Dombi-Normalized Weighted Bonferroni Mean Operators with Novel Multiple-Valued Complex Neutrosophic Uncertain Linguistic Sets and Their Application in Decision Making

Although fuzzy set concepts have evolved,neutrosophic sets are attractingmore attention due to the greater power of the structure of neutrosophic sets.The ability to account for components that are true,false or neither true nor false is useful in the resolution of real-life problems.However,simultaneous variations render neutrosophic sets unsuitable in specific circumstances.To enable the management of these sorts of issues,we combine the principle of multi-valued neutrosophic uncertain linguistic sets and complex fuzzy sets to develop the principle of multivalued complex neutrosophic uncertain linguistic sets.Multi-valued complex neutrosophic uncertain linguistic sets can contain grades of truth,abstinence,and falsity,and uncertain linguistic terms,which are expressed as complex numbers whose real and imaginary parts are limited to the unit interval.Some important Dombi laws are elaborated along with Bonferroni mean operators,which offer a flexible general structure with modifiable factors.Bonferroni means aggregation operators perform a significant role in conveying the magnitude level of options and characteristics.To determine relationships among any number of attributes,we develop multi-valued complex neutrosophic uncertain linguistic Dombi-normalized weighted Bonferroni mean operators and discuss their important properties with some special cases.By using these laws,we can deploy themulti-attribute decisionmaking(MADM)technique using the novel principle of multi-valued complex neutrosophic uncertain linguistic sets.To determine the power and flexibility of the elaborated approach,we resolve some numerical examples based on the proposed operator.Finally,the work is validated with the help of comparative analysis,a discussion of its advantages,and geometric expressions of the elaborated theories.

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.

Interval-Valued Neutrosophic Soft Expert Set from Real Space to Complex Space

A fuzzy system is a novel computing technique that accesses uncertain information by fuzzy representation.In the decision-making process,fuzzy system and soft computing are effective tools that are tolerant to imprecision,uncertainty,and partial truths.Evolutionary fuzzy systems have been developed with the appearance of interval fuzzy,dual fuzzy,hesitant fuzzy,neutrosophic,plithogenic representations,etc.Moreover,by capturing compound features and convey multi-dimensional data,complex numbers are utilized to generalize fuzzy and neutrosophic fuzzy sets.In this paper,a representation of neutrosophic soft expert systems based on the real and complex numbers in the interval form is proposed.The interval-valued neutrosophic soft expert set(I-VNSES)is defined,and the interval-valued complex neutrosophic soft expert set(I-VCNSES)is formally generalized from the concept of IVNSES.For both I-VNSES and I-VCNSES,we introduce the relevant basic theoretical operations and study their properties.Based on these new concepts,a generalized algorithm is proposed and applied to handle the imbedded indeterminacy in the two-dimensional interval data.The proposed algorithm is tested on the economic factors that affected the Malaysian economy in 2020 to see which ones are the most influential.Eventually,a comparison of three current approaches is used to back up this study.

Sine Trigonometry Operational Laws for Complex Neutrosophic Sets and Their Aggregation Operators in Material Selection

In this paper,sine trigonometry operational laws(ST-OLs)have been extended to neutrosophic sets(NSs)and the operations and functionality of these laws are studied.Then,extending these ST-OLs to complex neutrosophic sets(CNSs)forms the core of thiswork.Some of themathematical properties are proved based on ST-OLs.Fundamental operations and the distance measures between complex neutrosophic numbers(CNNs)based on the ST-OLs are discussed with numerical illustrations.Further the arithmetic and geometric aggregation operators are established and their properties are verified with numerical data.The general properties of the developed sine trigonometry weighted averaging/geometric aggregation operators for CNNs(ST-WAAO-CNN&ST-WGAO-CNN)are proved.A decision making technique based on these operators has been developed with the help of unsupervised criteria weighting approach called Entropy-ST-OLs-CNDM(complex neutrosophic decision making)method.A case study for material selection has been chosen to demonstrate the ST-OLs of CNDM method.To check the validity of the proposed method,entropy based complex neutrosophic CODAS approach with ST-OLs has been executed numerically and a comparative analysis with the discussion of their outcomes has been conducted.The proposed approach proves to be salient and effective for decision making with complex information.

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.

