An Evaluation Model of Graduation Thesis Results Based on Triangular Fuzzy Number

The evaluation of thesis by undergraduate has the characteristics of multi-factor, multi-layer and easy to be affected by subjective factors. To reduce the subjectivity, triangular fuzzy number is used as index set to give weight, and on this basis, fuzzy comprehensive evaluation is used to evaluate the quality of graduation thesis. The empirical analysis shows that the combination of triangular fuzzy number and fuzzy comprehensive evaluation has certain practical value in the quality evaluation of graduation thesis.

Obtaining Crisp Priorities for Triangular and Trapezoidal Fuzzy Judgments

This paper proposes anoptimal fuzzy-based model for obtaining crisp priorities for Fuzzy-AHP comparison matrices.Crisp judgments cannot be given for real-life situations,as most of these include some level of fuzziness and com-plexity.In these situations,judgments are represented by the set of fuzzy numbers.Most of the fuzzy optimization models derive crisp priorities for judgments repre-sented with Triangular Fuzzy Numbers(TFNs)only.They do not work for other types of Triangular Shaped Fuzzy Numbers(TSFNs)and Trapezoidal Fuzzy Numbers(TrFNs).To overcome this problem,a sum of squared error(SSE)based optimization model is proposed.Unlike some other methods,the proposed model derives crisp weights from all of the above-mentioned fuzzy judgments.A fuzzy number is simulated using the Monte Carlo method.A threshold-based constraint is also applied to minimize the deviation from the initial judgments.Genetic Algorithm(GA)is used to solve the optimization model.We have also conducted casestudiesto show the proposed approach’s advantages over the existingmethods.Results show that the proposed model outperforms other models to minimize SSE and deviation from initial judgments.Thus,the proposed model can be applied in various real time scenarios as it can reduce the SSE value upto 29%compared to the existing studies.

Application of Nonlinear Triangular Fuzzy Fault Tree Algorithm in Predicting Lithium Battery Air Transport Accidents

The traditional triangular fuzzy fault tree prediction model adopts the linear approximation method.Therefore,the accident prediction error is large.Based on the analysis of the error sources and the fuzzy set,the precise calculation method of the event at the top of the fault tree is given.By using the numerical calculation software,an accurate calculation method of nonlinear triangular fuzzy accident prediction was adopted to predict lithium battery air transport fire accidents,and the fuzzy importance of the cause event was calculated.

New Methods to Solve Fuzzy Shortest Path Problems

This paper discusses the problem of finding a shortest path from a fixed origin s to a specified node t in a network with arcs represented as typical triangular fuzzy numbers (TFN). Because of the characteristic of TFNs, the length of any path p from s to t , which equals the extended sum of all arcs belonging to p , is also TFN. Therefore, the fuzzy shortest path problem (FSPP) becomes to select the smallest among all those TFNs corresponding to different paths from s to t (specifically, the smallest TFN represents the shortest path). Based on Adamo's method for ranking fuzzy number, the pessimistic method and its extensions - optimistic method and λ combination method, are presented, and the FSPP is finally converted into the crisp shortest path problems.

Method based on fuzzy linguistic scale and FIOWGA operator for decision-making problems

In this paper, we present a fuzzy linguistic scale, which is characterized by triangular fuzzy numbers on [1/9, 9], for the comparison between two alternatives, and introduce a possibility degree formula for comparing triangular fuzzy numbers. We utilize the fuzzy linguistic scale to construct a linguistic preference matrix, and propose a fuzzy induced ordered weighted geometric averaging (FIOWGA) operator to aggregate linguistic preference information. A method based on the fuzzy linguistic scale and FIOWGA operator for decision-making problems is presented. Finally, an illustrative example is given to verify the developed method and to demonstrate its feasibility and effectiveness.

