Fuzzy Zero Research Articles

An optimization of the fully fuzzy transportation problem with triangular type-2 fuzzy parameters using novel ranking technique

This paper focuses on solving the fully fuzzy transportation problem in which the parameters are triangular Type-2 fuzzy numbers due to the instinctive of human imprecision. To deal with uncertainty more precisely, a triangular Type-1 fuzzy transportation problem is reformed as a transportation problem with triangular Type-2 fuzzy parameters in this paper. In order to compare triangular Type-2 fuzzy numbers, a new ranking(ordering) technique is proposed by extending the Yager’s function. However, two efficient algorithmic approaches namely, triangular Type-2 fuzzy zero suffix method (TT2FZSM) and triangular Type-2 fuzzy zero average method (TT2FZAM) are proposed to generate the initial transportation cost of the fully triangular Type-2 fuzzy transportation problem. Both TT2FZSM and TT2FZAM are converging towards an optimal solution. In addition to TT2FZSM and TT2FZAM, the modified distribution method is applied to ensure optimality. Subsequently, we carry out a comprehensive discussion of the obtained results to establish the validation of the proposed approach.

Stability analysis for delayed T-S fuzzy systems: A compensation Lyapunov–Krasovskii functional method combined with free-weighting matrices

A compensation Lyapunov–Krasovskii functional (LKF) method combined with free-weighting matrices is presented to analyze the stability of delayed Takagi–Sugeno fuzzy systems. Firstly, the fuzzy LKF containing membership functions is constructed. Then, the compensation LKF method is presented to introduce the common double and triple integral terms to compensate the single and double integral terms related to the membership functions’ derivatives, respectively, which arise in the derivative of the fuzzy LKF. Consequently, following the feature of the membership functions’ derivatives, the fuzzy zero equations containing free-weighting matrices of integral terms are proposed to improve the relaxation quality in fuzzy integral terms. Resultantly, the stability criteria with less conservativeness are yielded. Moreover, the conservatism is reduced further by establishing the relaxed fuzzy LKF. Finally, the numerical example is employed to verify the merits of the presented method.

Fractional derivatives of fuzzy complex-variable functions and application to fuzzy fractional complex differential equations

In this paper, through theory of fuzzy complex analysis, we introduce some representations of r-cuts of trivial fuzzy zero, nontrivial fuzzy zero and fuzzy complex numbers in polar form on complex plane and establish some of their basic properties. Based on this, the addition and scalar multiplication operations of fuzzy complex numbers are established and the calculus of fuzzy complex-variable functions is studied. Moreover, we introduce a notion of fuzzy Ortigueira fractional derivative of fuzzy complex-variable functions and develop a theory of fuzzy fractional calculus on complex plane including some geometric features. As applications, the existence and uniqueness theorem of solutions for nonlinear fuzzy fractional complex-variable differential equations is established and some examples are provided.

A New Fuzzy Propagation Model for Influence Maximization in Social Networks

In this paper we introduce a fuzzy propagation model to deal with the influence maximization (IM) problem. The IM problem for the most of existing propagation model is NP-hard. Here, we model social networks as fuzzy directed graphs to propose an application-oriented propagation process. To this aim, we investigate an interesting relationship between zero forcing set concept in graphs and IM problem in social networks. In spite of its attractive theory, its implementation is not efficient in the real world. Thus, we improve the fuzzy zero forcing set concept and suggest our fuzzy propagation model, simultaneously. Moreover, we present a polynomial time complexity algorithm to solve IM problems under the proposed propagation process. In particular, we consider a propagation parameter to control the size of the seed set and its coverage. Also, experimental results on some real world social networks show that the propagation model finds optimal and flexible seed set.

Introducing and solving the hesitant fuzzy system AX = B

Abstract In this paper the solution for hesitant fuzzy system as AX = B is introduced where A is an n × n known hesitant fuzzy matrix, B is an n × 1 known hesitant fuzzy vector and X is an n × 1 unknown hesitant fuzzy vector. First, L ∞-norm and L 1-norm of a hesitant fuzzy vector are introduced. Then, the concepts of hesitant fuzzy zero, ’almost equal’ and ’less than’ and ’equal’ are defined for two hesitant fuzzy numbers. Finally, using a minimization problem; the hesitant fuzzy system is solved. At the end, some numerical examples are presented to show the effectiveness of the proposed method.

Decomposition of fuzzy zero divisor graph

Let Γ(Zn ) be the zero-divisor graph whose vertices are the nonzero zero divisors of Zn , and such that two vertices u,υ are adjacent if n divides uυ. Let denotes the fuzzy complete graph on p − 1 vertices and let denote a fuzzy star with p − 1 edges. In this paper, we have analyzed the fuzzy zero divisor graph of Γf (Zp 3) is decomposition into 1-complete and p(p − 1) copies of star graph where p is prime number and p > 2.

