Cardinal Numbers of Fuzzy Sets

Up to now, the study on the cardinal number of fuzzy sets has advanced at on pace since it is very hard to give it an appropriate definition. Althrough for it in [1], it is with some harsh terms and is not reasonable as we point out in this paper. In the paper, we give a general definition of fuzzy cardinal numbers. Based on this definition, we not only obtain a large part of results with re spect to cardinal numbers, but also give a few of new properties of fuzzy cardinal numbers.

F-rough law and the discovery of rough law

By using function one direction S-rough sets （function one direction singular rough sets）, this article presents the concepts of F-law, F-rough law, and the relation metric of rough law; by using these concepts, this article puts forward the theorem of F-law relation metric, two orders theorem of F-rough law relation metric, the attribute theorem of F-rough law band, the extremum theorem of F-rough law relation metric, the discovery principle of F-rough law and the application of F-rough law.

Impacts of future climate change(2030-2059)on debris flow hazard:A case study in the Upper Minjiang River basin,China

An increase in extreme precipitation events due to future climate change will have a decisive influence on the formation of debris flows in earthquake-stricken areas. This paper aimed to describe the possible impacts of future climate change on debris flow hazards in the Upper Minjiang River basin in Northwest Sichuan of China, which was severely affected by the 2008 Wenchuan earthquake. The study area was divided into 1285 catchments, which were used as the basic assessment units for debris flow hazards. Based on the current understanding of the causes of debris flows, a binary logistic regression model was used to screen key factors based on local geologic, geomorphologic, soil,vegetation, and meteorological and climatic conditions. We used the weighted summation method to obtain a composite index for debris flow hazards, based on two weight allocation methods: Relative Degree Analysis and rough set theory. Our results showed that the assessment model using the rough set theory resulted in better accuracy. According to the bias corrected and downscaled daily climate model data, future annual precipitation(2030-2059) in the study area are expected to decrease, with an increasing number of heavy rainfall events. Under future climate change, areas with a high-level of debris flow hazard will be even more dangerous, and 5.9% more of the study area was categorized as having a high-level hazard. Future climate change will cause an increase in debris flow hazard levels for 128 catchments, accounting for 10.5% of the total area. In the coming few decades, attention should be paid not only to traditional areas with high-level of debris flow hazards, but also to those areas with an increased hazard level to improve their resilience to debris flow disasters.

Generating Set of the Complete Semigroups of Binary Relations

Difficulties encountered in studying generators of semigroup of binary relations defined by a complete X -semilattice of unions D arise because of the fact that they are not regular as a rule, which makes their investigation problematic. In this work, for special D, it has been seen that the semigroup , which are defined by semilattice D, can be generated by the set .

Multi-hierarchical fuzzy judgment and nested dominance relation of rough set theory-based environmental risk evaluation for tailings reservoirs

Environmental risk assessment of tailings reservoir assessment system is complex and has many index factors.In order to accurately judge surrounding environmental risks of tailings reservoirs and determinate the corresponding prevention and control work,multi-hierarchical fuzzy judgment and nested dominance relation of rough set theory are implemented to evaluate them and find out the rules of this evaluation system with 14 representative cases.The methods of multi-hierarchical fuzzy evaluation can overall consider each influence factor of risk assessment system and their mutual impact,and the index weight based on the analytic hierarchy process is relatively reasonable.Rough set theory based on dominance relation reduces each index attribute from the top down,largely simplifies the complexity of the original evaluation system,and considers the preferential information in each index.Furthermore,grey correlation theory is applied to analysis of importance of each reducted condition attribute.The results demonstrate the feasibility of the proposed safety evaluation system and the application potential.

Fixed Point Theorems for Increasing Operators of None－continuity and None－compactness Conditions

In this paper, the fixed point theorems of composite set-valued increasing operators are given. As a corollary, the fixed point theorem for increasing operator of none-continuity and nonecompactness conditions is also given. Some relevant results are improved and generalized.

