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.

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.

Entropy-based procedures for intuitionistic fuzzy multiple attribute decision making

The class of multiple attribute decision making （MADM） problems is studied, where the attribute values are intuitionistic fuzzy numbers, and the information about attribute weights is completely unknown. A score function is first used to calculate the score of each attribute value and a score matrix is constructed, and then it is transformed into a normalized score matrix. Based on the normalized score matrix, an entropy-based procedure is proposed to derive attribute weights. Furthermore, the additive weighted averaging operator is utilized to fuse all the normalized scores into the overall scores of alternatives, by which the ranking of all the given alternatives is obtained. This paper is concluded by extending the above results to interval-valued intuitionistic fuzzy set theory, and an illustrative example is also provided.

Solving Intuitionistic Fuzzy Linear Programming Problem

Intuitionistic Fuzzy Set (IFS) can be used as a general tool for modeling problems of decision making under uncertainty where, the degree of rejection is defined simultaneously with the degree of acceptance of a piece of information in such a way that these degrees are not complement to each other. Accordingly, an attempt is made to solve intuitionistic fuzzy linear programming problems using a technique based on an earlier technique proposed by Zimmermann to solve fuzzy linear programming problem. Our proposed technique does not require the existing ranking of intuitionistic fuzzy numbers. This method is also different from the existing weight assignment method or the Angelov’s method. A comparative study is undertaken and interesting results have been presented.

Solution of Matrix Game with Triangular Intuitionistic Fuzzy Pay-Off Using Score Function

Using score function in a matrix game is very rare. In the proposed paper we have considered a matrix game with pay-off as triangular intuitionistic fuzzy number and a new ranking order has been proposed using value judgement index, available definitions and operations. A new concept of score function has been developed to defuzzify the pay-off matrix and solution of the matrix game has been obtained. A numerical example has been given in support of the proposed method.

Solving Intuitionistic Fuzzy Linear Programming Problem—II

Under non-random uncertainty, a new idea of finding a possibly optimal solution for linear programming problem is examined in this paper. It is an application of the intuitionistic fuzzy set concept within scope of the existing fuzzy optimization. Here, we solve a linear programming problem (LPP) in an intuitionistic fuzzy environment and compare the result with the solution obtained from other existing techniques. In the process, the result of associated fuzzy LPP is also considered for a better understanding.

Derivatives and differentials for multiplicative intuitionistic fuzzy information

By using the unsymmetrical scale instead of the symmetrical scale,the multiplicative intuitionistic fuzzy sets(MIFSs) reflect our intuition more objectively.Each element in a MIFS is expressed by an ordered pair which is called a multiplicative intuitionistic fuzzy number(MIFN)and is based on the unbalanced scale(i.e.,Saaty’s 1-9 scale).In order to describe the derivatives and differentials for multiplicative intuitionistic fuzzy information more comprehensively,in this paper,we firstly propose two new basic operational laws for MIFNs,which are the subtraction law and the division law.Secondly,we describe the change values of MIFNs when considering them as variables,classify these change values based on the basic operational laws for MIFNs,and depict the convergences of sequences of MIFNs by the subtraction and division laws.Finally,we focus on the multiplicative intuitionistic fuzzy functions and derive some basic results related to their continuities,derivatives and differentials,and also give their application in selecting the configuration of a computer.

基于直觉模糊n-cell数的多属性决策方法及应用

针对权重已知的直觉模糊多属性决策问题,提出了一种基于直觉模糊n-cell数的决策方法。定义了直觉模糊n-cell数的偏序和两种基于均值和离散度的弱序。研究了所提出序的理论性质,并进行比较分析。最后,将相关排序方法应用于一类人才选拔的问题之中,在解决问题的同时验证了方法的有效性。

基于模糊DEMATEL-超效率DEA的可再生能源发电技术综合效益评估方法

“双碳”目标下,各类可再生能源发电技术发展迅速,综合权衡不同可再生能源发电方案的综合效益对可再生能源的优化设计具有重要意义。综合考虑经济效益、环境效益、能源效益和社会效益4个层面,提出了一种基于模糊决策试验和评价实验(decision making trial and evaluation laboratory,DEMATEL)与超效率数据包络分析(data envelopment analysis,DEA)模型的可再生能源发电技术综合效益评估方法。该方法分为投入-产出指标体系构建和综合评估2个阶段。首先,利用三角直觉模糊数处理模糊评价信息,将其与DEMATEL相结合量化各指标之间相互影响关系,基于指标间逻辑分析结果建立投入-产出评估指标体系。然后,基于超效率DEA模型对各可再生能源发电方案进行评估排序,结合投入冗余和产出不足分析结果给出各方案的针对性改善建议,以期为进一步选择和确定可再生能源产业发展战略提供参考。最后以某省10类可再生能源发电单元为研究对象,基于所提研究方法进行综合评估和分析,并与多准则妥协解排序法和熵权法进行对比分析,验证了所提方法的有效性。

