Regression Analysis of a Kind of Trapezoidal Fuzzy Numbers Based on a Shape Preserving Operator

Fuzzy regression provides more approaches for us to deal with imprecise or vague problems. Traditional fuzzy regression is established on triangular fuzzy numbers, which can be represented by trapezoidal numbers. The independent variables, coefficients of independent variables and dependent variable in the regression model are fuzzy numbers in different times and TW, the shape preserving operator, is the only T-norm which induces a shape preserving multiplication of LL-type of fuzzy numbers. So, in this paper, we propose a new fuzzy regression model based on LL-type of trapezoidal fuzzy numbers and TW. Firstly, we introduce the basic fuzzy set theories, the basic arithmetic propositions of the shape preserving operator and a new distance measure between trapezoidal numbers. Secondly, we investigate the specific model algorithms for FIFCFO model (fuzzy input-fuzzy coefficient-fuzzy output model) and introduce three advantages of fit criteria, Error Index, Similarity Measure and Distance Criterion. Thirdly, we use a design set and two reference sets to make a comparison between our proposed model and the reference models and determine their goodness with the above three criteria. Finally, we draw the conclusion that our proposed model is reasonable and has better prediction accuracy, but short of robust, comparing to the reference models by the three goodness of fit criteria. So, we can expand our traditional fuzzy regression model to our proposed new model.

Aggregation operators on intuitionistic trapezoidal fuzzy number and its application to multi-criteria decision making problems

Intuitionistic trapezoidal fuzzy numbers and their operational laws are defined. Based on these operational laws, some aggregation operators, including intuitionistic trapezoidal fuzzy weighted arithmetic averaging operator and weighted geometric averaging operator are proposed. Expected values, score function, and accuracy function of intuitionitsic trapezoidal fuzzy numbers are defined. Based on these, a kind of intuitionistic trapezoidal fuzzy multi-criteria decision making method is proposed. By using these aggregation operators, criteria values are aggregated and integrated intuitionistic trapezoidal fuzzy numbers of alternatives are attained. By comparing score function and accuracy function values of integrated fuzzy numbers, a ranking of the whole alternative set can be attained. An example is given to show the feasibility and availability of the method.

A novel similarity measure between intuitionistic fuzzy sets based on the mid points of transformed triangular fuzzy numbers with applications to pattern recognition and medical diagnosis

Similarity measure is an essential tool to compare and determine the degree of similarity between intuitionistic fuzzy sets (IFSs). In this paper, a new similarity measure between intuitionistic fuzzy sets based on the mid points of transformed triangular fuzzy numbers is proposed. The proposed similarity measure provides reasonable results not only for the sets available in the literature but also gives very reasonable results, especially for fuzzy sets as well as for most intuitionistic fuzzy sets. To provide supportive evidence, the proposed similarity measure is tested on certain sets available in literature and is also applied to pattern recognition and medical diagnosis problems. It is observed that the proposed similarity measure provides a very intuitive quantification.

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.

Complex Decision Modeling Framework with Fairly Operators and Quaternion Numbers under Intuitionistic Fuzzy Rough Context

The main goal of informal computing is to overcome the limitations of hypersensitivity to defects and uncertainty while maintaining a balance between high accuracy,accessibility,and cost-effectiveness.This paper investigates the potential applications of intuitionistic fuzzy sets(IFS)with rough sets in the context of sparse data.When it comes to capture uncertain information emanating fromboth upper and lower approximations,these intuitionistic fuzzy rough numbers(IFRNs)are superior to intuitionistic fuzzy sets and pythagorean fuzzy sets,respectively.We use rough sets in conjunction with IFSs to develop several fairly aggregation operators and analyze their underlying properties.We present numerous impartial laws that incorporate the idea of proportionate dispersion in order to ensure that the membership and non-membership activities of IFRNs are treated equally within these principles.These operations lead to the development of the intuitionistic fuzzy rough weighted fairly aggregation operator(IFRWFA)and intuitionistic fuzzy rough ordered weighted fairly aggregation operator(IFRFOWA).These operators successfully adjust to membership and non-membership categories with fairness and subtlety.We highlight the unique qualities of these suggested aggregation operators and investigate their use in the multiattribute decision-making field.We use the intuitionistic fuzzy rough environment’s architecture to create a novel strategy in situation involving several decision-makers and non-weighted data.Additionally,we developed a novel technique by combining the IFSs with quaternion numbers.We establish a unique connection between alternatives and qualities by using intuitionistic fuzzy quaternion numbers(IFQNs).With the help of this framework,we can simulate uncertainty in real-world situations and address a number of decision-making problems.Using the examples we have released,we offer a sophisticated and systematically constructed illustrative scenario that is intricately woven with the complexity ofmedical evaluation in order to thoroughly assess the relevance and efficacy of the suggested methodology.

