FUZZY ARITHMETIC AND SOLVING OF THE STATIC GOVERNING EQUATIONS OF FUZZY FINITE ELEMENT METHOD

The key component of finite element analysis of structures with fuzzy parameters, which is associated with handling of some fuzzy information and arithmetic relation of fuzzy variables, was the solving of the governing equations of fuzzy finite element method. Based on a given interval representation of fuzzy numbers, some arithmetic rules of fuzzy numbers and fuzzy variables were developed in terms of the properties of interval arithmetic. According to the rules and by the theory of interval finite element method, procedures for solving the static governing equations of fuzzy finite element method of structures were presented. By the proposed procedure, the possibility distributions of responses of fuzzy structures can be generated in terms of the membership functions of the input fuzzy numbers. It is shown by a numerical example that the computational burden of the presented procedures is low and easy to implement. The effectiveness and usefulness of the presented procedures are also illustrated.

Lanchester equation for cognitive domain using hesitant fuzzy linguistic terms sets

Intelligent wars can take place not only in the physical domain and information domain but also in the cognitive domain.The cognitive domain will become the key domain to win in the future intelligent war.A Lanchester equation considering cognitive domain is proposed to fit the development tendency intelligent wars in this paper.One party is considered to obtain the exponential enhancement advantage on combat forces in combat if it can gain an advantage in the cognitive domain over the other party according to the systemic advantage function.The operational effectiveness of the cognitive domain in war is considered to consist of a series of indicators.Hesitant fuzzy sets and linguistic term sets are powerful tools when evaluating indicators,hence the indicators are scored by experts using hesitant fuzzy linguistic terms sets here.A unique hesitant fuzzy hybrid arithmetical averaging operator is used to aggregate the evaluation.

Group Decision-Making Model of Renal Cancer Surgery Options Using Entropy Fuzzy Element Aczel-Alsina Weighted Aggregation Operators under the Environment of Fuzzy Multi-Sets

Since existing selection methods of surgical treatment schemes of renal cancer patients mainly depend on physicians’clinical experience and judgments,the surgical treatment options of renal cancer patients lack their scientifical and reasonable information expression and group decision-making model for renal cancer patients.Fuzzy multi-sets(FMSs)have a number of properties,which make them suitable for expressing the uncertain information of medical diagnoses and treatments in group decision-making(GDM)problems.To choose the most appropriate surgical treatment scheme for a patient with localized renal cell carcinoma(RCC)(T1 stage kidney tumor),this article needs to develop an effective GDM model based on the fuzzy multivalued evaluation information of the renal cancer patients.First,we propose a conversionmethod of transforming FMSs into entropy fuzzy sets(EFSs)based on the mean and Shannon entropy of a fuzzy sequence in FMS to reasonably simplify the information expression and operations of FMSs and define the score function of an entropy fuzzy element(EFE)for ranking EFEs.Second,we present the Aczel-Alsina t-norm and t-conorm operations of EFEs and the EFE Aczel-Alsina weighted arithmetic averaging(EFEAAWAA)and EFE Aczel-Alsina weighted geometric averaging(EFEAAWGA)operators.Third,we develop a multicriteria GDM model of renal cancer surgery options in the setting of FMSs.Finally,the proposed GDM model is applied to two clinical cases of renal cancer patients to choose the best surgical treatment scheme for a renal cancer patient in the setting of FMSs.The selected results of two clinical cases verify the efficiency and rationality of the proposed GDM model in the setting of FMSs.

A novel fuzzy neural network and its approximation capability

The polygonal fuzzy numbers are employed to define a new fuzzy arithmetic. A novel ex-tension principle is also introduced for the increasing function σ:R→R. Thus it is convenient to con-struct a fuzzy neural network model with succinct learning algorithms. Such a system possesses some universal approximation capabilities, that is, the corresponding three layer feedforward fuzzy neural networks can be universal approximators to the continuously increasing fuzzy functions.

A Temporally Piecewise Adaptive Scaled Boundary Finite Element Method for Solving the Fuzzy Uncertain Viscoelastic Problems

The numerical solutions for uncertain viscoelastic problems have important theo- retical and practical significance. The paper develops a new approach by combining the scaled boundary finite element method （SBFEM） and fuzzy arithmetic. For the viscoelastic problems with zero uncertainty, the SBFEM and the temporally piecewise adaptive algorithm is employed in the space domain and the time domain, respectively, in order to provide an accurate semi- analytical boundary-based approach and to ensure the accuracy of discretization in the time domain with different sizes of time step at the same time. The fuzzy arithmetic is used to address the uncertainty analysis of viscoelastic material parameters, and the transformation method is used for computation with the advantages of effectively avoiding overestimation and reducing the computational costs. Numerical examples are provided to test the performance of the proposed method. By comparing with the analytical solutions and the Monte Carlo method, satisfactory results are achieved.

Fully fuzzy linear systems of triangular fuzzy numbers(a,b,c)

Purpose–The purpose of this paper is to study a nascent theory and an emerging concept of solving a fully fuzzy linear system(FFLS)with no non negative restrictions on the triangular fuzzy numbers chosen as parameters.Two new simplified computational methods are proposed to solve a FFLS without any sign restrictions.The first method eliminates the non-negativity constraint from the coefficient matrix while the second method eliminates the constraint of non-negativity on the solution vector.The methods are introduced with an objective to broaden the domain of fuzzy linear systems to encompass a wide range of problems occurring in reality.Design/methodology/approach–The design of numerical methods is motivated by decomposing the fuzzy based linear system into its equivalent crisp linear form which can be further solved by variety of classical methods to solve a crisp linear system.Further the paper investigates Schur complement technique to solve the crisp equivalent of the FFLS.Findings–The results that are obtained reveal interesting properties of a FFLS.By using the proposed methods,the authors are able to check the consistency of the fuzzy linear system as well as obtain the nature of obtained solutions,i.e.trivial,unique or infinite.Further it is also seen that an n£n FFLS may yield finitely many solutions which may not be entirely feasible(strong).Also the methods successfully remove the non-negativity restriction on the coefficient matrix and the solution vector,respectively.Research limitations/implications–Evolving methods with better computational complexity and that which remove the non-negativity restriction jointly on all the parameters are left as an open problem.Originality/value–The proposed methods are new and conceptually simple to understand and apply in several scientific areas where fuzziness persists.The methods successfully remove several constraints that have been employed exhaustively by researchers and thus eventually tend to widen the breadth of applicability and usability of fuzzy linear models in real life situations.Heretofore,the usability of FFLS is largely dormant.

Research on Similarity Assessment Method of Case-based Reasoning

This paper mainly studies case representation based on fuzzy technology, the comparing framework of case properties and the method of similarity assessment. Firstly, this paper proposes the method of case representation based on fuzzy technology. Secondly, it discusses the comparing framework of case fuzzy properties. Thirdly, it presents the case representation framework composed of structure data and related properties and b＇ased on which it studies the method and step of gaining case similarity assessment through adjusting similarity value of a property. This paper proposes a similarity assessment method in comparing stage of CBR using fuzzy technology. This method not only simples the computing complexity of CBR in comparing stage but also resolves the difficulties of similarity assessment on different levels.