A Complex Fuzzy LSTM Network for Temporal-Related Forecasting Problems

Time-stamped data is fast and constantly growing and it contains significant information thanks to the quick development ofmanagement platforms and systems based on the Internet and cutting-edge information communication technologies.Mining the time series data including time series prediction has many practical applications.Many new techniques were developed for use with various types of time series data in the prediction problem.Among those,this work suggests a unique strategy to enhance predicting quality on time-series datasets that the timecycle matters by fusing deep learning methods with fuzzy theory.In order to increase forecasting accuracy on such type of time-series data,this study proposes integrating deep learning approaches with fuzzy logic.Particularly,it combines the long short-termmemory network with the complex fuzzy set theory to create an innovative complex fuzzy long short-term memory model(CFLSTM).The proposed model adds a meaningful representation of the time cycle element thanks to a complex fuzzy set to advance the deep learning long short-term memory(LSTM)technique to have greater power for processing time series data.Experiments on standard common data sets and real-world data sets published in the UCI Machine Learning Repository demonstrated the proposedmodel’s utility compared to other well-known forecasting models.The results of the comparisons supported the applicability of our proposed strategy for forecasting time series data.

Rare-earth and trace element imprints on the origin and tectonic setting of gabbro-diorite complex in the Pan-African belt of Southeast Obudu Plateau,Nigeria

A gabbro-diorite plutonic complex from the Southeast Obudu Plateau, representing limited volumes of magma, was studied for its trace and rare-earth element characteristics, in an attempt to document its genetic and geodynamic history. Geochemical studies indicate that the gabbro samples are characterized by variable concentrations and low averages of such index elements as Cr (40×10-6–200×10-6; av. 80×10-6), Ni (40×10-6–170×10-6; 53.33×10-6) and Zr (110×10-6–240×10-6; 116.67×10-6); variable and high averages of Rb (3×10-6–270×10-6; 80.67×10-6), Sr (181×10-6–1610×10-6; 628.17×10-6) and U (0.14×10-6–3.46×10-6; 1.51×10-6), and fairly uniform Co (34×10-6–49×10-6; 36.33×10-6) and Sc (23×10-6–39×10-6; 34.5×10-6), while the diorite samples exhibit higher trace element compositions. The range of REE contents and distinctive chondrite-normalized patterns indicate moderate fractionation with slight positive Eu anomaly in the diorites to very low fractionation with flat patterns and slight positive Eu anomaly in the gabbros. However, the general element systematics of the samples, especially LILE (Ba, Rb, Sr, Cs and Pb), HFSE (Zr, Th, U, Hf, Mo, W, Nb and Sn), relatively immobile elements (Zr, Ni, Cr) and REE, suggests a differentiation model, involving fractional crystallization of olivine and clinopyroxene from a partial melt generated beneath an island arc complex. A possible model for the complex is therefore an island arc setting, the development of which was dominated by calc-alkaline magmatism across the Obudu Plateau.

基于梯度增量level-set方法的复杂物体入水砰击数值模拟

复杂结构物自由表面砰击问题,如空投鱼雷、水空无人航行器潜水和高速船出入水,一直是海洋工程领域的研究热点。本文采用梯度增量level-set和虚拟网格法数值模拟复杂结构物的入水砰击,采用时间半隐式有限差分法求解不可压缩Navier-Stokes方程,虚拟网格法可重构复杂结构物界面插值模块并施加无滑移边界条件,梯度增量level-set法可捕捉非线性自由表面翻卷、射流等物理现象。基于以上方法模拟二维圆柱的常速入水砰击,并与试验和数值结果对比,验证本文数值方法的正确性。最后,数值模拟二维船型剖面和飞机剖面的入水砰击,分析了冲击压力、运动响应、压力分布和自由表面运动随入水角度的变化规律。同时,通过模拟可观察到复杂结构浸入水中后的流体分离、射流和小角度空气腔等典型砰击物理现象。

3-Set Packing参数化计数问题的复杂性及近似算法

3-Set Packing参数化计数问题即在一个3-Set Packing实例中统计所有大小为k的不同packing的个数。首先证明了该问题的计算复杂性是#W[1]-难的,表明该问题不大可能存在固定参数可解的精确算法(除非#W[1]=FPT)。然后,通过拓展3-D Matching参数化计数问题的算法对3-Set Packing参数化计数问题提出了一个基于Monte-Carlo自适应覆盖算法和着色技术的随机近似算法。

