MULTI-GRAY EDGE DETECTION BASED ON GENERALIZED FUZZY SET

In this letter, drawbacks of the classical algorithm to enhance the fuzzy contrast among adjacent regions are analyzed. Based on it, a new fuzzy enhancement algorithm and a linear fuzzy distribution that maps the gray images to corresponding generalized fuzzy set are proposed. Results of two examples illustrate that the algorithm is more effective and faster when used to detect the multi-level edges of images.

Fuzzy Adaptive Tracking Control of Uncertain Strict-Feedback Nonlinear Systems with Disturbances Based on Generalized Fuzzy Hyperbolic Model

In this paper, a fuzzy adaptive tracking control for uncertain strict-feedback nonlinear systems with unknown bounded disturbances is proposed. The generalized fuzzy hyperbolic model (GFHM) with better approximation performance is used to approximate the unknown nonlinear function in the system. The dynamic surface control (DSC) is used to design the controller, which not only avoids the “explosion of complexity” problem in the process of repeated derivation, but also makes the control system simpler in structure and lower in computational cost because only one adaptive law is designed in the controller design process. Through the Lyapunov stability analysis, all signals in the closed loop system designed in this paper are semi-globally uniformly ultimately bounded (SGUUB). Finally, the effectiveness of the method is verified by a simulation example.

A New Kind of Generalized Pythagorean Fuzzy Soft Set and Its Application in Decision-Making

The aim of this paper is to introduce the concept of a generalized Pythagorean fuzzy soft set(GPFSS),which is a combination of the generalized fuzzy soft sets and Pythagorean fuzzy sets.Several of important operations of GPFSS including complement,restricted union,and extended intersection are discussed.The basic properties of GPFSS are presented.Further,an algorithm of GPFSSs is given to solve the fuzzy soft decision-making.Finally,a comparative analysis between the GPFSS approach and some existing approaches is provided to show their reliability over them.

Arithmetic Operations of Generalized Trapezoidal Picture Fuzzy Numbers by Vertex Method

In this article, we define the arithmetic operations of generalized trapezoidal picture fuzzy numbers by vertex method which is assembled on a combination of the (α, γ, β)-cut concept and standard interval analysis. Various related properties are explored. Finally, some computations of picture fuzzy functions over generalized picture fuzzy variables are illustrated by using our proposed technique.

Minimum Cross Fuzzy Entropy Problem, The Existence of Its Solution and Generalized Minimum Cross Fuzzy Entropy Problems

In the present study we have formulated a Minimum Cross Fuzzy Entropy Problem （Minx（F）EntP） and proposed sufficient conditions for existence of its solution. Mentioned problem can be formulated as follows. In the set of membership functions satisfying the given moment constraints generated by given moment functions it is required to choose the membership function that is closest to a priori membership function in the sense of cross fuzzy entropy measure. The existence of solution of formulated problem is proved by virtue of concavity property of cross fuzzy entropy measure, the implicit function theorem and Lagrange multipliers method. Moreover, Generalized Cross Fuzzy Entropy Optimization Methods in the form of MinMinx（F）EntM and MaxMinx（F）EntM are suggested on the basis of primary phase of minimizing cross fuzzy entropy measure for fixed moment vector function and on the definition of the special functional with Minx（F）Ent values of cross fuzzy entropy measure. Next phase for obtaining mentioned distributions consists of optimization of defined functional with respect to moment vector functions. Distributions obtained by mentioned methods are defined as （MinMinx（F）Ent）m and （MaxMinx（F）Ent）m distributions.

The Well-Posedness for Generalized Fuzzy Games

This paper establishes the stable results for generalized fuzzy games by using a nonlinear scalarization technique. The authors introduce some concepts of well-posedness for generalized fuzzy games. Moreover, the authors identify a class of generalized fuzzy games such that every element of the collection is generalized well-posed, and there exists a dense residual subset of the collection, where every generalized fuzzy game is robust well-posed.

Category of Generalized Intuitionistic Fuzzy Sets

In this paper, category GIFS of generalized intuitionistic fuzzy sets(GIF) is built up. Topoi properties of category GIFS are studied. Firstly, it is proved that the category GIFS has all topoi properties except that it has no subobject classifiers, Secondly, it is proved that the category GIFS has middle object and consequently GIFS is a weak topos. Thirdly, by the use of theory of weak topos GIFS, the power object of an object in GIFS is studied.

Minimization of Fuzzy Finite Generalized Automata

Some concepts in Fuzzy Generalized Automata （FGA） are established. Then an important new algorithm which would calculate the minimal FGA is given. The new algorithm is composed of two parts： the first is called E-reduction which contracts equivalent states, and the second is called RE-reduction which removes retrievable states. Finally an example is given to illuminate the algorithm of minimization.

