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.

Fuzzy topological relations between fuzzy spatial objects

Fuzziness is an internal property of spatial objects.How to model fuzziness of a spatial object is a main task of next generation GIS.This paper proposes basic fuzzy spatial object types based on fuzzy topology.These object types are the natural extension of current nonfuzzy spatial object types.A fuzzy cell complex structure is defined for modeling fuzzy regions,lines and points.Furthermore,fuzzy topological relations between these fuzzy spatial objects are formalized based on the 9intersection approach.This model can be implemented for GIS applications due to its scientific theory basis.

New approach to determine the priorities from interval fuzzy preference relations

An approach is proposed to solve the problem how to obtain the priorities from interval fuzzy preference relations. Firstly, another expression of interval numbers is given. Then, some basic definitions on consistency and weak transitivity of real and interval fuzzy preference relations are described. Based on these definitions, a two-phase process for determining the priorities from interval fuzzy preference relations is presented. Finally, two exam- ples are used to illustrate the use of the proposed approach.

Using Fuzzy Relations and GIS Method to Evaluate Debris Flow Hazard

The study area, located in the southeast of Tibet along the Sichuan-Tibet highway, is a part of Palongzangbu River basin where mountain hazards take place frequently. On the ground of field surveying, historical data and previous research, a total of 31 debris flow gullies are identified in the study area and 5 factors are chosen as main parameters for evaluating the hazard of debris flows in this study. Spatial analyst functions of geographic information system （GIS） are utilized to produce debris flow inventory and parameter maps. All data are built into a spatial database for evaluating debris flow hazard. Integrated with GIS techniques,the fuzzy relation method is used to calculate the strength of relationship between debris flow inventory and parameters of the database. With this methodology,a hazard map of debris flows is produced. According to this map,6.6% of the study area is classified as very high hazard, 7.3% as high hazard,8.4% as moderate hazard,32. 1% as low hazard and 45.6% as very low hazard or non-hazard areas. After validating the results, this methodology is ultimately confirmed to be available.

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.

A User-Transformer Relation Identification Method Based on QPSO and Kernel Fuzzy Clustering

User-transformer relations are significant to electric power marketing,power supply safety,and line loss calculations.To get accurate user-transformer relations,this paper proposes an identification method for user-transformer relations based on improved quantum particle swarm optimization(QPSO)and Fuzzy C-Means Clustering.The main idea is:as energymeters at different transformer areas exhibit different zero-crossing shift features,we classify the zero-crossing shift data from energy meters through Fuzzy C-Means Clustering and compare it with that at the transformer end to identify user-transformer relations.The proposed method contributes in three main ways.First,based on the fuzzy C-means clustering algorithm(FCM),the quantum particle swarm optimization(PSO)is introduced to optimize the FCM clustering center and kernel parameters.The optimized FCM algorithm can improve clustering accuracy and efficiency.Since easily falls into a local optimum,an improved PSO optimization algorithm(IQPSO)is proposed.Secondly,considering that traditional FCM cannot solve the linear inseparability problem,this article uses a FCM(KFCM)that introduces kernel functions.Combinedwith the IQPSOoptimization algorithm used in the previous step,the IQPSO-KFCM algorithm is proposed.Simulation experiments verify the superiority of the proposed method.Finally,the proposed method is applied to transformer detection.The proposed method determines the class members of transformers and meters in the actual transformer area,and obtains results consistent with actual user-transformer relations.This fully shows that the proposed method has practical application value.

Practical Method for Determining All the Minimum Solutions of Fuzzy Matrix Equation and Transitive Closure of Fuzzy Relation

In this paper,the new theory frame and practical method for determining all the minimum solutions of Fuzzy matrix equation and transitive closure of Fuzzy relation is described,and it has been carried out on the miero-computer quickly and accurately.

The Fuzzy Grey Relational Analysis of the Factors Influencing Farm Produce Logistics

The farm produce logistics plays an important role in promoting the agricultural production and prosperity of the rural economy,so grasping the main factors influencing the development of farm produce logistics,is of important significance to accelerating the development of farm produce logistics. The values of identification coefficient in the grey relational analysis are taken based on the experience,so the accuracy of the results is affected. This article uses the improved fuzzy grey relational analysis to analyze the main factors influencing farm produce logistics. The results show that the number of storage companies has a great impact on the development of farm produce logistics,followed by the farm produce processing machinery capacity,rural transport infrastructure,farm produce market conditions and government financial support for agriculture,while the total number of Internet users in rural areas has an limited impact on the development of farm produce logistics.

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.

Fuzzy Consistent Relation and Decision Making

This paper presents a kind of fuzzy consistent relation, discusses its main properties - center-division transitivity, describes its combined operation. At the same time, introduce the applications of fuzzy consistent relation in decision making.

