RELATIVELY WEAKLY COMPACT SETS IN THE DENJOY SPACE

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FIXED POINT THEOREMS FOR MAPPINGS SATISFYING IMPLICIT RELATION ON TWO COMPLETE AND COMPACT METRIC SPACES

First, the implicit relations were given. A common fixed point theorem was proved for two mappings satisfying implicit relation functions. A further fixed point theorem was proved for mappings satisfying implicit relation functions on two compact metric spaces.

Brezis-Nirenberg Theorem on Non_compact Sets

In present paper we prove that on non_compact sets the conclusion in the Brezis_Nirenberg Theorem is also true.

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.

Cost Sensitive Multi-Granulation Preference Relation Rough Set for Ordinal Decision System

The preference analysis is a class of important issues in multi-criteria ordinal decision making.The rough set is an effective approach to handle preference analysis.In order to solve the multi-criteria preference analysis problems,this paper improves the preference relation rough set model and expands it to multi-granulation cases.Cost is also an important issue in the field of decision analysis.Taking the cost into consideration,we also expand the model to the cost sensitive multi-granulation preference relation rough set.Some theorems are represented,and the granule structure selection based on approximation quality is investigated.The experimental results show that the multi-granulation preference rough set approach with the consideration of cost has a better performance in granule structure selection than that without cost consideration.

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 .

Ontology mapping approach based on set & relation theory and OCL

An ontology mapping approach based on set & relation theory and OCL is introduced,then an ontology mapping meta-model is established which is composed of ontology related elements,mapping related elements and definition rule related elements.This ontology mapping meta-model can be regarded as a unified mechanism to realize different kinds of ontology mappings.The powerful computation capability of set and relation theory and the flexible expressive capability of OCL can be used in the computation of ontology mapping meta-model to realize the unified mapping among different ontology models.Based on the mapping meta-model,a general mapping management framework is developed to provide a common mapping storage mechanism,some mapping APIs and mapping rule APIs.

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.

Relative Strong F Compactness and Relative Ultra-F Compactness in L-topological Spaces

In this paper, two concepts of relative compactness-the relative strong fuzzy compactness and the relative ultra-fuzzy compactness are defined in L-topological spaces for an arbitrary L-set. Properties of relative strong fuzzy sets and relative ultra-fuzzy compact sets are studied in detail and some characteristic theorems are given. Some examples are illustrated.

A Construction of Relative Difference Set

In this paper, we give a construction of RDS in Galois ring by using some bent function, and obtain the equivalent relationship between RDS and a kind of bent function. At the same time, its existence is demonstrated.

Relative N-compactness in L-fuzzy Topological Spaces

The concept of relative N-compactness is defined and characterized in terms ofnets. It is shown that the relative N-compactness is hereditary with respect to L-fuzzy setsand the relative N-compactness is L-good extension. Some connections between the N-compactness and the relative N-compactness are investigated. It is also proved that inducedrelative N-compact spaces are productive, and the product of finite relative compact sets isrelative compact.

Influence of relative compaction and degree of saturation on the deformation characteristics of bentonite under freeze-thaw cycles

Bentonite,consisting of clay minerals of the montmorillonite group,has been widely used as an adsorbent and backfill material in nuclear waste disposal and groundwater remediation.It is challenging to use bentonite as a filling material in cold regions since bentonite is highly sensitive to thermal environmental changes,during which its bulk volume and microstructure change significantly.In this study,a series of one-dimensional and three-dimensional freeze-thaw tests were carried out within a closed system to investigate the influencing factors of the deformation of bentonite under freeze-thaw cycles.Results show that the initial soil water content greatly impacts bentonite's deformation during freeze-thaw cycles.For an initial higher degree of saturation(Sr),the expansion caused by the formation of ice lenses has a greater impact than the shrinkage induced by dehydration,ice-cementation,and so on.Conversely,bentonite tends to shrink at a lower degree of saturation during freezing.And the critical degree of saturation that determines bentonite's behavior of frost heave or frost shrinkage seems to be roughly 0.8.As the number of freeze-thaw cycles rises,initially uncompacted bentonite clay becomes more compacted,and initially compacted bentonite clay remains unchanged.