Alternative Method of Constructing Granular Neural Networks

Utilizing granular computing to enhance artificial neural network architecture, a newtype of network emerges—thegranular neural network (GNN). GNNs offer distinct advantages over their traditional counterparts: The ability toprocess both numerical and granular data, leading to improved interpretability. This paper proposes a novel designmethod for constructing GNNs, drawing inspiration from existing interval-valued neural networks built uponNNNs. However, unlike the proposed algorithm in this work, which employs interval values or triangular fuzzynumbers for connections, existing methods rely on a pre-defined numerical network. This new method utilizesa uniform distribution of information granularity to granulate connections with unknown parameters, resultingin independent GNN structures. To quantify the granularity output of the network, the product of two commonperformance indices is adopted: The coverage of numerical data and the specificity of information granules.Optimizing this combined performance index helps determine the optimal parameters for the network. Finally,the paper presents the complete model construction and validates its feasibility through experiments on datasetsfrom the UCIMachine Learning Repository. The results demonstrate the proposed algorithm’s effectiveness andpromising performance.

Extension of TOPSIS for fuzzy multi-attribute decision making problem based on experimental analysis

This paper is concerned with a technique for order performance by similarity to ideal solution（TOPSIS） method for fuzzy multi-attribute decision making,in which the information about attribute weights is partly known and the attribute values take form of triangular fuzzy numbers.Considering the fact that the triangular fuzzy TOPSIS results yielded by different distance measures are different from others,a comparative analysis of triangular fuzzy TOPSIS ranking from each distance measure is illustrated with discussion on standard deviation.By applying the most reasonable distance,the deviation degrees between attribute values are measured.A linear programming model based on the maximal deviation of weighted attribute values is established to obtain the attribute weights.Therefore,alternatives are ranked by using TOPSIS method.Finally,a numerical example is given to show the feasibility and effectiveness of the method.

Site selection of emergency material warehouse under fuzzy environment

The objective of this work was to determine the location of emergency material warehouses. For the site selection problem of emergency material warehouses, the triangular fuzzy numbers are respectively demand of the demand node, the distance between the warehouse and demand node and the cost of the warehouse, a bi-objective programming model was established with minimum total cost of the system and minimum distance between the selected emergency material warehouses and the demand node. Using the theories of fuzzy numbers, the fuzzy programming model was transformed into a determinate bi-objective mixed integer programming model and a heuristic algorithm for this model was designed. Then, the algorithm was proven to be feasible and effective through a numerical example. Analysis results show that the location of emergency material warehouse depends heavily on the values of degree a and weight wl. Accurate information of a certain emergency activity should be collected before making the decision.

Return Contract of Supply Chain with Fuzzy Continuous Demand

In a two-stage supply chain composed of one supplier and one retailer,the supply chain coordination mechanism in a fuzzy continuous demand environment is researched.A positive triangular fuzzy number is used to model the external market demand.Using the method of fuzzy cut sets theory,both fuzzy decentralized and centralized decision-making processes are analyzed,and another model of fuzzy return contract is proposed to help coordinate such supply chain.It is shown that in fuzzy environment there exists a unique solution of the retailer＇s optimal order quantity,the double marginalization problem can be solved by providing different tactics for wholesale pricing and return pricing,and the fuzzy expected profit of each actor can be expected to improve in the return contract.Finally,a numerical example is given to illustrate the models and the solution-seeking process.

Method for solving fully fuzzy linear programming problems using deviation degree measure

A new fully fuzzy linear programming （FFLP） problem with fuzzy equality constraints is discussed. Using deviation degree measures, the FFLP problem is transformed into a crisp 6-parametric linear programming （LP） problem. Giving the value of deviation degree in each constraint, the 6-fuzzy optimal solution of the FFLP problem can be obtained by solving this LP problem. An algorithm is also proposed to find a balance-fuzzy optimal solution between two goals in conflict： to improve the values of the objective function and to decrease the values of the deviation degrees. A numerical example is solved to illustrate the proposed method.