Development of Granular Fuzzy Relation Equations Based on a Subset of Data

Developing and optimizing fuzzy relation equations are of great relevance in system modeling,which involves analysis of numerous fuzzy rules.As each rule varies with respect to its level of influence,it is advocated that the performance of a fuzzy relation equation is strongly related to a subset of fuzzy rules obtained by removing those without significant relevance.In this study,we establish a novel framework of developing granular fuzzy relation equations that concerns the determination of an optimal subset of fuzzy rules.The subset of rules is selected by maximizing their performance of the obtained solutions.The originality of this study is conducted in the following ways.Starting with developing granular fuzzy relation equations,an interval-valued fuzzy relation is determined based on the selected subset of fuzzy rules(the subset of rules is transformed to interval-valued fuzzy sets and subsequently the interval-valued fuzzy sets are utilized to form interval-valued fuzzy relations),which can be used to represent the fuzzy relation of the entire rule base with high performance and efficiency.Then,the particle swarm optimization(PSO)is implemented to solve a multi-objective optimization problem,in which not only an optimal subset of rules is selected but also a parameterεfor specifying a level of information granularity is determined.A series of experimental studies are performed to verify the feasibility of this framework and quantify its performance.A visible improvement of particle swarm optimization(about 78.56%of the encoding mechanism of particle swarm optimization,or 90.42%of particle swarm optimization with an exploration operator)is gained over the method conducted without using the particle swarm optimization algorithm.

Common New Fixed Point Theorem in Modified Intuitionistic Fuzzy Metric Spaces Using Implicit Relation

In this paper, we prove some common fixed point theorems for two pair of compatible and subsequentially continuous mappings satisfying an implicit relation in Modified Intuitionistic fuzzy metric spaces. Consequently, our results improve and sharpen many known common fixed point theorems available in the existing literature of metric fixed point theory.

Group Decision-Making Method with Incomplete Intuitionistic Fuzzy Preference Relations Based on a Generalized Multiplicative Consistent Concept

Based on the analyses of existing preference group decision-making(PGDM)methods with intuitionistic fuzzy preference relations(IFPRs),we present a new PGDM framework with incomplete IFPRs.A generalized multiplicative consistent for IFPRs is defined,and a mathematical programming model is constructed to supplement the missing values in incomplete IFPRs.Moreover,in this study,another mathematical programming model is constructed to improve the consistency level of unacceptably multiplicative consistent IFPRs.For group decisionmaking(GDM)with incomplete IFPRs,three reliable sources influencing the weights of experts are identified.Subsequently,a method for determining the weights of experts is developed by simultaneously considering three reliable sources.Furthermore,a targeted consensus process(CPR)is developed in this study with reference to the actual situation of the consensus level of each IFPR.Meanwhile,in response to the proposed multiplicative consistency definition,a novel method for determining the optimal priority weights of alternatives is redefined.Lastly,based on the above theory,a novel GDM method with incomplete IFPRs is developed,and the comparative and sensitivity analysis results demonstrate the utility and superiority of this work.

Research on the fuzzy relationship between the precursory anomalous elements and earthquake elements

This paper deals with the fuzzy information processing method in the research of the relationship between two variables or among multi-variables, with the undetermined or fuzzy features, different from that in the traditional statistical method. The reliability and effectiveness of the method have been tested and confirmed in the numerical simulation for a set of man-made data of precursory anomalous parameters and earthquake elements. Finally the relation between the actual monthly frequency of small earthquakes occurring in Huoshan, Anhui Province, China and the magnitude of future stronger earthquakes, as two variables, has been analyzed by the method. It seems to the authors that more reasonable and perfect results could be given with a quantitative analysis of accession degree in fuzzy mathematics by using this method than that of traditional statistical correlation analysis.

Fixed Point Theorems in Intuitionistics Fuzzy Metric Spaces Using Implicit Relations

In this paper, we proved some fixed point theorems in intuitionistic fuzzy metric spaces applying the properties of weakly compatible mapping and satisfying the concept of implicit relations for t norms and t connorms.

On the Relation Redundancy in Fuzzy Databases

This paper concentrates on the problem of data redundancy under the extended-possibility-based model. Based on the information gain in data classification, a measure - relation redundancy - is proposed to evaluate the degree of a given relation being redundant in whole. The properties of relation redundancy are also investigated. This new measure is useful in dealing with data redundancy.

Selection method of risk response schemes for mining project based on fuzzy preference relations

To overcome the subjectivity of experts in the process of risk response scheme selection, according to the theory of group decision making, a selection method and flow of the risk response schemes for a mining project was proposed based on fuzzy preference relation and consistency induced ordered weighted averaging (C-IOWA) operator,which can overcome the loss of information in the process of group decision making to a great degree, and improve its efficiency and quality.A numeric example was introduced to illustrate the application of the method, also validating the method as scientific and practicable.

Research on supplier evaluation and selection based on fuzzy hierarchy analysis and grey relational analysis

Considering the disadvantages of selecting evaluation index of supplier based on old purchase relation and in view of transformation of relation between manufacture and supplier under the dynamic, cooperative, competitive and quickly response environment, research on supplier selection evaluation was presented based on enterprise capability, cooperation degree and service level from the perspective of cooperative partnership and coordination, and the evaluation index system was established. A more objective and veracious supplier selection and evaluation method based on fuzzy analysis hierarchy process and grey relational analysis was developed, and then empirical research on electric equipment manufacturer was explored to analyze the supplier selection and evaluation.