基于直觉模糊环境的海上风机选型

选择合适的海上风力发电机机型对海上风电场的长期高效运行起着至关重要的作用。针对决策者在风机选型决策过程中存在不确定性和主观偏好等问题,提出一种改进的多准则决策(multi-criteria decision making, MCDM)框架及方法:在权重求解算法中将群体决策和直觉模糊数与层次分析法相结合,提出群体直觉模糊层次分析法(group intuitionistic fuzzy analytic hierarchy process, GIAHP)计算指标权重;在备选方案排序算法中将余弦距离引入接近理想点法(technique for order preference by similarity to an ideal solution, TOPSIS),提出多距离TOPSIS确定备选方案排序。最后以山东省海上风电场风机选型为例,并通过敏感性分析验证框架及方法的鲁棒性。该框架及方法为中国海上风电场风机选型提供理论依据,可确保海上风电场长期稳定运行。

基于三角直觉模糊数的多阶段任务系统可靠性评估

针对多阶段任务系统(Phased Mission System,PMS)可靠性评估中对系统或部件退化规律认识不清、主观知识不完备、环境变化等原因造成部件的信息不足或不精确问题,基于三角直觉模糊数(Triangular Intuitionistic Fuzzy Number,TIFN)和二元决策图(Binary Decision Diagram,BDD)模型,提出了一种PMS可靠性评估方法。首先,定义了TIFN的指数运算法则,证明了其满足的性质;其次,通过多位专家对部件平均故障时间(Mean Time to Failure,MTTF)进行评估,利用TIFN量化专家意见,建立了直觉模糊失效率评估模型,构建了一种计算TIFN的隶属度和非隶属度的方法,根据TIFN的运算法则和指数分布函数定义了部件的模糊失效函数;最后,运用示例说明了该方法的有效性,并与传统PMS-BDD方法、模糊故障树方法和直觉模糊故障树方法进行了对比分析。

基于直觉Fuzzy关系的综合决策

借助K .Atanassov提出的直觉Fuzzy集 ,推广原有的Fuzzy综合决策模型 ,给出基于直觉Fuzzy关系的综合决策模型 .

区间值直觉Fuzzy度量空间及其完备性

给出区间值直觉Fuzzy数的定义 ,并引入区间值直觉Fuzzy数间的区间值直觉Fuzzy距离 ,建立区间值直觉Fuzzy度量空间并讨论其完备性 .

基于模糊多属性群决策理论的课堂教学质量评价研究

考虑学生给定评价信息时的犹豫特性、学生主体之间的差异性以及信息共享的关联性,采用直觉梯形模糊数转换学生群体给定的评价信息,引入模糊测度和Shapley函数值处理存在关联性学生群体的客观权重,并由此构建基于模糊多属性群决策理论的教师课堂教学评价模型,以便于科学、合理地对高校教师课堂教学进行综合评价。

基于改进TOPSIS的三角直觉模糊多属性群决策方法

针对属性值为三角直觉模糊数,决策者权重已知的多属性群决策问题,提出基于灰色关联度的TOPSIS多属性群决策方法。首先根据决策者对各个属性的打分评级结果,将模糊的语言变量转化为三角直觉模糊数,集结决策者评价信息矩阵,基于属性值离差最大化求出各属性的权重向量,计算备选方案加权决策矩阵;其次,引入灰色关联度,基于模糊正理想点和模糊负理想点计算每个备选方案的灰色关联度,计算每个备选方案的相对贴近度,从而确定每个备选方案的顺序;最后,通过实例分析,验证该方法的有效性。

改进的直觉模糊得分函数及其决策应用

直觉模糊数之间的比较问题一直都是直觉模糊决策理论的核心课题。针对已有得分函数区分能力不足、构造过于复杂等问题,从全新视角出发,提出新的直觉模糊得分函数,并对其适用性进行必要拓展,定义了用于定量比较两个直觉模糊数区分程度的新可能度公式;基于所提公式,构建了适用于直觉模糊环境的新型多属性决策方法,并将其应用于具体的决策实践。理论分析和实验结果表明,新得分函数是对Ata-nassov偏序关系的精炼,能够在直觉模糊数集中建立起更为合理、可信的弱序关系;所提公式具有一定优势,能够有效拓展所提得分函数的适用性;基于可能度矩阵构建的直觉模糊多属性决策方法在决策过程中具有较强的自检能力,能够通过保证决策过程的正确性来确保最终结果的可靠性,且便于大规模决策运用。

直觉模糊多目标证券投资组合决策

针对证券投资产品收益的直觉模糊不确定性,运用直觉模糊数来弹性评估投资产品预期收益,并通过直觉模糊可能性均值和方差来度量投资组合收益和风险。接着基于投资组合收益最大和风险最小及信息熵最小等多个目标构建一个新的直觉模糊投资组合决策模型,进而再运用线性加权方法将其转化为单目标模型来快速获取最优投资组合策略。最后通过真实股票投资实例表明该投资组合模型方法的有效性,且投资者可根据不同目标偏好适时调整优化投资策略。

多层次直觉Fuzzy综合决策及其应用

借助K.A tanassov提出的直觉Fuzzy集和直觉Fuzzy关系,在直觉Fuzzy关系的基础上提出多层次综合决策模型,并用于解决实际问题.