Symmetric Triangular Fuzzy Numbers Research Articles

Heat transfer analysis of Maxwell tri-hybridized nanofluid through Riga wedge with fuzzy volume fraction

This contribution aims to optimize nonlinear thermal flow for Darcy-Forchheimer Maxwell fuzzy left( {{text{Al}}_{{2}} {text{O}}_{{3}} + {text{Cu }} + {text{TiO}}_{{2}} {text{/EO}}} right) tri-hybrid nanofluid flow across a Riga wedge in the context of boundary slip. Three types of nanomaterials, {text{Al}}_{{2}} {text{O}}_{{3}} , Cu and {text{TiO}}_{2} have been mixed into the basic fluid known as engine oil. Thermal properties with the effects of porous surface and nonlinear convection have been established for the particular combination left( {{text{Al}}_{{2}} {text{O}}_{{3}} + {text{Cu}} + {text{TiO}}_{{2}} {text{/EO}}} right){.} Applying a set of appropriate variables, the set of equations that evaluated the energy and flow equations was transferred to the dimensionless form. For numerical computing, the MATLAB software's bvp4c function is used. The graphical display is used to demonstrate the influence of several influential parameters. It has been observed that flow rate decay with expansion in porosity parameter and nanoparticles volumetric fractions. In contrast, it rises with wedge angle, Grashof numbers, Darcy-Forchheimer, nonlinear Grashof numbers, and Maxwell fluid parameter. Thermal profiles increase with progress in the heat source, nanoparticles volumetric fractions, viscous dissipation, and nonlinear thermal radiation. The percentage increases in drag force for ternary hybrid nanofluid are 13.2 and 8.44 when the Modified Hartmann number takes input in the range 0.1 le {text{Mh}} le 0.3 and wedge angle parameters 0.1 le m le 0.3. For fuzzy analysis, dimensionless ODEs transformed into fuzzy differential equations and employed symmetrical triangular fuzzy numbers (TFNs). The TFN makes a triangular membership function (M.F.) that describes the fuzziness and comparison. This study compared nanofluids, hybrid nanofluids, and ternary nanofluids through triangular M.F. The boundary layer flow caused by a wedge surface plays a crucial role in heat exchanger systems and geothermal.

Application of the Double Fuzzy Sawi Transform for Solving a Telegraph Equation

The main purpose of this study is to introduce a new double fuzzy transform called the double fuzzy Sawi transform. A proof of some basic properties of the single fuzzy Sawi transform and the double fuzzy Sawi transform are provided. These new results are implemented to obtain the exact solution of a non-homogeneous linear fuzzy telegraph equation under a generalized Hukuhara partial differentiability. In addition, by using the symmetric triangular fuzzy numbers, numerical examples are given to demonstrate the validity and superiority of the double fuzzy Sawi transform in solving the fuzzy linear telegraph equation.

A fuzzy based solution to multiple objective LPP

<abstract><p>This study presents a Fuzzy Multiple Objective Linear Programming Problem (FMOLPP) method to solve the Linear Programming Problem (LPP). Initially Multiple Objective Linear Programming Problem (MOLPP) is solved using Chandra Sen's approach along with various types of mean approaches. Furthermore, FMOLPP is solved using Chandra Sen's approach and various categories of fuzzy mean techniques. The simplex form is used to solve the LPP, where the three-tuple symmetric triangular fuzzy number with the constraints of the fuzzy objective function is considered. We have presented a comparative study of optimum values of MOLPP with optimum values of FMOLPP, to show the significance of our proposed method.</p></abstract>

Fuzzy finite element analysis based on the transformation between fuzzy and random variables

In this paper, a fuzzy finite element method (FFEM) for determining the responses of structures is proposed by using the transformation between fuzzy and random variables. Firstly, the formulae for establishing normal random variables equivalent to symmetric triangular fuzzy numbers are presented based on the combination of the principle of insufficient reason and that of maximum specificity. As a result, fuzzy finite element analysis is transferred into stochastic finite element analysis. To solve this problem, the response surface method with the aid of standard normal random variables is utilized to approximate the real responses of structures. Then, the errors between the training and test sets are estimated to select a suitable response surface model amongst the regression models. Lastly, the formulae for determining the mean and the standard deviation values of the responses of structures are established. The accuracy and effectiveness of the proposed method are verified via an illustrative example.

