ELXED POINT THEOREM OF COMPOSITION g-CONTRACTION MAPPING AND ITS APPLICATIONS

Any composition sequential mapping, periodic composition mapping of a complete non-empty metric space M into M with geometric mean contraction ratio less than 1 ( simplifying as 'g-contraction mapping' ) has a unique fixed point in M . Applications of the theorem to the proof of existence and uniqueness of the solutions of a set of non-linear differential equations and a coupled integral equations of symmetric bending of shallow shell of revolution are given.

Landslides susceptibility mapping in Guizhou province based on fuzzy theory

The purpose of this study was to assess the susceptibility of landslides around the area of Guizhou province based on fuzzy theory.In first instance, slope, elevation, lithology, proximity to tectonic lines, proximity to drainage and annual precipitation were taken as independent, causal factors in this study.A landslide hazard evaluation factor system was established by classifying these factors into more subclasses according to some rules.Secondly, a trapezoidal fuzzy number weighting(TFNW) approach was used to assess the importance of six causal factors to landslides in an ArcGIS environment.Thirdly, a landslide susceptibility map was created based on a weighted linear combination model.According to this susceptibility map, the study area was classified into four categories of landslide susceptibility:low, moderate, high and very high.Finally, in order to verify the results obtained, the susceptibility map and the landslide inventory map were combined in the GIS.In addition, the weighting procedure showed that TFNW is an efficient method for weighting causal landslide factors.

Generalized contraction mapping principle in intuitionistic Menger spaces and application to differential equations

Using the idea of Atanassov, we define the notion of intuitionistic Menger spaces as a netural generalizations of Menger spaces due to Menger. We also obtain a new generalized contraction mapping and utilize this contraction mapping to prove the existance theorems of solutions to differential equations in intuitionistic Menger spaces.

Chinese Fuzzy Ontology Mapping Based on Support Vector Machine

Taking into account that fuzzy ontology mapping has wide application and cannot be dealt with in many fields at present,a Chinese fuzzy ontology model and a method for Chinese fuzzy ontology mapping are proposed.The mapping discovery between two ontologies is achieved by computing the similarity between the concepts of two ontologies.Every concept consists of four features of concept name,property,instance and structure.First,the algorithms of calculating four individual similarities corresponding to the four features are given.Secondly,the similarity vectors consisting of four weighted individual similarities are built,and the weights are the linear function of harmony and reliability.The similarity vector is used to represent the similarity relation between two concepts which belong to different fuzzy ontolgoies.Lastly,Support Vector Machine(SVM) is used to get the mapping concept pairs by the similarity vectors.Experiment results are satisfactory.

Some New Fixed Point Theorems for Fuzzy Iterated Contraction Maps in Fuzzy Metric Spaces

The purpose of this paper is to introduce the notion of fuzzy iterated contraction maps in fuzzy metric spaces and establish some new fixed point theorems for fuzzy iterated contraction maps in fuzzy metric spaces.

The Pointwise Characterizations of Fuzzy Mappings and Fuzzy Cardinal Numbers

In this paper,the pointwise characterizations of fuzzy mappings are given. Based of this definition,we give a few of new properties of fuzzy cardinal numbers.

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.

Common Fixed Point Theorems for Weakly Compatible Mappings in Fuzzy Metric Spaces Using (JCLR) Property

In this paper, we prove a common fixed point theorem for a pair of weakly compatible mappings in fuzzy metric space using the joint common limit in the range property of mappings called (JCLR) property. An example is also furnished which demonstrates the validity of main result. We also extend our main result to two finite families of self mappings. Our results improve and generalize results of Cho et al. [Y. J. Cho, S. Sedghi and N. Shobe, “Generalized fixed point theorems for compatible mappings with some types in fuzzy metric spaces,” Chaos, Solitons & Fractals, Vol. 39, No. 5, 2009, pp. 2233-2244.] and several known results existing in the literature.