The Optimization of Manufacturing Resources Allocation Considering the Geographical Distribution

From the perspective of the geographical distribution, considering production fare, supply chain information and quality rating of the manufacturing resource(MR), a manufacturing resource allocation(MRA) model considering the geographical distribution in cloud manufacturing(CM) environment is built. The model includes two stages, preliminary selection stage and optimal selection stage. The membership function is used to select MRs from cloud resource pool(CRP) in the first stage, and then the candidate resource pool is built. In the optimal selection stage, a multi-objective optimization algorithm, particle swarm optimization(PSO) based on the method of relative entropy of fuzzy sets(REFS_PSO), is used to select optimal MRs from the candidate resource pool, and an optimal manufacturing resource supply chain is obtained at last. To verify the performance of REFS_PSO, NSGA-Ⅱ and PSO based on random weighting(RW_PSO) are selected as the comparison algorithms. They all are used to select optimal MRs at the second stage. The experimental results show solution obtained by REFS_PSO is the best. The model and the method proposed are appropriate for MRA in CM.

Estimation of the Population Mean Using Paired Ranked Set Sampling

In the situation where the sampling units in a study can be easily ranked than quantified, the ranked set sampling methods are found to be more efficient and cost effective as compared to SRS. In this paper we propose an estimator of the population mean using paired ranked set sampling (RSS) method. The proposed estimator is an unbiased estimator of the population mean when the set size is even. In case of odd set size the estimator is unbiased when the underlying distribution is symmetric. It is shown that the proposed estimator is more efficient than its counterpart SRS method for all distributions considered in this study.

Computer Administering of the Psychological Investigations: Set-Relational Representation

Computer administering of a psychological investigation is the computer representation of the entire procedure of psychological assessments—test construction, test implementation, results evaluation, storage and maintenance of the developed database, its statistical processing, analysis and interpretation. A mathematical description of psychological assessment with the aid of personality tests is discussed in this article. The set theory and the relational algebra are used in this description. A relational model of data, needed to design a computer system for automation of certain psychological assessments is given. Some finite sets and relation on them, which are necessary for creating a personality psychological test, are described. The described model could be used to develop real software for computer administering of any psychological test and there is full automation of the whole process: test construction, test implementation, result evaluation, storage of the developed database, statistical implementation, analysis and interpretation. A software project for computer administering personality psychological tests is suggested.

An Efficient Class of Estimators for the Finite Population Mean in Ranked Set Sampling

In this paper, we propose a class of estimators for estimating the finite population mean of the study variable under Ranked Set Sampling (RSS) when population mean of the auxiliary variable is known. The bias and Mean Squared Error (MSE) of the proposed class of estimators are obtained to first degree of approximation. It is identified that the proposed class of estimators is more efficient as compared to [1] estimator and several other estimators. A simulation study is carried out to judge the performances of the estimators.

Ground-0 Axioms vs.First Principles and Second Law:From the Geometry of Light and Logic of Photon to Mind-Light-Matter Unity-AI&QI

Without the geometry of light and logic of photon,observer-observability forms a paradox in modern science,truthequilibrium finds no unification,and mind-light-matter unity is unreachable in spacetime.Subsequently,quantum mechanics has been shrouded with mysteries preventing itself from reaching definable causality for a general purpose analytical quantum computing paradigm.Ground-0 Axioms are introduced as an equilibrium-based,dynamic,bipolar set-theoretic unification of the first principles of science and the second law of thermodynamics.Related literatures are critically reviewed to justify the self-evident nature of Ground-0 Axioms.A historical misinterpretation by the founding fathers of quantum mechanics is identified and corrected.That disproves spacetime geometries(including but not limited to Euclidean and Hilbert spaces)as the geometries of light and truth-based logics(including but not limited to bra-ket quantum logic)as the logics of photon.Backed with logically definable causality and Dirac 3-polarizer experiment,bipolar quantum geometry(BQG)and bipolar dynamic logic(BDL)are identified as the geometry of light and the logic of photon,respectively,and wave-particle complementarity is shown less fundamental than bipolar complementarity.As a result,Ground-0 Axioms lead to a geometrical and logical illumination of the quantum and classical worlds as well as the physical and mental worlds.With logical resolutions to the EPR and Schr?dinger’s cat paradoxes,an analytical quantum computing paradigm named quantum intelligence(QI)is introduced.It is shown that QI makes mind-light-matter unity and quantum-digital compatibility logically reachable for quantumneuro-fuzzy AI-machinery with groundbreaking applications.It is contended that Ground-0 Axioms open a new era of science and philosophy—the era of mind-light-matter unity in which humanlevel white-box AI&QI is logically prompted to join Einstein’s grand unification to foster major scientific advances.