Fuzzy Delay Tumor Growth with Quiescence Cells: Stability of Steady States

This paper presents a system of delay tumor growth that describes an interaction between the proliferating and quiescent cells tumor. This system is fuzzified by parametric form of α-cut representation of symmetric triangular fuzzy number. The steady state and linear stability of fuzzy tumor growth system with quiescence and without quiescence cells are determined and analyzed. Here, we show that the trivial steady state of the system with quiescence is stable for τ =0 by Routh Hurwitz conditions. For increasing delay the steady state is unstable by using Strum theorem.

Similarity Measures Based on T-Spherical Fuzzy Information with Applications to Pattern Recognition and Decision Making

T-spherical fuzzy set (TSFS) is a fuzzy layout aiming to provide a larger room for the processing of uncertain information-based data where four aspects of unpredictable information are studied. The frame of picture fuzzy sets (PFSs) and intuitionistic fuzzy sets (IFSs) provide limited room for processing such kinds of information. On a scale of zero to one, similarity measures (SMs) are a tool for evaluating the degrees of resemblance between various items or phenomena. The goal of this paper is to investigate the shortcomings of picture fuzzy (PF) SMs in order to introduce a new SM in a T-spherical fuzzy (TSF) environment. The newly improved SM has a larger ground for accommodating the uncertain information with three degrees and is also responsible for the reduction of information loss. The proposed SM’s validity is demonstrated mathematically and by examples. To examine the application of the suggested SM two real-life issues are discussed, including the concerns of medical diagnosis and pattern recognition. A comparison of the suggested SMs with current SMs is also made to assess the proposed work’s reliability. Since symmetric triangular fuzzy numbers are quite useful in database acquisition, we will consider the proposed SM for symmetric T-spherical triangular fuzzy numbers in the near future.

An Optimization Model of Integrated AGVs Scheduling and Container Storage Problems for Automated Container Terminal Considering Uncertainty

The running path of automated guided vehicles (AGVs) in the automated terminal is affected by the storage location of containers and the running time caused by congestion, deadlock and other problems during the driving process is uncertain. In this paper, considering the different AGVs congestion conditions along the path, a symmetric triangular fuzzy number is used to describe the AGVs operation time distribution and a multi-objective scheduling optimization model is established to minimize the risk of quay cranes (QCs) delay and the shortest AGVs operation time. An improved genetic algorithm was designed to verify the effectiveness of the model and algorithm by comparing the results of the AGVs scheduling and container storage optimization model based on fixed congestion coefficient under different example sizes. The results show that considering the AGVs task allocation and container storage location allocation optimization scheme with uncertain running time can reduce the delay risk of QCs, reduce the maximum completion time and have important significance for improving the loading and unloading efficiency of the automated terminal.

Hesitant Fuzzy Linear Regression Model for Decision Making

An expert may experience difficulties in decision making when evaluating alternatives through a single assessment value in a hesitant environment. A fuzzy linear regression model (FLRM) is used for decision-making purposes, but this model is entirely unreasonable in the presence of hesitant fuzzy information. In order to overcome this issue, in this paper, we define a hesitant fuzzy linear regression model (HFLRM) to account for multicriteria decision-making (MCDM) problems in a hesitant environment. The HFLRM provides an alternative approach to statistical regression for modelling situations where input–output variables are observed as hesitant fuzzy elements (HFEs). The parameters of HFLRM are symmetric triangular fuzzy numbers (STFNs) estimated through solving the linear programming (LP) model. An application example is presented to measure the effectiveness and significance of our proposed methodology by solving a MCDM problem. Moreover, the results obtained employing HFLRM are compared with the MCDM tool called technique for order preference by similarity to ideal solution (TOPSIS). Finally, Spearman’s rank correlation test is used to measure the significance for two sets of ranking.