Solving Fully Fuzzy Nonlinear Eigenvalue Problems of Damped Spring-Mass Structural Systems Using Novel Fuzzy-Affine Approach

The dynamic analysis of damped structural system by using finite element method leads to nonlinear eigenvalue problem(NEP)(particularly,quadratic eigenvalue problem).In general,the parameters of NEP are considered as exact values.But in actual practice because of different errors and incomplete information,the parameters may have uncertain or vague values and such uncertain values may be considered in terms of fuzzy numbers.This article proposes an efficient fuzzy-affine approach to solve fully fuzzy nonlinear eigenvalue problems(FNEPs)where involved parameters are fuzzy numbers viz.triangular and trapezoidal.Based on the parametric form,fuzzy numbers have been transformed into family of standard intervals.Further due to the presence of interval overestimation problem in standard interval arithmetic,affine arithmetic based approach has been implemented.In the proposed method,the FNEP has been linearized into a generalized eigenvalue problem and further solved by using the fuzzy-affine approach.Several application problems of structures and also general NEPs with fuzzy parameters are investigated based on the proposed procedure.Lastly,fuzzy eigenvalue bounds are illustrated with fuzzy plots with respect to its membership function.Few comparisons are also demonstrated to show the reliability and efficacy of the present approach.

Properties of Fuzzy Entropy Based on the Shape Change of Membership Function

Modification of a fuzzy partition often leads to the change of fuzziness of a fuzzy system. Researches on the change of fuzzy entropy of a fuzzy set, responding to shape alteration of membership function, therefore, play a significant role in analysis of the change of fuzziness of a fuzzy system because a fuzzy partition consists of a set of fuzzy sets which satisfy some special constraints. This paper has shown several results about entropy changes of a fuzzy set. First, the entropies of two same type of fuzzy sets have a constant proportional relationship which depends on the ratio of the sizes of their support intervals. Second, as for Triangular Fuzzy Numbers （TFNs）, the entropies of any two TFNs which can not be always the same type, also, have a constant proportional relationship which depends on the ratio of the sizes of their support intervals. Hence, any two TFNs with the same sizes of support intervals have the same entropies. Third, concerning two Triangular Fuzzy Sets （TFSs） with same sizes of support intervals and different heights, the relationship of their entropies lies on their height. Finally, we point it out a mistake that Chen＇s assertion that the entropy of resultant fuzzy set of elevation operation is directly to that of the original one while elevation factor just acts as a propartional factor. These results should contribute to the analysis and design of a fuzzy system.

Evaluation of the asset＇s value by using fuzzy two-stage discounted cash flow model

This paper establishes the fuzzy discounted cash flow model to settle the uncertainties of the cash flow and discount rate in two-stage DCF model, to take the imprecise of the time period of the supernormal growth phase with considering the investor＇s attitude to risk. Firstly, the discount rate and the growth rate are fuzzified as triangular fuzzy numbers in this fuzzy discounted cash flow model. Then the intrinsic value of an asset can be evaluated by the arithmetic operation on interval and λ- signed distance method under the framework of DCF approach. Finally, a listed company at Shanghai Stock Exchange is analyzed as the case to demonstrate the process of stock value calculation by the fuzzy discounted cash flow model.

Optimization Model on Quadratic Programming Problem with Fuzzy

In this paper, the authors propose a computational procedure by using fuzzy approach to fred the optimal solution of quadratic programming problems. The authors divide the calculation of the optimal solution into two stages. In the first stage the authors determine the unconstrained minimization and check its feasibility. The second stage, the authors explore the feasible region from initial point to another point until the authors get the optimal point by using Lagrange multiplier. A numerical example is included to support as illustration of the paper.

Fuzzy computational study on the generalized fractional smoking model with caputo gH-type derivatives

This work considers a generalized fuzzy fractional smoking model with Caputo gHtypes fractional derivatives upon considering the case of uncertainty quantification.The disease-free equilibrium point and stability of the equilibrium point have been discussed for the fuzzy nonlinear fractional smoking model.The analytical proofs for the existence and uniqueness of the proposed model are concerned with the help of the fixed-point theorem,Banach contraction,and Schauder theorem.A robust double parametric approach with a generalized transform is used to study the behavior of the fuzzy fractional model in an uncertain context and obtain the convergence analysis of the study in a crisp context.Finally,the obtained results of the proposed model have been validated with the Runge-Kutta method of fourth order in crisp case(s=1,l=O).