基于Rough Set的目标快速识别方法

主要研究了基于粗糙集和支持向量机的模式分类技术,结合遥感图像中军用飞机目标识别进行了理论分析和实验研究。设计了基于粗糙集和决策有向无环图的支持向量机模式识别分类器,对分类的性能进行了分析研究,利用粗糙集理论中属性约简方法去除冗余属性,降低飞机特征维数,提出使用决策有向无环图支持向量机进行训练并对待识别目标预测。实验表明,本文提出的方法可提高识别速度及预测分类精度。

Geochemical characteristics and tectonic setting of the Tuerkubantao mafic-ultramafic intrusion in West Junggar,Xinjiang,China

Mineral chemistry, whole-rock major oxide, and trace element compositions have been determined for the Tuerkubantao mafic-ultramafic intrusion, in order to understand the early Paleozoic tectonic evolution of the West Junggar orogenic belt at the southern margin of the Central Asian orogenic belt. The Tuerkubantao mafic-ultramafic intrusion is a well-differentiated complex comprising peridotite, olivine pyroxenite, gabbro, and diorite. The ultramafic rocks are mostly seen in the central part of the intrusion and surrounded by mafic rocks. The Tuerkubantao intrusive rocks are characterized by enrichment of large ion lithophile elements and depleted high field strength elements relative to N-MORB. In addition, the Tuerkubantao intrusion displays relatively low Th/U and Nb/U （1.13-2.98 and 2.53-7.02, respectively） and high La/Nb and Ba/Nb （1.15 4.19 and 37.7-79.82, respectively）. These features indicate that the primary magma of the intrusion was derived from partial melting of a previously metasomatized mantle source in a subduction setting. The trace element patterns of peridotites, gabbros, and diorite in the Tuerkubantao intrusion have sub-parallel trends, suggesting that the different rock types are related to each other by differentiation of the same primary magma. The intrusive contact between peridotite and gabbro clearly suggest that the Tuerkubantao is not a fragment of an ophiolite. However, the Tuerkubantao intrusion displays many similarities with Alaskan-type mafic-ultramafic intrusions along major sutures of Phanerozoic orogenic belts. Common features include their geodynamic setting, internal lithological zoning, and geochemistry. The striking similarities indicate that the middle Devonian Tuerkubantao intrusion likely formed in a subduction-related setting similar to that of the Alaskan-type intrusions. In combination with the Devonian magmatism and porphyry mineralization, we propose that subduction of the oceanic slab has widely existed in the expansive oceans during the Devonian around the Junggar block.

Set Packing问题的研究进展

Set Packing问题起源于分割问题的应用,是在强约束条件对元素进行划分。在复杂性理论中,此问题是一类重要的NP难问题,被广泛应用于调度、代码优化和生物信息学等领域。特别是在参数计算理论产生后。此问题再次成为研究的热点问题。依据所研究问题的差异,本文将Set Packing问题分成5类,并给出了具体的定义。在此基础上,分别介绍了求解这5类问题的相关算法,着重分析和比较了参数算法中所运用的各项技术,并提出了该问题算法研究的一些发展方向。

Study on the accuracy of comprehensive evaluating method based on fuzzy set theory

The evaluation method and its accuracy for evaluating complex systems are considered. In order to evaluate accurately complex systems, the existed evaluating methods are simply analyzed, and a new comprehensive evaluating method is developed. The new method is integration of Delphi approach, analytic hierarchy process, gray interconnect degree and fuzzy evaluation (DHGF). Its theory foundation is the meta-synthesis methodology from qualitative analysis to quantitative analysis. According to fuzzy set approach, using the methods of concordance of evaluation, redundant verify, double models redundant, and limitations of the method etc, the accuracy of evaluating method of DHGF is estimated, and a practical example is given. The result shows that using the method to evaluate complex system projects is feasible and credible.