FIXED POINT THEOREMS OF LOCAL CONTRACTION MAPPINGS ON MENGER SPACES

In this paper,we introduce the concept ofε-chainable PM-space,and give severalfixed point theorems of one-valued and multivalued local contraction mapping on the kindof spaces.

Manufacturing Oriented Fuzzy Function-Feature Mapping

The mechanism of the Concurrent Engineering(CE)and the methods of the manufacturing consultation are discussed. CE-oriented computer aided manufacture consulting methods are one of the key issues in concurrent design. The problems are settled in part function-feature mapping in concurrent design. The fuzzy set theory is applied to the function-feature mapping. A method for part function-feature mapping based on fuzzy theory is presented.

Some Fixed Point Theorems for Fuzzy Iterated Contraction Maps in Fuzzy Metric Spaces

In 1975, Kramosil and Michalek [1] first introduced the concept of a fuzzy metric space. In 1994, George and Veeramani [2] slightly modified the concept of fuzzy metric space introduced by Kramosil and Michalek, defined a Hausdorff topology and proved some known results. In 1969, Rheinboldt [3] initiated the study of iterated contraction. The concept of iterated contraction proves to be very useful in the study of certain iterative process and has wide applicability in metric spaces. In this paper we introduce the notion of fuzzy iterated contraction maps in fuzzy metric spaces and establish some fixed point theorems for fuzzy iterated contraction maps in fuzzy metric spaces.

B-vex Fuzzy Mappings and Its Application to Fuzzy Optimization Problems

The concept of b-vex and logarithmic b-vex for fuzzy mappings are introduced by relaxing the definition of convexity of a fuzzy mapping. Most of the basic properties of b-vex fuzzy mapping are discussed and established for the nondifferentiable case. Necessary and sufficient conditions for b-vex fuzzy mapping are presented. Sevaral important results are given for nonlinear fuzzy optimization problems assuming that the objective and constraint functions are b-vex fuzzy mappings.

Mapping the risk of winter storm damage using GIS-based fuzzy logic

Abiotic and biotic factors that cause damage to forest trees also threaten the sustainability of forest resources.Although winter storms can be one of the most damaging forces,very few studies have focused on winter storm damage in Turkey.To prevent or minimize storm damage,we must evaluate the factors that influence the degree of damage and develop storm risk maps for the forested areas.Here,a GIS-based mathematical model(fuzzy logic)was used to develop such a risk map by considering risk factors such as tree species,tree age,crown density,site quality,topographical features(elevation,slope,aspect),climatic variables(wind,precipitation),and soil depth.The Alabarda Forest Enterprise Chief within the borders of Tavs?anl?Forest Enterprise Directorate was selected as the study area due to high occurrence of storm damage in the region during winter 2015–2016.For model verification,the risk map of storm damage was compared to the actual areal distribution of storm damage reported by the Enterprise Directorate.The model based on fuzzy logic indicated that slightly more than half of the study area(52.49%)was under very low storm damage risk,28.12%was under low risk and 19.19%was classified as high risk.A very small portion of the total study area was classified as very high risk.These results indicated a close relation with the storm damage map generated using Tavsanl?FED records.The results revealed that the most effective risk predictors for overall storm damage risk were wind direction and speed,followed by slope and site quality factors.

Switching Regimes in Economics: The Contraction Mapping and the ω-Limit Set

This paper considers a dynamical system defined by a set of ordinary autonomous differential equations with discontinuous right-hand side. Such systems typically appear in economic modelling where there are two or more regimes with a switching between them. Switching between regimes may be a consequence of market forces or deliberately forced in form of policy implementation. Stiefenhofer and Giesl [1] introduce such a model. The purpose of this paper is to show that a metric function defined between two adjacent trajectories contracts in forward time leading to exponentially asymptotically stability of (non)smooth periodic orbits. Hence, we define a local contraction function and distribute it over the smooth and nonsmooth parts of the periodic orbits. The paper shows exponentially asymptotical stability of a periodic orbit using a contraction property of the distance function between two adjacent nonsmooth trajectories over the entire periodic orbit. Moreover it is shown that the ω-limit set of the (non)smooth periodic orbit for two adjacent initial conditions is the same.