Multi Criteria Decision Making for Evaluation and Ranking of Cancer Information

Cancer is a disease that is rapidly expanding in prevalence all over the world.Cancer cells canmetastasize,or spread,across the body and impact several different cell types.Additionally,the incidence rates of several subtypes of cancer have been on the rise in India.The countermeasures for the cancer disease can be taken by determining the specific expansion rate of each type.To rank the various forms of cancer’s rate of progression,we used some of the available data.Numerous studies are available in the literature which show the growth rate of cancer by different techniques.The accuracy of the scheme in determining the highest growth rate may vary due to the variation in the dependent factors.Within the context of this research,the Fuzzy triangular technique for order preference by similarity to ideal solution(TOPSIS),is utilized to rank the various categorizations of cancer with the help of four groups of medical professionals acting in the capacity of decision-makers.The number of decision-makers may variate according to the required accuracy of results.The findings of the three-dimensional Fuzzy TOPSIS analysis categorize each variety of cancer according to the rate at which it spreads over time.Numerical results along with visual representation are presented to examine the efficiency of our proposed work.

Surface accuracy optimization of mechanical parts with multiple circular holes for additive manufacturing based on triangular fuzzy number

Surface accuracy directly affects the surface quality and performance of mechanical parts.Circular hole,especially spatial non-planar hole set is the typical feature and working surface of mechanical parts.Compared with traditional machining methods,additive manufacturing(AM)technology can decrease the surface accuracy errors of circular holes during fabrication.However,an accuracy error may still exist on the surface of circular holes fabricated by AM due to the influence of staircase effect.This study proposes a surface accuracy optimization approach for mechanical parts with multiple circular holes for AM based on triangular fuzzy number(TFN).First,the feature lines on the manifold mesh are extracted using the dihedral angle method and normal tensor voting to detect the circular holes.Second,the optimal AM part build orientation is determined using the genetic algorithm to optimize the surface accuracy of the circular holes by minimizing the weighted volumetric error of the part.Third,the corresponding weights of the circular holes are calculated with the TFN analytic hierarchy process in accordance with the surface accuracy requirements.Lastly,an improved adaptive slicing algorithm is utilized to reduce the entire build time while maintaining the forming surface accuracy of the circular holes using digital twins via virtual printing.The effectiveness of the proposed approach is experimentally validated using two mechanical models.

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.

EPQ model with the effect of inflation and reliability for partial trade credit under fuzzy and cloudy fuzzy environment

The proposed study offers the first-of-its-kind economic production quantity model for deteriorating items having a demand rate to be price dependent under the effect of inflation and reliability with partial trade credit.The model is extended under an uncertain environment by assuming inventory parameters to be triangular fuzzy numbers and cloudy triangular fuzzy numbers.The objective of the study is to maximize the profit of the inventory system and to identify the most suitable environment for the proposed problem.Results are verified using the numerical study.Furthermore,the comparative study is presented to justify the nature of fuzzy and cloudy fuzzy environments.Sensitivity analysis under all environments is conducted to identify the most sensitive parameters of all.

Fuzzy Reliability and Availability of System under a Calendar-based Inspection Involving Multiple Failures and Its Application to Wind Turbine System

Uncertainty is an important factor that needs to be considered while analyzing the performance of any engineering system.In order to quantify uncertainty,fuzzy set theory is frequently used by most of researchers,including energy system experts.According to the classical reliability theory,component lifetimes have crisp parameters,but due to uncertainty and inaccuracy in data,it is sometimes very difficult to determine the exact values of these parameters in real-world systems.To overcome this difficulty in the current research,failure and repair rates were taken as triangular fuzzy numbers to determine the fuzzy availability of a system undergoing calendar-based periodic inspection subject to multiple failure modes(FMs).It was assumed that each component in the system had an exponential failure rate and repair rate with fuzzy parameters.System FMs were explicitly taken into account when a functional state of the system was considered.Each FM had a random failure time.On the occurrence of any failure,a random time was selected for the relevant corrective repair work.The proposed research was studied for one of the major sources of green energy,namely a wind turbine system wherein all the derived propositions have been implemented on it.