Optimization Algorithms of PERT/CPM Network Diagrams in Linear Diophantine Fuzzy Environment

The idea of linear Diophantine fuzzy set(LDFS)theory with its control parameters is a strong model for machine learning and optimization under uncertainty.The activity times in the critical path method(CPM)representation procedures approach are initially static,but in the Project Evaluation and Review Technique(PERT)approach,they are probabilistic.This study proposes a novel way of project review and assessment methodology for a project network in a linear Diophantine fuzzy(LDF)environment.The LDF expected task time,LDF variance,LDF critical path,and LDF total expected time for determining the project network are all computed using LDF numbers as the time of each activity in the project network.The primary premise of the LDF-PERT approach is to address ambiguities in project network activity timesmore simply than other approaches such as conventional PERT,Fuzzy PERT,and so on.The LDF-PERT is an efficient approach to analyzing symmetries in fuzzy control systems to seek an optimal decision.We also present a new approach for locating LDF-CPM in a project network with uncertain and erroneous activity timings.When the available resources and activity times are imprecise and unpredictable,this strategy can help decision-makers make better judgments in a project.A comparison analysis of the proposed technique with the existing techniques has also been discussed.The suggested techniques are demonstrated with two suitable numerical examples.

Trapezoidal Approximation of a Fuzzy Number Preserving the Expected Interval and Including the Core

In this paper, we introduce a method to obtain the nearest trapezoidal approximation of fuzzy numbers so that preserving conditions expect interval and include the core of a fuzzy number.

Distinguished Representation of Criteria Based on Trapezoidal Fuzzy Numbers and Fuzzy Memberships in Selection of Contractors

More attention has been drawn to the selection of contractors in recent years,but little research has been conducted on distinguishing representation of performance values for qualitative and quantitative criteria in one decision-making(DM) problem yet.Thus a novel method based on fuzzy number is proposed to solve the representation issue,in which linguistic terms and fuzzy memberships are used to separately describe qualitative and quantitative criteria,and then the linguistic terms are translated into fuzzy numbers which will be defuzzified and unified with fuzzy memberships.The novel method is used to develop a synthetic decision model for selection of contractors.The model is developed to verify the feasibility of the novel method,which(1) builds a twolevel criteria system based on survey and literature summary;(2)utilizes the analytic network process(ANP) to determine criteria weights;(3) uses the novel method to make different representations of performance values for qualitative and quantitative criteria in one DM problem and then unifies different representations for decision matrices;(4) utilizes three multi-criteria decision-making(MCDM) methods containing simple additive weighting(SAW),technique for order preference by similarity to ideal solution(TOPSIS) and complex proportional assessment(COPRAS) to deal with decision matrices.Besides,a case of contractor selection is given to check the novel method by applying developed model,and the case results show that the novel method can suitably solve the representation issue of the performance values for two types of criteria as well as simplify the processes of TOPSIS and COPRAS.

The Application of Trapezoidal Fuzzy AHP on Evaluation Item Weight Calculation of Highway Network Programming Schemes

The fuzzy theory is invited in this paper to calculate weights of evaluation items, which is a very important stage in highway network evaluation. Highway network evaluation is a composite of various attributes that lack of pertinency and comparability, and their commonality is that they are more or less tainted with uncertainty, with different daily decision making problems of diverse intensity, the results can be misleading if the fuzziness of human decision-making is not taken into account. So we introduce fuzzy theory into the measurement of evaluating weights to overcome the issue and Analytic Hierarchy Process in scheme ranking. It is testified to be a more reliable way through the case study of Yangtze River Delta highway network evaluation.

Application of Fuzzy Optimization Method in Decision-Making for Personnel Selection

The paper describes the necessity of application of intelligent technologies to support decisions of more objective problems in human resource management. In this paper, we describe the methodology for personnel selection problem for the vacancy with regard to the importance and nonequivalence of numerous indicators characterizing the alternatives. The specific features of the selection problem are highlighted, immersing the problem into a fuzzy environment. A fuzzy multicriterial model of the personnel selection problem is proposed. A technique of order preference by similarity to ideal solition (TOPSIS), was applied for evaluation and regulation of alternatives. This technique is based on criteria of qualitative character, which are hierarchically structured by multiple experts to intellectually support decisions made in personnel selection problem. Using TOPSIS method and generated criteria system an experiment was conducted for evaluation of the candidates during solution of hiring problems. The obtained and reviewed results were compared with results obtained using in reality.

