Fully Completed Spherical Fuzzy Approach-Based Z Numbers(PHIModel)for Enhanced Group Expert Consensus

This study aims to establish an expert consensus and enhance the efficacy of decision-making processes by integrating Spherical Fuzzy Sets(SFSs)and Z-Numbers(SFZs).A novel group expert consensus technique,the PHImodel,is developed to address the inherent limitations of both SFSs and the traditional Delphi technique,particularly in uncertain,complex scenarios.In such contexts,the accuracy of expert knowledge and the confidence in their judgments are pivotal considerations.This study provides the fundamental operational principles and aggregation operators associated with SFSs and Z-numbers,encompassing weighted geometric and arithmetic operators alongside fully developed operators tailored for SFZs numbers.Subsequently,a case study and comparative analysis are conducted to illustrate the practicality and effectiveness of the proposed operators and methodologies.Integrating the PHI model with SFZs numbers represents a significant advancement in decision-making frameworks reliant on expert input.Further,this combination serves as a comprehensive tool for decision-makers,enabling them to achieve heightened levels of consensus while concurrently assessing the reliability of expert contributions.The case study results demonstrate the PHI model’s utility in resolving complex decision-making scenarios,showcasing its ability to improve consensus-building processes and enhance decision outcomes.Additionally,the comparative analysis highlights the superiority of the integrated approach over traditional methodologies,underscoring its potential to revolutionize decision-making practices in uncertain environments.

Pythagorean Fuzzy Einstein Aggregation Operators with Z-Numbers:Application in Complex Decision Aid Systems

The primary goal of this research is to determine the optimal agricultural field selection that would most effectively support manufacturing producers in manufacturing production while accounting for unpredictability and reliability in their decision-making.The PFS is known to address the levels of participation and non-participation.To begin,we introduce the novel concept of a PFZN,which is a hybrid structure of Pythagorean fuzzy sets and the ZN.The PFZN is graded in terms of membership and non-membership,as well as reliability,which provides a strong advice in real-world decision support concerns.The PFZN is a useful tool for dealing with uncertainty in decision-aid problems.The PFZN is a practical way for dealing with such uncertainties in decision-aid problems.The list of aggregation operators:PFZN Einstein weighted averaging and PFZN Einstein weighted geometric,is established under the novel Pythagorean fuzzy ZNs.It is a more precise mathematical instrument for dealing with precision and uncertainty.The core of this research is to develop a numerical algorithmto tackle the uncertainty in real-life problems using PFZNs.To show the applicability and effectiveness of the proposed algorithm,we illustrate the numerical case study related to determining the optimal agricultural field.The main purpose of this work is to describe the extended EDAS approach,then compare the proposed methodology with many other methodologies now in use,and then demonstrate how the suggested methodology may be applied to real-world problems.In addition,the final ranking results that were obtained by the devised techniques weremore efficient and dependable in comparison to the results provided by other methods presented in the literature.

Application of Intuitionistic Z-Numbers in Supplier Selection

Intuitionistic fuzzy numbers incorporate the membership and non-membership degrees.In contrast,Z-numbers consist of restriction components,with the existence of a reliability component describing the degree of certainty for the restriction.The combination of intuitionistic fuzzy numbers and Z-numbers produce a new type of fuzzy numbers,namely intuitionistic Z-numbers(IZN).The strength of IZN is their capability of better handling the uncertainty compared to Zadeh's Z-numbers since both components of Z-numbers are charac-terized by the membership and non-membership functions,exhibiting the degree of the hesitancy of decision-makers.This paper presents the application of such numbers in fuzzy multi-criteria decision-making problems.A decision-making model is proposed using the trapezoidal intuitionistic fuzzy power ordered weighted average as the aggregation function and the ranking function to rank the alternatives.The proposed model is then implemented in a supplier selection problem.The obtained ranking is compared to the existing models based on Z-numbers.The results show that the ranking order is slightly different from the existing models.Sensitivity analysis is performed to validate the obtained ranking.The sensitivity analysis result shows that the best supplier is obtained using the proposed model with 80%to 100%consistency despite the drastic change of criteria weights.Intuitionistic Z-numbers play a very important role in describing the uncertainty in the decision makers’opinions in solving decision-making problems.