Minimum Cycle of Row Vector of a Generalized Circulant Fuzzy Matrix

In this paper,we intreduce the concept and discuss the properties of minimum cycle of row vector in a generalized circulant Fuzzy matrix. We present a new expression for circulant Fuzzy matrix,and discuss some properties of the idempotent elements of the semigroup of generalized circulant Fuzzy matrixes in connection with minimum cycle of row vector.

Algorithm of solutions for generalized nonlinear implicit quasivariational inclusions with fuzzy mappings

A class of generalized implicit quasivariational inclusions with fuzzy mappings in Hilbert space is discussed in this paper which proves an existence theorem of the solutions and proposes a new iterative algorithm and the convergence of the iterative sequence generated by the new algorithm. These results extend and improve some recent corresponding achievements.

Generalized Maximum Fuzzy Entropy Methods with Applications on Wind Speed Data

This study is connected with new Generalized Maximum Fuzzy Entropy Methods （GMax（F）EntM） in the form of MinMax（F）EntM and MaxMax（F）EntM belonging to us. These methods are based on primary maximizing Max（F）Ent measure for fixed moment vector function in order to obtain the special functional with maximum values of Max（F）Ent measure and secondary optimization of mentioned functional with respect to moment vector functions. Distributions, in other words sets of successive values of estimated membership function closest to （furthest from） the given membership function in the sense of Max（F）Ent measure, obtained by mentioned methods are defined as （MinMax（F）Ent）m which is closest to a given membership function and （MaxMax（F）Ent）m which is furthest from a given membership function. The aim of this study consists of applying MinMax（F）EntM and MaxMax（F）EntM on given wind speed data. Obtained results are realized by using MATLAB programme. The performances of distributions （MinMax（F）En0m and （MaxMax（F）Ent）m generated by using Generalized Maximum Fuzzy Entropy Methods are established by Chi-Square, Root Mean Square Error criterias and Max（F）Ent measure.

Robust adaptive fuzzy control scheme for nonlinear system with uncertainty

In this paper, a robust adaptive fuzzy control scheme for a class of nonlinear system with uncertainty is proposed. First, using prior knowledge about the plant we obtain a fuzzy model, which is called the generalized fuzzy hyperbolic model （GFHM）. Secondly, for the case that the states of the system are not available an observer is designed and a robust adaptive fuzzy output feedback control scheme is developed. The overall control system guarantees that the tracking error converges to a small neighborhood of origin and that all signals involved are uniformly bounded. The main advantages of the proposed control scheme are that the human knowledge about the plant under control can be used to design the controller and only one parameter in the adaptive mechanism needs to be on-line adjusted.

A New Hesitant Fuzzy Multiple Attribute Decision Making Method with Unknown Weight Information

In this paper, we focus on a new approach based on new generalized hesitant fuzzy hybrid weighted aggregation operators, in which the evaluation information provided by decision makers is expressed in hesitant fuzzy elements (HFEs) and the information about attribute weights and aggregation-associated vector is unknown. More explicitly, some new generalized hesitant fuzzy hybrid weighted aggregation operators are proposed, such as the new generalized hesitant fuzzy hybrid weighted averaging (NGHFHWA) operator and the new generalized hesitant fuzzy hybrid weighted geometric (NGHFHWG) operator. Some desirable properties and the relationships between them are discussed. Then, a new algorithm for hesitant fuzzy multi-attribute decision making (HF-MADM) problems with unknown weight information is introduced. Further, a practical example is used to illustrate the detailed implementation process of the proposed approach. A sensitivity analysis of the decision results is analyzed with different parameters. Finally, comparative studies are given to verify the advantages of our method.

NEW METHOD FOR MEASURING FUZZINESS IN ROUGH SETS

A method with the fuzzy entropy for measuring fuzziness to fuzzy problem in rough sets is proposed. A new sort of the fuzzy entropy is given. The calculating formula and the equivalent expression method with the fuzzy entropy in rough sets based on equivalence relation are provided, and the properties of the fuzzy entropy are proved. The fuzzy entropy based on equivalent relation is extended to generalize the fuzzy entropy based on general binary relation, and the calculating formula and the equivalent expression of the generalized fuzzy entropy are also given. Finally, an example illustrates the way for getting the fuzzy entropy. Results show that the fuzzy entropy can conveniently measure the fuzziness in rough sets.