Fuzzy Sawi Decomposition Method for Solving Nonlinear Partial Fuzzy Differential Equations

The main goal of this paper is to propose a new decomposition method for finding solutions to nonlinear partial fuzzy differential equations (NPFDE) through the fuzzy Sawi decomposition method (FSDM). This method is a combination of the fuzzy Sawi transformation and Adomian decomposition method. For this purpose, two new theorems for fuzzy Sawi transformation regarding fuzzy partial gH-derivatives are introduced. The use of convex symmetrical triangular fuzzy numbers creates symmetry between the lower and upper representations of the fuzzy solution. To demonstrate the effectiveness of the method, a numerical example is provided.

Unit hydrograph identification based on fuzzy regression analysis

A methodology has been developed to treat the uncertainties of the unit hydrograph rainfall-runoff transformation based on the fuzzy linear regression model. The components of the unit hydrograph are proposed to be symmetric triangular fuzzy numbers. The main idea is to develop a fuzzified version of the widely—used unit hydrograph. The input of the model is the effective rainfall (which is a set of crisp numbers) and the output is the runoff (which is a set of fuzzy numbers). The problem of determining the fuzzy components of the unit hydrograph is transformed into a linear optimization approach based on the fuzzy linear regression of Tanaka. The condition applied is that the data must be included in the fuzzy band of discharge produced by the fuzzy unit hydrograph. However, some modifications of the widely-used fuzzy regression are proposed in order to be compatible with the unit hydrograph implementation. The model was tested based on twenty real rainfall-runoff events, the conclusion being that it works well in the case of an individual storm event. However, the consideration of many storms seems to be required in order to increase the applicability of the produced fuzzy hydrograph to other storms in such a way that the fuzziness is increased. Several measures of suitability are proposed in order to check the efficiency of the proposed method. Several other useful comments according to the comparison with other unit hydrograph considerations are made.

Конфиденциальное двустороннее вычисление параметров нечеткой линейной регрессионной модели

Purpose: describe two-party computation of fuzzy linear regression with horizontal partitioning of data, while maintaining data confidentiality. Methods: the computation is designed using a transformational approach. The optimization problems of each of the two participants are transformed and combined into a common problem. The solution to this problem can be found by one of the participants. Results: A protocol is proposed that allows two users to obtain a fuzzy linear regression model based on the combined data. Each of the users has a set of data about the results of observations, containing the values of the explanatory variables and the values of the response variable. The data structure is shared: both users use the same set of explanatory variables and a common criterion. Regression coefficients are searched for as symmetric triangular fuzzy numbers by solving the corresponding linear programming problem. It is assumed that both users are semihonest (honest but curious, or passive and curious), i.e. they execute the protocol, but can try to extract information about the source data of the partner by applying arbitrary processing methods to the received data that are not provided for by the protocol. The protocol describes the transformed linear programming problem. The solution of this problem can be found by one of the users. The number of observations of each user is known to both users. The observation data remains confidential. The correctness of the protocol is proved and its security is justified. Keywords: fuzzy numbers, collaborative solution of a linear programming problem, two-way computation, transformational approach, cloud computing, federated machine learning.

Structural fuzzy reliability analysis using the classical reliability theory

This study is focused on a novel approach for calculating structural fuzzy reliability by using the classical reliability theory. In order to handle the structural fuzzy reliability problem, the formulae for establishing normal random variables equivalent to symmetric triangular fuzzy number are presented. From these equivalent random ones, the original problem is converted to the basic structural reliability problems, then the methods of the classical reliability theory should be applied to calculate. Moreover, this study proposes two notions in terms of central fuzzy reliability and standard deviation of fuzzy reliability as well as a calculation procedure to define them. Lastly, the ultimate fuzzy reliability of the proposed method is established and utilized to compare the allowable reliability in the design codes. Numerical results are supervised to verify the accuracy of the proposed method.