基于Z-number模糊数的管理信息系统开发项目缓冲区研究

为提高管理信息系统(MIS)开发项目管理的效率,同时优化项目缓冲的估算精度,从工期估计和缓冲区计算两方面对关键链缓冲区计算进行优化。通过Z-number模糊数的引入,更加有效地表达工期估算的不确定性;同时定义高延期风险性活动,并根据项目活动不确定性对缓冲区计算方法进行改进。最后通过一个具体的MIS开发案例,将研究提出的方法与传统缓冲区设置方法进行对比,结果表明新的缓冲区设置方法可以保证有足够的项目缓冲来吸收项目的各种不确定性,并具有较高的完工率。

Application of Operational Approaches to Solving Decision Making Problem Using Z-Numbers

The combination of fuzzy logic tools and multi-criteria decision making has a great relevance in literature. Compared with the classical fuzzy number, Z-number has more ability to describe the human knowledge. It can describe both restraint and reliability. Prof. L. Zadeh introduced the concept of Z-numbers to describe the uncertain information which is a more generalized notion closely related to reliability. Use of Z-information is more adequate and intuitively meaningful for formalizing information of a decision making problem. In this paper, Z-number is applied to solve multi-criteria decision making problem. In this paper, we consider two approaches to decision making with Z-information. The first approach is based on converting the Z-numbers to crisp number to determine the priority weight of each alternative. The second approach is based on Expected utility theory by using Z-numbers. To illustrate a validity of suggested approaches to decision making with Z-information the numerical examples have been used.

A Review on Ranking of Z-numbers

There are numerous studies about Z-numbers since its inception in 2011.Because Z-number concept reflects human ability to make rational decisions,Z-number based multi-criteria decision making problems are one of these studies.When the problem is translated from linguistic information into Z-number domain,the important question occurs that which Z-number should be selected.To answer this question,several ranking methods have been proposed.To compare the performances of these methods,benchmark set of fuzzy Z-numbers has been created in time.There are relatively new methods that their performances are not examined yet on this benchmark problem.In this paper,we worked on these studies which are relative entropy based Z-number ranking method and a method for ranking discrete Z-numbers.The authors tried to examine their performances on the benchmark problem and compared the results with the other ranking algorithms.The results are consistent with the literature,mostly.The advantages and the drawbacks of the methods are presented which can be useful for the researchers who are interested in this area.

TODIM and TOPSIS with Z-numbers

In this paper, we present an approach that can handle Z-numbers in the context of multi-criteria decision-making problems. The concept of Z-number as an ordered pair Z=(A, B) of fuzzy numbers A and B is used, where A is a linguistic value of a variable of interest and B is a linguistic value of the probability measure of A. As human beings, we communicate with each other by means of natural language using sentences like "the journey from home to university most likely takes about half an hour." The Z-numbers are converted to fuzzy numbers. Then the Z-TODIM and Z-TOPSIS are presented as a direct extension of the fuzzy TODIM and fuzzy TOPSIS, respectively. The proposed methods are applied to two case studies and compared with the standard approach using crisp values. The results obtained show the feasibility of the approach.

模糊理论在机械设计中的应用

机械设计中的模糊现象是普遍存在的。传统的设计模型不能恰当描述设计中的模糊性 ,因而未能提供有效的处理带模糊性的设计问题的办法。这里应用模糊数学理论 ,针对模糊设计计算问题 ,提出了基于模糊数的设计计算方法 ,并给出了具体的设计计算实例。

基于模糊数学综合评价法优化椒麻鸡片调理食品的开发

以川菜的传统椒麻味型调制为基础,开发出椒麻鸡片调理食品。试验采用模糊数学综合评价法,对影响椒麻味型复合调味料品质的主要因素进行评定。结果表明,制作椒麻味型调味料包的最佳配方为:以加工100g鸡脯肉制作椒麻鸡片为准,青花椒1g、小葱叶5g、鲜汤15mL、食盐1g、酱油2mL、香油8mL、味精0.3g。该椒麻鸡片的营养成分含量为:能量648.3kJ、蛋白质14.6g、脂肪11.3g、碳水化合物3.3g、钠455.4mg。