基于FUZZY-BN-FTA的厂区架空燃气管道泄漏可能性研究

为研究厂区架空燃气管道泄漏的故的可能性,提出模糊数学方法、贝叶斯网络模型以及故障树模型相结合的集成模型。通过GeNIe软件建立架空燃气管道泄漏事故的模糊贝叶斯网络模型;引入Leaky Noisy-or Gate扩展模型对模糊贝叶斯网络中节点的条件概率表进行修正,结合基本事件先验概率预测架空燃气管道泄漏的概率值,并引入3个基本事件重要度确定基本事件的重要性排序,同时进行敏感性分析确定主要影响因素,提出控制措施。研究结果表明:厂区车辆撞击、管道疲劳损耗、管材质量不佳、安装设计不合理、焊接缺陷为导致架空燃气管道泄漏的主要因素。研究结果可为工业企业安全管理人员有针对性地制定控制措施,减少事故发生率提供参考。

Fuzzy Inventory Model under Selling Price Dependent Demand and Variable Deterioration with Fully Backlogged Shortages

The objective is to develop a model considering demand dependent on selling price and deterioration occurs after a certain period of time, which follows two-parameter Weibull distribution. Shortages are allowed and fully backlogged. Fuzzy optimal solution is obtained by considering hexagonal fuzzy numbers and for defuzzification Graded Mean Integration Representation Method. A numerical example is provided for the illustration of crisp and fuzzy, both models. To observe the effect of changes in parameters, sensitivity analysis is carried out.

A Choquet integral-based TODIM method for q-rung trapezoidal fuzzy numbers and its application in group decision-making

Purpose–The purpose of this paper is to develop a multi-attribute group decision-making(MAGDM)method under the q-rung orthopair trapezoidal fuzzy environment,which calculates the interaction between the criteria depending on the proposed q-rung orthopair trapezoidal fuzzy aggregation Choquet integral(q-ROTrFACI)and employ TODIM(an acronym in Portuguese of Interactive and Multi-criteria Decision Making)to consider the risk psychology of decision-makers,to determine the optimal ranking of alternatives.Design/methodology/approach–In MAGDM,q-rung orthopair trapezoidal fuzzy numbers(q-ROTrFNs)are efficient to indicate the quantitative vagueness of decision-makers.The q-ROTrFACI operator is defined and some properties are proved.Then,a novel similarity measure is developed by fusing the area and coordinates of the q-rung orthopair trapezoidal fuzzy function.Based on the above,a Choquet integral-based TODIM(CI-TODIM)method to consider the risk psychology of decision-makers is proposed and two cases are provided to prove superiority of the method.Findings–The paper investigates q-ROTrFACI operator to productively solve problems with interdependent criteria.Then,an approach is proposed to determine the center point of q–ROTrFNs and a q-rung orthopair trapezoidal fuzzy similarity is constructed.Furthermore,CI-TODIM method is devised based on the proposed q-ROTrFACI operator and similarity in q-rung orthopair trapezoidal fuzzy context.The illustration example of business models’solutions and hypertension health management are given to demonstrate the effectiveness and superiority of proposed method.Originality/value–Thepaperdevelops a novelCI-TODIMmethodthat effectivelysolves the MAGDM problems under the premise of fully considering the priority of criteria and the risk preference of decision-makers,which provides guiding advantages for practical decision-making and enriches the application of decision-making theory.

New Ranking of Generalized Quadrilateral Shape Fuzzy Number Using Centroid Technique

The output of the fuzzy set is reduced by one for the defuzzification procedure.It is employed to provide a comprehensible outcome from a fuzzy inference process.This page provides further information about the defuzzifica-tion approach for quadrilateral fuzzy numbers,which may be used to convert them into discrete values.Defuzzification demonstrates how useful fuzzy ranking systems can be.Our major purpose is to develop a new ranking method for gen-eralized quadrilateral fuzzy numbers.The primary objective of the research is to provide a novel approach to the accurate evaluation of various kinds of fuzzy inte-gers.Fuzzy ranking properties are examined.Using the counterexamples of Lee and Chen demonstrates the fallacy of the ranking technique.So,a new approach has been developed for dealing with fuzzy risk analysis,risk management,indus-trial engineering and optimization,medicine,and artificial intelligence problems:the generalized quadrilateral form fuzzy number utilizing centroid methodology.As you can see,the aforementioned scenarios are all amenable to the solution pro-vided by the generalized quadrilateral shape fuzzy number utilizing centroid methodology.It’s laid out in a straightforward manner that’s easy to grasp for everyone.The rating method is explained in detail,along with numerical exam-ples to illustrate it.Last but not least,stability evaluations clarify why the Gener-alized quadrilateral shape fuzzy number obtained by the centroid methodology outperforms other ranking methods.