A Characterization of Strong Completeness in Fuzzy Metric Spaces

Here, we deal with the concept of fuzzy metric space ( X , M , ∗ ) , due to George and Veeramani. Based on the fuzzy diameter for a subset of X , we introduce the notion of strong fuzzy diameter zero for a family of subsets. Then, we characterize nested sequences of subsets having strong fuzzy diameter zero using their fuzzy diameter. Examples of sequences of subsets which do or do not have strong fuzzy diameter zero are provided. Our main result is the following characterization: a fuzzy metric space is strongly complete if and only if every nested sequence of close subsets which has strong fuzzy diameter zero has a singleton intersection. Moreover, the standard fuzzy metric is studied as a particular case. Finally, this work points out a route of research in fuzzy fixed point theory.

Complete and star graph covers in fuzzy zero divisor graph

Complete and star graph covers in fuzzy zero divisor graph

Intuitionistic fuzzy zero point method for solving type-2 intuitionistic fuzzy transportation problem

In conventional transportation problem, supply, demand and costs are fixed crisp numbers. Therefore, in this situation, the decision maker (DM) can predict transportation cost exactly. On the contrary, in real world transportation problems the costs are in uncertain quantities with hesitation due to various factors like variation in rates of fuels, traffic jams, weather in hilly areas, etc. In such situations, the DM cannot predict transportation cost exactly and it will force the DM to hesitate. So, to counter these uncertainties, in this article, the author designed a transportation problem in which supplies, demands are crisp numbers and cost is intuitionistic fuzzy number. This type of problem is termed as type-2 intuitionistic fuzzy transportation problem (type-2 IFTP). Hence to deal with uncertainty and hesitation in transportation problem, intuitionistic fuzzy zero point method is proposed to find out optimal solution to the type-2 IFTP. Moreover, special kind of type-2 IFTP is proposed and its related theorems are proved. Finally, the ideas of the proposed method are illustrated with the help of numerical example which is followed by the results and discussion.

Zero forcing number of fuzzy graphs with application

We introduce and study forcing number for fuzzy graphs. Also, we compute zero forcing numbers for some classes of graphs and extend this concept to fuzzy graphs. In this regard we obtain upper bounds for zero forcing of some classes of fuzzy graphs. We will proceed to obtain a new algorithm to computing zero forcing set and finding a formula for zero forcing number, and by some examples we illustrate these notions. Finally, we introduce some applications of fuzzy zero forcing in medical treatments.

Intuitionistic fuzzy zero point method for solving type-2 intuitionistic fuzzy transportation problem

Intuitionistic fuzzy zero point method for solving type-2 intuitionistic fuzzy transportation problem

English

English

A note on 'a new approach for solving intuitionistic fuzzy transportation problem of type-2'

In real-life decisions, usually we happen to suffer through different states of uncertainties. In order to counter these uncertainties, in this paper, the author formulated a transportation problem in which costs are triangular intuitionistic fuzzy numbers, supplies and demands are crisp numbers. In this paper, a simple method for solving type-2 intuitionistic fuzzy transportation problem (type-2 IFTP) is proposed and optimal solution is obtained without using intuitionistic fuzzy modified distribution method and intuitionistic fuzzy zero point method. So, the proposed method gives the optimal solution directly. The solution procedure is illustrated with the help of three real life numerical examples. Defect of existing results proposed by Singh and Yadav (2016a) is discussed. Validity of Pandian's (2014) method is reviewed. Finally, the comparative study, results and discussion are given.

A SYSTEMATIC APPROACH FOR SOLVING MIXED INTUITIONISTIC FUZZY TRANSPORTATION PROBLEMS

In this paper, we formulate a transportation problem in which supplies, demands and costs are different types of real, fuzzy and intuitionistic fuzzy numbers. The new multiplication operations of triangular intuitionistic fuzzy numbers are employed to get the optimal solution. Mixed Intuitionistic fuzzy zero point method is proposed to find the optimal solution in terms of triangular intuitionistic fuzzy numbers. The proposed method is easy to understand and to apply for finding the intuitionistic fuzzy optimal solution in a mixed intuitionistic fuzzy transportation problem. The method is illustrated by a numerical example. AMS Subject Classification: 03E72, 03F55, 90B06

Evaluation of fully fuzzy matrix equations by fuzzy neural network

In this paper, a new hybrid method based on fuzzy neural network for approximate solution of fully fuzzy matrix equations of the form AX=D, where A and D are two fuzzy number matrices and the unknown matrix X is a fuzzy number matrix, is presented. Then, we propose some definitions which are fuzzy zero number, fuzzy one number and fuzzy identity matrix. Based on these definitions, direct computation of fuzzy inverse matrix is done using fuzzy matrix equations and fuzzy neural network. It is noted that the uniqueness of the calculated fuzzy inverse matrix is not guaranteed. Here a neural network is considered as a part of a large field called neural computing or soft computing. Moreover, in order to find the approximate solution of fuzzy matrix equations that supposedly has a unique fuzzy solution, a simple algorithm from the cost function of the fuzzy neural network is proposed. To illustrate the easy application of the proposed method, numerical examples are given and the obtained results are discussed.