The Use of Fuzzy Linear Regression and ANFIS Methods to Predict the Compressive Strength of Cement

In this paper, the prediction of compressive cement strength using the fuzzy linear regression (FLR) and adaptive neuro-fuzzy inference system (ANFIS) methods was studied. Specifically, an accurate prediction method is needed as the modeling of cement strength is a difficult task, which is based on its composite nature. However, many approaches are widely implemented in strength-predicting problems, such as the artificial neural network (ANN), Mamdani fuzzy rules in MATLAB, FLR and ANFIS models. Applying these methods and comparing the results with the corresponding observed ones, we concluded that the ANFIS method successfully decreased the level of uncertainty in predicting cement strength, as the average percentage error level was extremely low. Although the FLR method had the highest average percentage error level compared with the other methods, it provides a standard equation to estimate the output values by using symmetric triangular fuzzy numbers and determines the most important factor in increasing compressive strength, in contrast to ANFIS and ANN, which are black box models, and to the fuzzy method, which uses rules without providing the specific way by which the results come out. Thus, ANFIS and FLR are appropriate methods for dealing with engineering mathematical models by using fuzzy logic.

Determining the relative importance of titania nanotubes characteristics on bone implant surface performance: A quality by design study with a fuzzy approach.

TiO2 nanotubes (TNTs) are a promising bone/dental implant surface modification strategy with enhanced bioactivity and local therapeutic functions. However, inconsistencies related to the understanding of the influence of various TNTs characteristics on Ti implant functions, and the multi-factorial inter-dependence of such characteristics, requires an in-depth Quality by Design (QbD) analysis towards optimizing TNTs-modified implants. To this end, an extensive systematic literature search was undertaken to identify the various TNTs characteristics that may influence implant performance. Subsequently, in order to facilitate a QbD analysis, an expert questionnaire survey was carried out to determine the perceived contribution of various TNTs characteristics on an implant's biological, physicochemical, and mechanical performance. To achieve this goal, the Quality Function Deployment method was employed using symmetrical triangular fuzzy numbers to translate qualitative expert opinion into meaningful quantitative information. The results show that pore diameter, inter-nanotube distance and wall thickness are the TNTs characteristics with the most influential effects on the overall implant performance. This pioneering study evaluates perceived importance of various parameters contributing to TNTs functionality, and represents a step forward in the implementation of QbD strategies towards optimizing nano-engineered Ti implants.

Residual Series Representation Algorithm for Solving Fuzzy Duffing Oscillator Equations

The mathematical structure of some natural phenomena of nonlinear physical and engineering systems can be described by a combination of fuzzy differential equations that often behave in a way that cannot be fully understood. In this work, an accurate numeric-analytic algorithm is proposed, based upon the use of the residual power series, to investigate the fuzzy approximate solution for a nonlinear fuzzy Duffing oscillator, along with suitable uncertain guesses under strongly generalized differentiability. The proposed approach optimizes the approximate solution by minimizing a residual function to generate r-level representation with a rapidly convergent series solution. The influence, capacity, and feasibility of the method are verified by testing some applications. Level effects of the parameter r are given graphically and quantitatively, showing good agreement between the fuzzy approximate solutions of upper and lower bounds, that together form an almost symmetric triangular structure, that can be determined by central symmetry at r = 1 in a convex region. At this point, the fuzzy number is a convex fuzzy subset of the real line, with a normalized membership function. If this membership function is symmetric, the triangular fuzzy number is called the symmetric triangular fuzzy number. Symmetrical fuzzy estimates of solutions curves indicate a sense of harmony and compatibility around the parameter r = 1. The results are compared numerically with the crisp solutions and those obtained by other existing methods, which illustrate that the suggested method is a convenient and remarkably powerful tool in solving numerous issues arising in physics and engineering.

A New Method to Support Decision-Making in an Uncertain Environment Based on Normalized Interval-Valued Triangular Fuzzy Numbers and COMET Technique

Multi-criteria decision-making (MCDM) plays a vibrant role in decision-making, and the characteristic object method (COMET) acts as a powerful tool for decision-making of complex problems. COMET technique allows using both symmetrical and asymmetrical triangular fuzzy numbers. The COMET technique is immune to the pivotal challenge of rank reversal paradox and is proficient at handling vagueness and hesitancy. Classical COMET is not designed for handling uncertainty data when the expert has a problem with the identification of the membership function. In this paper, symmetrical and asymmetrical normalized interval-valued triangular fuzzy numbers (NIVTFNs) are used for decision-making as the solution of the identified challenge. A new MCDM method based on the COMET method is developed by using the concept of NIVTFNs. A simple problem of MCDM in the form of an illustrative example is given to demonstrate the calculation procedure and accuracy of the proposed approach. Furthermore, we compare the solution of the proposed method, as interval preference, with the results obtained in the Technique for Order of Preference by Similarity to Ideal solution (TOPSIS) method (a certain preference number).

