCFNSS are also invented.Moreover,a technique for order preference by similarity to the ideal solution(TOPSIS)approach is devised in the setting of BCFN-SS for managing strategic decision-making(DM)dilemmas containing BCFN-SS information.Keeping in mind the usefulness and benefits of the TOPSIS approach,two various types of TOPSIS approaches in the environment of BCFN-SS are devised and then a numerical example for exposing the usefulness of the devised TOPSIS approach is interpreted.To disclose the prominence and benefits of the devised work,the devised approaches with numerous prevailing work are compared.

Aggregation operators and CRITIC-VIKOR method for confidence complex q-rung orthopair normal fuzzy information and their applications

Supply chain management is an essential part of an organisation's sustainable programme.Understanding the concentration of natural environment,public,and economic influence and feasibility of your suppliers and purchasers is becoming progressively familiar as all industries are moving towards a massive sustainable potential.To handle such sort of developments in supply chain management the involvement of fuzzy settings and their generalisations is playing an important role.Keeping in mind this role,the aim of this study is to analyse the role and involvement of complex q-rung orthopair normal fuzzy(CQRONF)information in supply chain management.The major impact of this theory is to analyse the notion of confidence CQRONF weighted averaging,confidence CQRONF ordered weighted averaging,confidence CQRONF hybrid averaging,confidence CQRONF weighted geometric,confidence CQRONF ordered weighted geometric,confidence CQRONF hybrid geometric operators and try to diagnose various properties and results.Furthermore,with the help of the CRITIC and VIKOR models,we diagnosed the novel theory of the CQRONF-CRITIC-VIKOR model to check the sensitivity analysis of the initiated method.Moreover,in the availability of diagnosed operators,we constructed a multi-attribute decision-making tool for finding a beneficial sustainable supplier to handle complex dilemmas.Finally,the initiated operator's efficiency is proved by comparative analysis.

Synchronous Control of Complex Networks with Fuzzy Connections

This article is based on the T-S fuzzy control theory and investigates the synchronization control problem of complex networks with fuzzy connections. Firstly, the main stability equation of a complex network system is obtained, which can determine the stability of the synchronous manifold. Secondly, the main stable system is fuzzified, and based on fuzzy control theory, the control design of the fuzzified main stable system is carried out to obtain a coupling matrix that enables the complex network to achieve complete synchronization. The numerical analysis results indicate that the control method proposed in this paper can effectively achieve synchronization control of complex networks, while also controlling the transition time for the network to achieve synchronization.

Decision Making Based on Valued Fuzzy Superhypergraphs

This paper explores the defects in fuzzy (hyper) graphs (as complex (hyper) networks) and extends the fuzzy(hyper) graphs to fuzzy (quasi) superhypergraphs as a new concept.We have modeled the fuzzy superhypergraphsas complex superhypernetworks in order to make a relation between labeled objects in the form of details andgeneralities. Indeed, the structure of fuzzy (quasi) superhypergraphs collects groups of labeled objects and analyzesthem in the form of the part to part of objects, the part of objects to the whole group of objects, and the whole tothe whole group of objects at the same time.We have investigated the properties of fuzzy (quasi) superhypergraphsbased on any positive real number as valued fuzzy (quasi) superhypergraphs, considering the complement of valuedfuzzy (quasi) superhypergraphs, the notation of isomorphism of valued fuzzy (quasi) superhypergraphs based onthe permutations, and we have presented the isomorphic conditions of (self complemented) valued fuzzy (quasi)superhypergraphs. The concept of impact membership value of fuzzy (quasi) superhypergraphs is introducedin this study and it is applied in designing the real problem in the real world. Finally, the problem of businesssuperhypernetworks is presented as an application of fuzzy valued quasi superhypergraphs in the real world.

Fuzzy Complex Index in Water Quality Assessment of Municipalities

Donghu Lake in Wuhan is a multipurpose complex water body. However, its eutrophication phenomenon becomes increasingly serious. By making use of detailed and accurate contamination monitoring data and several mathematics models, we probe into the dynamic state of water quality. The year’s average value of major contamination index in Donghu Lake from 2001 to 2008 and fuzzy complex index are used to assess its short-term state of water quality. The results show that its water quality is basically stable in the 4th class of water quality standard GB3838-2002.

Evaluating the conceptual design schemes of complex products based on FAHP using fuzzy number

In the conceptual design stage of complex products, CBR（Case-Based Reasoning） tool is useful to offer a feasible set of schemes. Then the most adaptive scheme can be generated through a procedure of comparison and evaluation. The procedure is essentially a multiple criteria decision-making problem. The traditional multiple criteria programming is not flexible enough in executing the system evaluation algorithm due to both the limited experimental data and the lack of human experiences. To make the CBR tool to be more efficient, a new method for the best choice among the feasible schemes based on the Fuzzy AHP using Fuzzy numbers （FFAHP） is proposed. Since the final results become a problem of ranking the mean of fuzzy numbers by the optimism of decision-maker using the FFAHP, its execution is much more intuitive and effective than with the traditional method.

A Novel Evolutionary-Fuzzy Control Algorithm for Complex Systems

This paper presents an adaptive fuzzy control scheme based on modified genetic algorithm. In the control scheme, genetic algorithm is used to optimze the nonlinear quantization functions of the controller and some key parameters of the adaptive control algorithm. Simulation results show that this control scheme has satisfactory performance in MIMO systems, chaotic systems and delay systems.