Amplification of the STOML3, FREM2, and LHFP Genes Is Associated with Mesenchymal Differentiation in Gliosarcoma

Gliosarcoma is a rare glioblastoma variant characterized by a biphasic tissue pattern with alternating areas that display either glial (glial fibrillary acidic protein-positive) or mesenchymal (reticulin-positive) differentiation. Previous analyses have shown identical genetic alterations in glial and mesenchymal tumor areas, suggesting that gliosarcomas are genetically monoclonal, and mesenchymal differentiation was considered to reflect the elevated genomic instability of glioblastomas. In the present study, we compared genome-wide chromosomal imbalances using array comparative genomic hybridization in glial and mesenchymal tumor areas of 13 gliosarcomas. The patterns of gain and loss were similar, except that the gain at 13q13.3-q14.1 (log(2) ratio >3.0), containing the STOML3, FREM2, and LHFP genes, which was restricted to the mesenchymal tumor area of a gliosarcoma. Further analyses of 64 cases of gliosarcoma using quantitative PCR showed amplification of the STOML3, FREM2, and LHFP genes in 14 (22%), 10 (16%), and 7 (11%) mesenchymal tumor areas, respectively, but not in glial tumor areas. Results of IHC analysis confirmed that overexpression of STOML3 and FREM2 was more extensive in mesenchymal than in glial tumor areas. These results suggest that the mesenchymal components in a small fraction of gliosarcomas may be derived from glial cells with additional genetic alterations.

Calculating fuzzy inverse matrix using fuzzy linear equation system

Linear equation systems play a very important role in engineering, mathematics, statistics and other disciplines. Fuzzifying either parameters or variables or both in these systems has been one of the research areas in the fuzzy literature since these kinds of systems are encountered in many applications. These systems are generally called fuzzy linear equations. Various types of these models have been examined for a decade. The solution procedures of these systems depend on different methods such as extension principle and interval arithmetic. Also, the method which is often used in computing inverse of a matrix in real case could be extended to fuzzy case, which employs linear equation system and identity matrix. For this purpose, we propose a new method which includes some new definitions which are fuzzy zero number, fuzzy one number and fuzzy identity matrix. Based on these definitions, direct computation of fuzzy inverse matrix is done using fuzzy arithmetic and fuzzy equation system. Actually, this simply extends the notion used in real case to fuzzy case. Calculation is realized with two different settings. While the first one is called direct numerical solution, the other is obtained by choice of decision maker. It is noted that the uniqueness of the calculated fuzzy inverse matrix is not guaranteed.

On the approximation of compact fuzzy sets

This paper suggests an approximation for a compact fuzzy set by a sequence of Lipschitz fuzzy sets. This approximation method involves the construction of Lipschitz fuzzy sets using the sup–min convolution of a compact fuzzy set with a fuzzy zero. Considering a similar procedure, we present the approximation of a trapezoidal type fuzzy interval by a sequence of differentiable fuzzy intervals. We show some important properties of both approximations and we give some numerical examples illustrating the results.

Fuzzy position control of hydraulic robots with valve deadbands

The development of a real-time fuzzy-logic controller for a class of industrial hydraulic robots is described. The main element of the controller is a PD-type fuzzy control technique which utilizes a simple set of membership functions and rules to meet the basic control requirements of such robots. The controller, although effective, is shown to produce steady-state errors. The steady-state error in a step input response is mainly due to the hydraulic valve deadband in which the control action is not effective. The steady-state position error in a ramp input response is due to both valve deadband and the nature of the controller, since zero position and velocity errors would result in the controller closing the valve and stopping the motion. Conceptually simple actions are then identified to be applied in parallel with the above PD-type fuzzy controller in order to eliminate the steady-state errors. In particular, two methods are developed. In one method, a control term proportional to the integral of the error is calculated and added to the output from the main controller. In the second method, the control measure of the steady-state error obtained from the PD-type fuzzy controller is used as an offset. Both actions are activated only in the region of fuzzy zero velocity error. The performances of the techniques developed in this paper are evaluated experimentally. The experiments are performed on an instrumented Unimate MK-II industrial hydraulic robot which has been retrofitted as a research robot.