Analysis of Syetem Reliability in Manufacturing Cell Based on Triangular Fuzzy Number

Due to lacking of test-data and field-data in reliability research during the design stage of manufacturing cell sys- tem.The degree of manufacturing cell system reliability research is increased.In order to deal with the deficient data and the un- certainty occurred from analysis and judgment,the paper discussed a method for studying reliability of manufacturing cell system through the analysis of fuzzy fault tree,which was based on triangular fuzzy number.At last,calculation case indicated that it would have great significance for ascertaining reliability index,maintenance and establishing keeping strategy towards manufac- turing cell system.

Fuzzy Modeling on L - R Fuzzy Number and Its Application

A new fuzzy modeling method, which based on L - R fuzzy number, is discussed in this paper. First, the fuzzy state equation model is constructed based on fuzzy state variable,fuzzy Input variable and fuzzy output variable whkh are represented by L - R fuzzy number. And then, identification of time - varying parameter in this model is discussed further. At the end, a simulated application is given to Indicate the effectiveness of this fuzzy modeling method.

Approximate Solution of Fuzzy Matrix Equations with LR Fuzzy Numbers

In the paper, a class of fuzzy matrix equations AX=B where A is an m × n crisp matrix and is an m × p arbitrary LR fuzzy numbers matrix, is investigated. We convert the fuzzy matrix equation into two crisp matrix equations. Then the fuzzy approximate solution of the fuzzy matrix equation is obtained by solving two crisp matrix equations. The existence condition of the strong LR fuzzy solution to the fuzzy matrix equation is also discussed. Some examples are given to illustrate the proposed method. Our results enrich the fuzzy linear systems theory.

Sequential Test of Fuzzy Hypotheses

In testing statistical hypotheses, as in other statistical problems, we may be confronted with fuzzy concepts. This paper deals with the problem of testing hypotheses, when the hypotheses are fuzzy and the data are crisp. We first give new definitions for notion of mass (density) probability function with fuzzy parameter, probability of type I and type II errors and then state and prove the sequential probability ratio test, on the basis of these new errors, for testing fuzzy hypotheses. Numerical examples are also provided to illustrate the approach.

Understanding the financial innovation priorities for renewable energy investors via QFD-based picture fuzzy and rough numbers

This study evaluates financial innovation priorities for renewable energy investors by generating a novel hybrid fuzzy decision-making model.First,SERVQUAL-based customer needs for financial innovation are weighted with decision-making trial and evaluation laboratory based on picture fuzzy sets.Second,the financial innovation priorities are ranked by technique for order preference by similarity to ideal solutions based on picture fuzzy rough sets.In this process,Theory of the solution of inventive problems-based technical characteristics for financial services,the process for innovative services,and competencies for financial innovation are considered using quality function deployment phases.In addition,the Vise Kriterijumska Optimizacija I Kompromisno Resenje method is also considered for an alternative ranking.Similarly,sensitivity analysis is also performed by considering five different cases.It is determined that the ranking priorities based on the proposed model are almost identical,demonstrating the proposed model’s validity and reliability.Assurance is the most crucial factor for the customer needs regarding the financial innovation priorities for renewable energy investors.Concerning the financial innovation priorities,the product is the essential priority for financial innovation;hence,it is recommended that companies engage qualified employees to effectively design the financial innovation for renewable energy investors.Additionally,necessary training should be given to the employees who currently work in the company,which can increase the renewable energy investors’trust in the innovative financial products.Companies should mainly focus on the product to provide better financial innovation to attract renewable energy investors.An effectively designed financial innovation product can help solve the financing problem of renewable energy investors.

Numerical investigation on MHD Jeffery-Hamel nanofluid flow with different nanoparticles using fuzzy extension of generalized dual parametric homotopy algorithm

This study considers an MHD Jeffery-Hamel nanofluid flow with distinct nanoparticles such as copper,Al_(2)O_(3)and SiO_(2)between two rigid non-parallel plane walls with the fuzzy extension of the generalized dual parametric homotopy algorithm.The nanofluids have been formulated to enhance the thermophysical characteristics of fluids,including thermal diffusivity,conductivity,convective heat transfer coefficients and viscosity.Due to the presence of distinct nanofluids,a change in the value of volume fraction occurs that influences the velocity profiles of the flow.The short value of nanoparticles volume fraction is considered an uncertain parameter and represented in a triangular fuzzy number range among[0.0,0.1,0.2].A novel generalized dual parametric homotopy algorithm with fuzzy extension is used here to study the fuzzy velocities at various channel positions.Finally,the effectiveness of the proposed approach has been demonstrated through a comparison with the available results in the crisp case.