Fuzzy c-means clustering method with the fuzzy distance definition applied on symmetric triangular fuzzy numbers

Fuzzy c-means clustering method with the fuzzy distance definition applied on symmetric triangular fuzzy numbers

Decision to Adopt Neuromarketing Techniques for Sustainable Product Marketing: A Fuzzy Decision-Making Approach

Sustainable products and their marketing have played a crucial role in developing more sustainable consumption patterns and solutions for socio-ecological problems. They have been demonstrated to significantly decrease social consumption problems. Neuromarketing has recently gained considerable popularity and helped companies generate deeper insights into consumer behavior. It has provided new ways of conceptualizing consumer behavior and decision making. Thus, this research aims to investigate the factors influencing managers’ decisions to adopt neuromarketing techniques in sustainable product marketing using the fuzzy analytic hierarchy process (AHP) approach. Symmetric triangular fuzzy numbers were used to indicate the relative strength of the elements in the hierarchy. Data were collected from the marketing managers of several companies who have experience with sustainable product marketing through online shopping platforms. The results revealed that the accuracy and bias of neuromarketing techniques have been the main critical factors for managers to select neuromarketing in their business for advertising and branding purposes. This research provides important results on the use of neuromarketing techniques for sustainable product marketing, as well as their limitations and implications, and it also presents useful information on the factors impacting business managers’ decision making in adopting neuroscience techniques for sustainable product development and marketing.

A credibility-based multi-objective temporary logistics hub location-allocation model for relief supply and distribution under uncertainty

Disaster response operations revolve around uncertainties. While uncertainties arising due to randomness can be avoided for post-disaster location problem, those arising because of impreciseness may persist long after the disaster's occurrence. Despite the uncertainties and lack of sufficient information about the extent of the damage, disaster response facilities must be established quickly after the occurrence of the disaster. Moreover, the decisions of whether to open, where to locate, and when to open disaster response facilities are based on the amount and quality of information available during the decision-making period. To address these issues, we develop a multi-objective location-allocation model for relief supply and distribution that accounts for the imprecise and time-varying nature of different parameters and time-varying coverage, while also accommodating the subjective attributes necessary to enable establishment and operation of the temporary logistics hubs (TLHs). A credibility-based fuzzy chance-constrained programming model is employed to account for the impreciseness inherent in predicting parameter values during disaster response. The results show where, when, and how many TLHs to open and how to allocate relief supplies. Meanwhile, the sensitivity analysis provides a broader understanding of the impact of limiting the number of TLHs as well as the confidence level and the spread of the symmetric triangular fuzzy numbers on the attainment of the model objectives.

(1712-4137) AN EPQ MODEL FOR AN IMPERFECT PRODUCTION PROCESS WITH FUZZY CYCLE TIME AND QUALITY SCREENING

This study has developed a production inventory model where the cycle timeis fuzzy, the existence of defective products is assumed in each batch andproduct screening is performed both in-production and after-production.Triangular fuzzy numbers serve to model uncertainties in the cycle time, anda fuzzified total inventory profit function is created by thedefuzzification method known as the signed distance method. The classicalapproach is used to determine the optimal policy, with the ideal cycle timematched to the total profit. Although assuming asymmetric triangular fuzzynumbers prevents the calculation of a clear analytical solution, the methodapproaches as closely as possible to an analytical solution. A numericalsolution to only one equation is needed to obtain the optimal configuration.Conversely, there is a positive trade-off, with an analytical solution tothe optimization problem if there is an assumption of symmetrical triangularfuzzy numbers. The proposed model is illustrated by a numerical example. Thepaper presents results and sensitivity analyses, in both tables and graphicillustrations. The effects on total profit are discussed in relation tovarious parameters. From the numerical studies, it is observed that thelevel of fuzziness influences the cycle time and an approximately linearrelationship, in the opposite direction, was found between the total profitand the level of fuzziness, when it was increased.