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.

Dynamic Analysis of Customer Demand Based on Intuitionistic Fuzzy Number in Product Planning

To address the fuzziness and variability in determining customer demand importance,a dynamic analysis method based on intuitionistic fuzzy numbers is proposed.First,selected customers use intuitionistic fuzzy numbers to represent the importance of each demand.Then,the preference information is aggregated using customer weights and time period weights through the intuitionistic fuzzy ordered weighted average operator,yielding a dynamic vector of the subjective importance of the demand index.Finally,the feasibility of the proposed method is demonstrated through an application example of a vibrating sorting screen.

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.

New two-dimensional fuzzy C-means clustering algorithm for image segmentation

To solve the problem of poor anti-noise performance of the traditional fuzzy C-means (FCM) algorithm in image segmentation, a novel two-dimensional FCM clustering algorithm for image segmentation was proposed. In this method, the image segmentation was converted into an optimization problem. The fitness function containing neighbor information was set up based on the gray information and the neighbor relations between the pixels described by the improved two-dimensional histogram. By making use of the global searching ability of the predator-prey particle swarm optimization, the optimal cluster center could be obtained by iterative optimization, and the image segmentation could be accomplished. The simulation results show that the segmentation accuracy ratio of the proposed method is above 99%. The proposed algorithm has strong anti-noise capability, high clustering accuracy and good segment effect, indicating that it is an effective algorithm for image segmentation.

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。

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.

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.

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.

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.

Effect of Particle Number Density on Wave Dispersion in a Two-Dimensional Yukawa System

Effect of the particle number density on the dispersion properties of longitudinal and transverse lattice waves in a two-dimensional Yukawa charged-dust system is investigated using molecular dynamics simulation. The dispersion relations for the waves are obtained. It is found that the frequencies of both the longitudinal and transverse dust waves increase with the density and when the density is sufficiently high a cutoff region appears at the short wavelength. With the increase of the particle number density, the common frequency tends to increase, and the sound speed of the longitudinal wave also increases, but that of the transverse wave remains low.

Cardinal Numbers of Fuzzy Sets

Up to now, the study on the cardinal number of fuzzy sets has advanced at on pace since it is very hard to give it an appropriate definition. Althrough for it in [1], it is with some harsh terms and is not reasonable as we point out in this paper. In the paper, we give a general definition of fuzzy cardinal numbers. Based on this definition, we not only obtain a large part of results with re spect to cardinal numbers, but also give a few of new properties of fuzzy cardinal numbers.

Reasoning complexity for extended fuzzy description logic with qualifying number restriction

To solve the extended fuzzy description logic with qualifying number restriction （EFALCQ） reasoning problems, EFALCQ is discretely simulated by description logic with qualifying number restriction （ALCQ）, and ALCQ reasoning results are reused to prove the complexity of EFALCQ reasoning problems. The ALCQ simulation method for the consistency of EFALCQ is proposed. This method reduces EFALCQ satisfiability into EFALCQ consistency, and uses EFALCQ satisfiability to discretely simulate EFALCQ satdomain. It is proved that the reasoning complexity for EFALCQ satisfiability, consistency and sat-domain is PSPACE-complete.

A New Method of Ranking Fuzzy Number Based on α-Cut

This paper presents a new method of comparing or ranking of interval and fuzzy numbers. Based on another way of understanding fuzzy concept, the paper proposes the concept of number meaning of interval and the comparison method of interval. The paper defines the new ranking method by the α cut intervals of fuzzy number, and proves that the new inequality relation of fuzzy numbers is transitive. Our approach is a simple way of considering all the existence levels and can be calculated at different exact level according to different applications.

Design of fuzzy number recognition based on embedded system platform

A system of number recognition with a graphic user interface （GUI） is implemented on the embedded development platform by using the fuzzy pattern recognition method. An application interface （API） of uC/ OS-Ⅱ is used to implement the features of multi-task concurrency and the communications among tasks. Handwriting function is implemented by the improvement of the interface provided by the platform. Fuzzy pattern recognition technology based on fuzzy theory is used to analyze the input of handwriting. A primary system for testing is implemented. It can receive and analyze user inputs from both keyboard and touch-screen. The experimental results show that the embedded fuzzy recognition system which uses the technology which integrates two ways of fuzzy recognition can retain a high recognition rate and reduce hardware requirements.

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.

Fuzzy Semi-continuity of fuzzy number-valued function

In this paper we discuss the conecept and property of fuzzy semi continuous function.

A METHOD OF SOLVING THE FUZZY FINITE ELEMENT EQUATIONS IN MONOSOURCE FUZZY NUMBERS

For same cases the rules of monosource fuzzy numbers con be used into the solution of fuzzy stochastic finite element equations in engineering. This method can reduce the computing quantity of the solution. It can be proved that the amount of the solution is nearly as much as that with the general stochastic finite element method (SFEM). In addition, a new method to appreciate the structural fuzzy failure probability is presented for the needs of the modem engineering design.

Evaluating the conceptual design schemes of complex products based on FAHP using fuzzy number

In the conceptual design stage of complex products, CBR（Case-Based Reasoning） tool is useful to offer a feasible set of schemes. Then the most adaptive scheme can be generated through a procedure of comparison and evaluation. The procedure is essentially a multiple criteria decision-making problem. The traditional multiple criteria programming is not flexible enough in executing the system evaluation algorithm due to both the limited experimental data and the lack of human experiences. To make the CBR tool to be more efficient, a new method for the best choice among the feasible schemes based on the Fuzzy AHP using Fuzzy numbers （FFAHP） is proposed. Since the final results become a problem of ranking the mean of fuzzy numbers by the optimism of decision-maker using the FFAHP, its execution is much more intuitive and effective than with the traditional method.

Ranking Method for Complementary Judgment Matrixes with Fuzzy Numbers Based on Hausdorff Metric Distance

A method for ranking complementary judgment matrixes with traspezoidal fuzzy numbers based on Hausdorff metric distance and fuzzy compromise decision approach is proposed. With regard to fuzzy number complementary judgment matrixes given by a decider group whose members have various weights, the expert＇s information was aggregated first by means of simple weight average（SWA） method and Bonissone calculational method. Hence a matrix including all the experts＇ preference information was got. Then the matrix＇ column members were added up and the fuzzy evaluation values of the alternatives were got. Lastly, the Hausdorff metric distance and fuzzy compromise decision approach were used to rank the fuzzy evaluation values and then the ranking values of all the alternatives were got. Because exact numbers and triangular fuzzy numbers could all be transformed into trapezoidal fuzzy numbers, the method developed can rank complementary judgment matrixes with trapezoidal fuzzy numbers, triangular fuzzy numbers and exact numbers as well. An illustrative example is also given to verify the developed method and to demonstrate its feasibility and practicality.