Geochemical Characteristics of Archean High-Grade Terrain of Kongling Complex and Early Crustal Evolution of Yangtze Craton

This paper reports the systematic studies of geochemistry on the meta sedimentary rocks, felsic gneisses and amphibolites of the Kongling complex from the Archean high grade terrain of the Yangtze craton. It shows that the amphibolites originated from a weakly depleted mantle resource. Nb negative anomaly, negative ε (Nd, t ) and the t DM ages which older than their isochron ages of the TTG gneisses imply the possible existence of the crust older than round about 2.7 Ga in the region. Three types of meta sedimentary rocks are identified from the Kongling complex. The first type originated from the juvenile crust with the features of the first cycle sedimentary rocks. Cratonic sedimentary rocks characterize the second type. Mobilization of REE and other elements resulted from partial melting during the migmatization is found in the third type of meta sedimentary rocks. Apart from the early TTG gneisses, some of the mafic rocks are also expected to be the source rocks of the first type of para rocks. The deposition times of the first and second type paragneisses are closed in the Neoarchean of about 2.7 Ga and the early period of Proterozoic respectively, and the period when cratonization of the Yangtze continental block completed is referred to be earlier than the Mesoproterozoic. Nd isotopic tracing on the magma sources of the Jinning granitic rocks in the region reveals that the major part of the Kongling basement is Neoarchean.

Improved Multi-objective Ant Colony Optimization Algorithm and Its Application in Complex Reasoning

The problem of fault reasoning has aroused great concern in scientific and engineering fields.However,fault investigation and reasoning of complex system is not a simple reasoning decision-making problem.It has become a typical multi-constraint and multi-objective reticulate optimization decision-making problem under many influencing factors and constraints.So far,little research has been carried out in this field.This paper transforms the fault reasoning problem of complex system into a paths-searching problem starting from known symptoms to fault causes.Three optimization objectives are considered simultaneously: maximum probability of average fault,maximum average importance,and minimum average complexity of test.Under the constraints of both known symptoms and the causal relationship among different components,a multi-objective optimization mathematical model is set up,taking minimizing cost of fault reasoning as the target function.Since the problem is non-deterministic polynomial-hard(NP-hard),a modified multi-objective ant colony algorithm is proposed,in which a reachability matrix is set up to constrain the feasible search nodes of the ants and a new pseudo-random-proportional rule and a pheromone adjustment mechinism are constructed to balance conflicts between the optimization objectives.At last,a Pareto optimal set is acquired.Evaluation functions based on validity and tendency of reasoning paths are defined to optimize noninferior set,through which the final fault causes can be identified according to decision-making demands,thus realize fault reasoning of the multi-constraint and multi-objective complex system.Reasoning results demonstrate that the improved multi-objective ant colony optimization(IMACO) can realize reasoning and locating fault positions precisely by solving the multi-objective fault diagnosis model,which provides a new method to solve the problem of multi-constraint and multi-objective fault diagnosis and reasoning of complex system.

COMPLEXITY OF LIMIT LANGUAGE OF THE ELEMENTARY CELLULAR AUTOMATON OF RULE 22

In this paper, the limit set of the elementary cellular automaton of rule 22 is considered. The limit language is defined from limit set and its complexity is studied by using formal language theory. It is proved that this language is not a regular language. This result shows that the dynamics of this cellular automaton is actually complicated.

The Computational Complexity of Untrapped Choice Procedures

In this paper, we define two versions of Untrapped set (weak and strong Untrapped sets) over a finite set of alternatives. These versions, considered as choice procedures, extend the notion of Untrapped set in a more general case (i.e. when alternatives are not necessarily comparable). We show that they all coincide with Top cycle choice procedure for tournaments. In case of weak tournaments, the strong Untrapped set is equivalent to Getcha choice procedure and the Weak Untrapped set is exactly the Untrapped set studied in the litterature. We also present a polynomial-time algorithm for computing each set.

A Low Complexity VCS Method for PAPR Reduction in Multicarrier Code Division Multiple Access

This paper investigates a peak to average power ratio （PAPR） reduction method in multicarrier code division multiple access （MC-CDMA） system. Variable code sets （VCS）, a spreading codes selection scheme, can improve the PAPR property of the MC-CDMA signals, but this technique requires an exhaustive search over the combinations of spreading code sets. It is observed that when the number of active users increases, the search complexity will increase exponentially. Based on this fact, we propose a low complexity VCS （LC-VCS） method to reduce the computational complexity. The basic idea of LC-VCS is to derive new signals using the relationship between candidature signals. Simulation results show that the proposed approach can reduce PAPR with lower comtational pucomplexity. In addition, it can be blindly received without any side information.