Evaluaton model for the geometry complexity of casting based on fuzzy theory

The parameters that describe the complex degree of a certain casting are of some uncertainty. Therefore, a new method based on the fuzzy theory to classify the complex degree of castings has been presented in this paper. The feasibility of fuzzy theory in describing the complex degree of castings has been discussed and the procedure of this method has been specified by analyzing the complex degrees of some typical castings. The element factors that influence the casting complexity, have been summarized, which include the wall-thickness and the number of transition surface, etc. The results show that it is reasonable and practicable to classify the complex degree of castings with the fuzzy theory.

Anomaly Detection of Complex Networks Based on Intuitionistic Fuzzy Set Ensemble

Ensemble learning for anomaly detection of data structured into a complex network has been barely studied due to the inconsistent performance of complex network characteristics and the lack of inherent objective function. We propose the intuitionistic fuzzy set（IFS）-based anomaly detection, a new two-phase ensemble method for anomaly detection based on IFS, and apply it to the abnormal behavior detection problem in temporal complex networks.Firstly, it constructs the IFS of a single network characteristic, which quantifies the degree of membership,non-membership and hesitation of each network characteristic to the defined linguistic variables so that makes the unuseful or noise characteristics become part of the detection. To build an objective intuitionistic fuzzy relationship, we propose a Gaussian distribution-based membership function which gives a variable hesitation degree. Then, for the fuzzification of multiple network characteristics, the intuitionistic fuzzy weighted geometric operator is adopted to fuse multiple IFSs and to avoid the inconsistence of multiple characteristics. Finally, the score function and precision function are used to sort the fused IFS. Finally, we carry out extensive experiments on several complex network datasets for anomaly detection, and the results demonstrate the superiority of our method to state-of-the-art approaches, validating the effectiveness of our method.

The Fuzzy Modeling Algorithm for Complex Systems Based on Stochastic Neural Network

A fuzzy modeling method for complex systems is studied. The notation of general stochastic neural network (GSNN) is presented and a new modeling method is given based on the combination of the modified Takagi and Sugeno's (MTS) fuzzy model and one-order GSNN. Using expectation-maximization(EM) algorithm, parameter estimation and model selection procedures are given. It avoids the shortcomings brought by other methods such as BP algorithm, when the number of parameters is large, BP algorithm is still difficult to apply directly without fine tuning and subjective tinkering. Finally, the simulated example demonstrates the effectiveness.

Complex Fuzzy Structured Element and Its Properties

The first part of this paper gives the definition about complex fuzzy structured element on the basis of one-dimensional fuzzy structured element and some of its property. The following part introduces its limit and continuity. All of this has opened up a vision for the research of fuzzy structured element, and also played an important role in promoting its progress.

An Equivalent Condition for （K） Integrability of Fuzzy-valued Mappings

In this paper, we first discuss the relationship between the McShane integral and Pettis integral for vector-valued functions. Then by using the embedding theorems for the fuzzy number space E^1, we give a new equivalent condition for （K） integrabihty of a fuzzy set-valued mapping F ： [a, b] → E^1.

复Fuzzy函数的Buckley导数与Buckley积分

本文对Ｊ．Ｊ．Ｂｕｃｋｌｅｙ在［１］、［２］中给出的实变量复Ｆｕｚｚｙ数值函数的导数与积分加以推广，引出复变量复Ｆｕｚｚｙ数值的导数与积分概念，为研究Ｆｕｚｚｙ复分析打下一定的基础。

广义复Fuzzy积分

为了研究复Fuzzy积分,与文献[3]中定义的复Fuzzy积分不同,重新定义了复Fuzzy积分的概念,并给出了广义复Fuzzy积分、(S)复Fuzzy积分和(N)复Fuzzy积分的概念,最后讨论它们的一些性质和收敛定理,为研究复模糊分析学打下一定的基础。

复Fuzzy级数及其收敛性的进一步讨论

给出复 Fuzzy数项级数与复 Fuzzy函数级数的概念 ,讨论它们的收敛性问题 ,给出它们收敛性的相应判别法则。

Fuzzy复值测度与Lebesgue积分

在Ｊ．Ｊ．Ｂｕｃｋｌｅｙ引进“Ｆｕｚｚｙ复数”理论的基础上，定义了Ｆｕｚｚｙ复值可测函数，Ｆｕｚｚｙ复值测度及相应的Ｆｕｚｙ复值积分，并讨论此积分的一些基本性质与收敛定理．

复Fuzzy测度与复Fuzzy积分

提出复Ｆｕｚｚｙ测度、复Ｆｕｚｚｙ可测函数及复Ｆｕｚｚｙ积分等概念，并讨论了其性质与收敛定理。

基于结构元理论的复Fuzzy数项数列收敛性

研究了基于结构元理论的复Fuzzy数项数列,给出了基于结构元理论线性生成的复模糊数及复模糊数项数列定义.探讨了数列的收敛性,给出了数列收敛的充要条件及收敛的唯一性、有界性、保号性等结论.

复Fuzzy函数级数的一致收敛及其若干性质

在给出复Fuzzy函数级数及其一致收敛的概念的基础上,补充了复Fuzzy函数级数一致收敛的判别方法并讨论了一致收敛的复Fuzzy函数级数的若干性质。

高师体育院系学生掌握技术程度Fuzzy综合评判的研究

目前对高师体育院、系学生技术掌握程度的测量与评价，方法较为简单，并受其主观因素的影响与制约，不能准确地反映学生掌握技术的程度，评价的信度、效度较低。依据教育测量与评价、体育测量与评价的理论，结合专业特点，确定短跑技术测量与评价指标体系，运用能包容所有专家反馈信息的重心法和集值统计迭代法确定短跑技术各大、小环节的权重值，优于其他权值确定的方法，最后运用模糊综合评判的数学模型评价学生掌握技术的程度。