Integral Sequences of Infinite Length Whose Terms Are Relatively Prime

It is given in Weil and Rosenlicht ([1], p. 15) that (resp. 2) for all non-negative integers m and n with m≠n if c is any even (resp. odd) integer. In the present paper we generalize this. Our purpose is to give other integral sequences such that G.C.D.(ym,yn)=1 for all positive integers m and n with m≠n. Roughly speaking we show the following 1) and 2). 1) There are infinitely many polynomial sequences such that G.C.D.(fm(a),fn(a))=1 for all positive integers m and n with with m≠n and infinitely many rational?integers a. 2) There are polynomial sequences such that G.C.D.(gm(a,b),gn(a,b))=1 for all positive integers m and n with m≠n and arbitrary (rational or odd) integers a and b with G.C.D.(a,b)=1. Main results of the present paper are Theorems 1 and 2, and Corollaries 3, 4 and 5.

Continuity of Solution Mappings for Parametric Set Optimization Problems under Partial Order Relations

This paper mainly investigates the semicontinuity of solution mappings for set optimization problems under a partial order set relation instead of upper and lower set less order relations. To this end, we propose two types of monotonicity definition for the set-valued mapping introduced by two nonlinear scalarization functions which are presented by these partial order relations. Then, we give some sufficient conditions for the semicontinuity and closedness of solution mappings for parametric set optimization problems. The results presented in this paper are new and extend the main results given by some authors in the literature.

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.

Research on Statistical Relational Learning and Rough Set in SRL

Statistical relational learning constructs statistical models from relational databases, combining relational learning and statistical learning. Its strong ability and special property make statistical relational learning become one of the important areas in machine learning research.In this paper,the general concepts and characters of statistical relational learning are presented firstly.Then some major branches of this newly emerging field are discussed,including logic and rule-based approaches,frame and object-oriented approaches,functional programming-based approaches.After that several methods of applying rough set in statistical relational learning are described,such as gRS-ILP and VPRSILP. Finally some applications of statistical relational leaning are briefly introduced and some future directions of statistical relational learning and the application of rough set in this area are pointed out.

THE GENERALIZED EINSTEIN RELATION ON A COMPACT ORIENTABLE RIMANNIAN MANIFOLD

A generalized Einstein relation is established for a drifted Brownian motion on a compact orientable Remannian manifole. The original form of such relation comes from an explicit formula of diffusion coeffcient by using the autocorrelation function of the velocity of the Einstein fluctuation theory of the diffusion process

Unified Approach to Assess Engineering Performance of Fill Improved by Shallow to Deep Compaction Based Techniques Using Relative Density

The setting of pre assessment criteria for soil compaction is hardly determined, especially, in case of undecided structure locations. Different design guidelines recommend achieving a specific value of relative density for the compaction of fill placement works. Alternatives were discussed through the literature to predict the value of relative density based on soil field tests (e.g. cone and standard penetration tests). This paper presents the weakness of using the Over Consolidation Ratio (OCR) as guidance to assess the value of cone tip resistance using the soil relative density. The variation of OCR (from 1 to 10) has a significant effect on the qc value up to 110% when compared to the normally consolidated state. Then normally consolidated state can logically cover the compaction process with variation of 20%, 33%, and 4% for relative density values 85%, 70%, and 60%, respectively. A unified approach is recommended to predict the compaction qc-performance line using normally consolidated condition and sand relative density.

Picture Fuzzy Relations over Picture Fuzzy Sets

Nowadays, picture fuzzy set theory is a flourishing field in mathematics with uncertainty by incorporating the concept of positive, negative and neutral membership degrees of an object. A traditional crisp relation represents the satisfaction or the dissatisfaction of relationship, connection or correspondence between the objects of two or more sets. However, there are some problems that can’t be solved through classical relationships, such as the relationship between two objects being vague. In those situations, picture fuzzy relation over picture fuzzy sets is an important and powerful concept which is suitable for describing correspondences between two vague objects. It represents the strength of association of the elements of picture fuzzy sets. It plays an important role in picture fuzzy modeling, inference and control system and also has important applications in relational databases, approximate reasoning, preference modeling, medical diagnosis, etc. In this article, we define picture fuzzy relations over picture fuzzy sets, including some other fundamental definitions with illustrations. The max-min and min-max compositions of picture fuzzy relations are defined in the light of picture fuzzy sets and discussed some properties related to them. The reflexivity, symmetry and transitivity of a picture fuzzy relation are described over a picture fuzzy set. Finally, various properties are explored related to the picture fuzzy relations over a picture fuzzy set.

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.