FUZZY APPROACHING SET AND FUZZYAPPROACHING FUNCTIONAL MAPPING

By establishing the concepts of fuzzy approaching set and fuzzy approaching functional mapping and making research on them, a new method for time series prediction is introduced.

Dissipative Properties of ω-Order Preserving Partial Contraction Mapping in Semigroup of Linear Operator

This paper consists of dissipative properties and results of dissipation on infinitesimal generator of a C0-semigroup of ω-order preserving partial contraction mapping (ω-OCPn) in semigroup of linear operator. The purpose of this paper is to establish some dissipative properties on ω-OCPn which have been obtained in the various theorems (research results) and were proved.

Common Fixed Point Theorem in Intuitionistic Fuzzy Metric Space Using <i>R</i>-Weakly Commuting Mappings

In this paper, we prove a common fixed point theorem in Intuitionistic fuzzy metric space by using pointwise R-weak commutativity and reciprocal continuity of mappings satisfying contractive conditions.

Variational Inclusions for Fuzzy Mappings

In this paper,a perturbed iterative algorithm for finding approximate solutions of variational inclusions for fuzzy mapping,is presented and a convergence result which includes,as a special case,some known results in this field,is given.

Proximal point algorithm for a new class of fuzzy set-valued variational inclusions with (H,η)-monotone mappings

We introduced a new class of fuzzy set-valued variational inclusions with (H,η)-monotone mappings. Using the resolvent operator method in Hilbert spaces, we suggested a new proximal point algorithm for finding approximate solutions, which strongly converge to the exact solution of a fuzzy set-valued variational inclusion with (H,η)-monotone. The results improved and generalized the general quasi-variational inclusions with fuzzy set-valued mappings proposed by Jin and Tian Jin MM, Perturbed proximal point algorithm for general quasi-variational inclusions with fuzzy set-valued mappings, OR Transactions, 2005, 9(3): 31-38, (In Chinese); Tian YX, Generalized nonlinear implicit quasi-variational inclusions with fuzzy mappings, Computers & Mathematics with Applications, 2001, 42: 101-108.

Feasibility of Simultaneous Application of Fuzzy Neural Network and TOPSIS Integrated Method in Potential Mapping of Lead and Zinc Mineralization in Isfahan-Khomein Metallogeny Zone

Iran is located on a silver, lead, and zinc belt and according to the latest studies holds 11 million tons of lead, zinc, and silver stones which constitute 4 percent of global resources. Considering that mineral materials are explored in an uncertain space, exploration investment risk is an inseparable part of these activities. The important fact is to minimize the effect of this undesired factor in exploration. To achieve this, it is required that exploration activities and withdrawals are performed in a certain framework in which risk minimization is considered. Using mineral potential modelling for determining promising zones which should be taken into consideration in more detailed stages could make achieving the purpose possibly. This work is aimed at applying fuzzy neural network and TOPSIS methods simultaneously in order to explore zinc and lead resources. In this article, geological, telemetry, geophysics, and geochemistry data is integrated using fuzzy-neural network (neuro fuzzy) and using TOPSIS method rating for lead and zinc ore deposit potential mapping in Isfahan-Khomein strip which has been introduced as one of zinc and leads mineral scopes in Iran. This area which is composed of several zinc and lead ore deposits has been considered as the target area. Fuzzy integration results of zinc and lead mineralization witness layers confirm the relatively high potential of lead and zinc mineralization in this region having a northwest-southeast trend and involving more than 90 percent of the known indices and ore deposits of the region. In this research, it was shown that the results of TOPSIS-Neuro-Fuzzy integrated model (a combination of neural network and fuzzy logic) have increased the resolution of talented areas from the areas with no mineralization potential in comparison with the fuzzy method individually.