DETERMINGING BPA UNDER UNCERTAINTY ENVIRONMENTS AND ITS APPLICATION IN DATA FUSION

Dempster-Shafer (DS) theory of evidence has been widely used in many data fusion ap- plication systems. However, how to determine basic probability assignment, which is the main and the first step in evidence theory, is still an open issue. In this paper, a new method to obtain Basic Probability Assignment (BPA) is proposed based on the similarity measure between generalized fuzzy numbers. In the proposed method, species model can be constructed by determination of the min, average and max value to construct a fuzzy number. Then, a new Radius Of Gravity (ROG) method to determine the similarity measure between generalized fuzzy numbers is used to calculate the BPA functions of each instance. Finally, the efficiency of the proposed method is illustrated by the classi- fication of Iris data.

A Novel Unsupervised Change Detection Method with Structure Consistency and GFLICM Based on UAV Images

With the rapid development of Unmanned Aerial Vehicle(UAV)technology,change detection methods based on UAV images have been extensively studied.However,the imaging of UAV sensors is susceptible to environmental interference,which leads to great differences of same object between UAV images.Overcoming the discrepancy difference between UAV images is crucial to improving the accuracy of change detection.To address this issue,a novel unsupervised change detection method based on structural consistency and the Generalized Fuzzy Local Information C-means Clustering Model(GFLICM)was proposed in this study.Within this method,the establishment of a graph-based structural consistency measure allowed for the detection of change information by comparing structure similarity between UAV images.The local variation coefficient was introduced and a new fuzzy factor was reconstructed,after which the GFLICM algorithm was used to analyze difference images.Finally,change detection results were analyzed qualitatively and quantitatively.To measure the feasibility and robustness of the proposed method,experiments were conducted using two data sets from the cities of Yangzhou and Nanjing.The experimental results show that the proposed method can improve the overall accuracy of change detection and reduce the false alarm rate when compared with other state-of-the-art change detection methods.

A MULTI-ATTRIBUTE LARGE GROUP EMERGENCY DECISION MAKING METHOD BASED ON GROUP PREFERENCE CONSISTENCY OF GENERALIZED INTERVAL-VALUED TRAPEZOIDAL FUZZY NUMBERS

In this paper, a new decision making approach is proposed for the multi-attribute large group emergency decision-making problem that attribute weights are unknown and expert preference information is expressed by generalized interval-valued trapezoidal fuzzy numbers （GITFNs）. Firstly, a degree of similarity formula between GITFNs is presented. Secondly, expert preference information on different alternatives is clustered into several aggregations via the fuzzy clustering method. As the clustering proceeds, an index of group preference consistency is introduced to ensure the clustering effect, and then the group preference information on different alternatives is obtained. Thirdly, the TOPSIS method is used to rank the alternatives. Finally, an example is taken to show the feasibility and effectiveness of this approach. These method can ensure the consistency degree of group preference, thus decision efficiency of emergency response activities can be improved.

Some Characterizations of Left Weakly Regular Ordered Semigroups

In this paper, the notion of left weakly regular ordered semigroups is introduced. Furthermore, left weakly regular ordered semigroups are characterized by the properties of their left ideals, right ideals and （generalized） bi-ideals, and also by the properties of their fuzzy left ideals, fuzzy right ideals and fuzzy （generalized） bi-ideals.

GENERALIZED INTUITIONISTIC FUZZY HYBRID CHOQUET AVERAGING OPERATORS

In this study a new hybrid aggregation operator named as the generalized intuitionistic fuzzy hybrid Choquet averaging（GIFHCA） operator is defined.Meantime,some desirable properties are studied, and several important cases are examined.Furthermore,we define the generalized Shapley GIFHCA （GS-GIFHCA） operator,which does not only overall consider the importance of elements and their ordered positions,but also globally reflect the correlations among them and their ordered positions.In order to simplify the complexity of solving a fuzzy measure,we further define the generalizedλ-Shapley GIFHCA（GλS-GIFHCA） operator.

Breakable Fuzzy Multi-stage Transportation Problem

In this paper,we investigate two new transportation models with breakability and restriction on transportation.Sometime in transportation process the items which are transported,have got damaged due to bad conditions of the road and vehicle.Here we consider the problem that there are so many plants and customers and the goods are transported in n-stages.We formulate two transportationmodels under crisp and fuzzy environment where we consider the transportation parameters are crisp and fuzzy in nature,respectively.We also consider the breakability(takes the deterministic value for the respectivemodels)at each stages.For the fuzzy model,generalized triangular fuzzy number and mean ofα-cut method are considered.Numerical illustration is provided to illustrate the developed models.