The Intelligent Decision Support System Model of SARS

Based on the intelligent decision support system, a new method was presented to defense the catastrophic infectious disease such as SARS, Bird Flu, etc.. By using All Set theory, the decision support system (DSS) model can be built to analyze the noise information and forecast the trend of the catastrophe then to give the method or policy to defend the disease. The model system is composed of four subsystems: the noise analysis subsystem, forecast and simulation subsystem, diagnosis subsystem and second recovery subsystem. They are discussed briefly in this paper.This model can be used not only for SARS but also for other paroxysmal accidences.

Approach to stochastic multi-attribute decision problems using rough sets theory

Multi-attribute decision problems where the performances of the alternatives are random variables are considered. The suggested approach grades the probabilities of preference of one alternative over another with respect to the same attribute. Based on the graded probabilistic dominance relation, the pairwise comparison information table is defined. The global preferences of the decision maker can be seen as a rough binary relation. The present paper proposes to approximate this preference relation by means of the graded probabilistic dominance relation with respect to the subsets of attributes. At last, the method is illustrated by an example.

Dynamic assessment method of air target threat based on improved GIFSS

As the air combat environment becomes more complicated and changeable, accurate threat assessment of air target has a significant impact on air defense operations. This paper proposes an improved generalized intuitionistic fuzzy soft set (GIFSS) method for dynamic assessment of air target threat. Firstly, the threat assessment index is reasonably determined by analyzing the typical characteristics of air targets. Secondly, after the GIFSS at different time is obtained, the index weight is determined by the intuitionistic fuzzy set entropy and the relative entropy theory. Then, the inverse Poisson distribution method is used to determine the weight of time series, and then the time-weighted GIFSS is obtained. Finally, threat assessment of five air targets is carried out by using the improved GIFSS (I-GIFSS) and comparison methods. The validity and superiority of the proposed method are verified by calculation and comparison.

On uniqueness of (fuzzy) relation in some generalized rough set model

In rough set theory, crisp and/or fuzzy binary relations play an important role in both constructive and axiomatic considerations of various generalized rough sets. This paper considers the uniqueness problem of the （fuzzy） relation in some generalized rough set model. Our results show that by using the axiomatic approach, the （fuzzy） relation determined by （fuzzy） approximation operators is unique in some （fuzzy） double-universe model.

Group Decision Making With Consistency of Intuitionistic Fuzzy Preference Relations Under Uncertainty

Intuitionistic fuzzy preference relation(IFPR) is a suitable technique to express fuzzy preference information by decision makers(DMs). This paper aims to provide a group decision making method where DMs use the IFPRs to indicate their preferences with uncertain weights. To begin with, a model to derive weight vectors of alternatives from IFPRs based on multiplicative consistency is presented. Specifically, for any IFPR,by minimizing its absolute deviation from the corresponding consistent IFPR, the weight vectors are generated. Secondly,a method to determine relative weights of DMs depending on preference information is developed. After that we prioritize alternatives based on the obtained weights considering the risk preference of DMs. Finally, this approach is applied to the problem of technical risks assessment of armored equipment to illustrate the applicability and superiority of the proposed method.

Rock burst laws in deep mines based on combined model of membership function and dominance-based rough set

Rock bursts are spontaneous, violent fracture of rock that can occur in deep mines, and the likelihood of rock bursts occurring increases as depth of the mine increases. Rock bursts are also affected by the compressive strength, tensile strength, tangential strength, elastic energy index, etc. of rock, and the relationship between these factors and rock bursts in deep mines is difficult to analyze from quantitative point. Typical rock burst instances as a sample set were collected, and membership function was introduced to process the discrete values of these factors with the discrete factors as condition attributes and rock burst situations as decision attributes. Dominance-based rough set theory was used to generate preference rules of rock burst, and eventually rock burst laws analysis in deep mines with preference relation was taken. The results show that this model for rock burst laws analysis in deep mines is more reasonable and feasible, and the prediction results are more scientific.

Coordinating control of multiple rigid bodies based on motion primitives

This paper studies the problem of coordinated motion generation for a group of rigid bodies. Two classes of coordinated motion primitives, relative equilibria and ma- neuvers, are given as building blocks for generating coordi- nated motions. In a motion-primitive based planning frame- work, a control method is proposed for the robust execution of a coordinated motion plan in the presence of perturba- tions. The control method combines the relative equilibria stabilization with maneuver design, and results in a close- loop motion planning framework. The performance of the control method has been illustrated through a numerical sim- ulation.