A vague-set-based fuzzy multi-objective decision making model for bidding purchase

A vague-set-based fuzzy multi-objective decision making model is developed for evaluating bidding plans in a bid- ding purchase process. A group of decision-makers (DMs) first independently assess bidding plans according to their experience and preferences, and these assessments may be expressed as linguistic terms, which are then converted to fuzzy numbers. The resulting decision matrices are then transformed to objective membership grade matrices. The lower bound of satisfaction and upper bound of dissatisfaction are used to determine each bidding plan’s supporting, opposing, and neutral objective sets, which together determine the vague value of a bidding plan. Finally, a score function is employed to rank all bidding plans. A new score function based on vague sets is introduced in the model and a novel method is presented for calculating the lower bound of sat- isfaction and upper bound of dissatisfaction. In a vague-set-based fuzzy multi-objective decision making model, different valua- tions for upper and lower bounds of satisfaction usually lead to distinct ranking results. Therefore, it is crucial to effectively contain DMs’ arbitrariness and subjectivity when these values are determined.

Fuzzy Multi-Objective Decision Model of Supplier Selection with Preference Information

Supplier selection is a multi-objective decision problem, which must be considered many objectives, some objectives are qualitative, and others are quantitative. Meanwhile, manufacturer has preference for different suppliers. In this paper, a new multi-objective decision model with preference information of supplier is established. A practical example of supplier selection problem utilizing this model is studied. The result demonstrates the feasibility and effectiveness of the methods proposed in the paper.

Multi-Objective Optimization Algorithm for Grouping Decision Variables Based on Extreme Point Pareto Frontier

The existing algorithms for solving multi-objective optimization problems fall into three main categories:Decomposition-based,dominance-based,and indicator-based.Traditional multi-objective optimization problemsmainly focus on objectives,treating decision variables as a total variable to solve the problem without consideringthe critical role of decision variables in objective optimization.As seen,a variety of decision variable groupingalgorithms have been proposed.However,these algorithms are relatively broad for the changes of most decisionvariables in the evolution process and are time-consuming in the process of finding the Pareto frontier.To solvethese problems,a multi-objective optimization algorithm for grouping decision variables based on extreme pointPareto frontier(MOEA-DV/EPF)is proposed.This algorithm adopts a preprocessing rule to solve the Paretooptimal solution set of extreme points generated by simultaneous evolution in various target directions,obtainsthe basic Pareto front surface to determine the convergence effect,and analyzes the convergence and distributioneffects of decision variables.In the later stages of algorithm optimization,different mutation strategies are adoptedaccording to the nature of the decision variables to speed up the rate of evolution to obtain excellent individuals,thusenhancing the performance of the algorithm.Evaluation validation of the test functions shows that this algorithmcan solve the multi-objective optimization problem more efficiently.

Large-Scale Multi-Objective Optimization Algorithm Based on Weighted Overlapping Grouping of Decision Variables

The large-scale multi-objective optimization algorithm(LSMOA),based on the grouping of decision variables,is an advanced method for handling high-dimensional decision variables.However,in practical problems,the interaction among decision variables is intricate,leading to large group sizes and suboptimal optimization effects;hence a large-scale multi-objective optimization algorithm based on weighted overlapping grouping of decision variables(MOEAWOD)is proposed in this paper.Initially,the decision variables are perturbed and categorized into convergence and diversity variables;subsequently,the convergence variables are subdivided into groups based on the interactions among different decision variables.If the size of a group surpasses the set threshold,that group undergoes a process of weighting and overlapping grouping.Specifically,the interaction strength is evaluated based on the interaction frequency and number of objectives among various decision variables.The decision variable with the highest interaction in the group is identified and disregarded,and the remaining variables are then reclassified into subgroups.Finally,the decision variable with the strongest interaction is added to each subgroup.MOEAWOD minimizes the interactivity between different groups and maximizes the interactivity of decision variables within groups,which contributed to the optimized direction of convergence and diversity exploration with different groups.MOEAWOD was subjected to testing on 18 benchmark large-scale optimization problems,and the experimental results demonstrate the effectiveness of our methods.Compared with the other algorithms,our method is still at an advantage.

Method for triangular fuzzy multiple attribute decision making based on two-dimensional density operator method

Aiming at the triangular fuzzy(TF)multi-attribute decision making(MADM)problem with a preference for the distribution density of attribute(DDA),a decision making method with TF number two-dimensional density(TFTD)operator is proposed based on the density operator theory for the decision maker(DM).Firstly,a simple TF vector clustering method is proposed,which considers the feature of TF number and the geometric distance of vectors.Secondly,the least deviation sum of squares method is used in the program model to obtain the density weight vector.Then,two TFTD operators are defined,and the MADM method based on the TFTD operator is proposed.Finally,a numerical example is given to illustrate the superiority of this method,which can not only solve the TF MADM problem with a preference for the DDA but also help the DM make an overall comparison.

Attribute Reduction of Hybrid Decision Information Systems Based on Fuzzy Conditional Information Entropy

The presence of numerous uncertainties in hybrid decision information systems(HDISs)renders attribute reduction a formidable task.Currently available attribute reduction algorithms,including those based on Pawlak attribute importance,Skowron discernibility matrix,and information entropy,struggle to effectively manages multiple uncertainties simultaneously in HDISs like the precise measurement of disparities between nominal attribute values,and attributes with fuzzy boundaries and abnormal values.In order to address the aforementioned issues,this paper delves into the study of attribute reduction withinHDISs.First of all,a novel metric based on the decision attribute is introduced to solve the problem of accurately measuring the differences between nominal attribute values.The newly introduced distance metric has been christened the supervised distance that can effectively quantify the differences between the nominal attribute values.Then,based on the newly developed metric,a novel fuzzy relationship is defined from the perspective of“feedback on parity of attribute values to attribute sets”.This new fuzzy relationship serves as a valuable tool in addressing the challenges posed by abnormal attribute values.Furthermore,leveraging the newly introduced fuzzy relationship,the fuzzy conditional information entropy is defined as a solution to the challenges posed by fuzzy attributes.It effectively quantifies the uncertainty associated with fuzzy attribute values,thereby providing a robust framework for handling fuzzy information in hybrid information systems.Finally,an algorithm for attribute reduction utilizing the fuzzy conditional information entropy is presented.The experimental results on 12 datasets show that the average reduction rate of our algorithm reaches 84.04%,and the classification accuracy is improved by 3.91%compared to the original dataset,and by an average of 11.25%compared to the other 9 state-of-the-art reduction algorithms.The comprehensive analysis of these research results clearly indicates that our algorithm is highly effective in managing the intricate uncertainties inherent in hybrid data.

Improved Fuzzification Method for Multi-Objective Decision-Making and Its Application in Evaluation of Highway Planning

A new fuzzification method for multi-objective decision-making and selective sorting is proposed on the basis of the fuzzy consistent relation, and the specific algorithm is presented. The method is applied to the evaluation of highway planning of Zhanjiang city. To decrease the subjectivity in the process of decision-making, the LOWA operator is introduced, and a discussion on how to select appropriate weights involved in multi-objective sorting is made. It is concluded that it is feasible to apply the fuzzy consistent relation to multi-objective decision-making analysis, and the improved fuzzication method is workable.

Three-Way Behavioral Decision Making With Hesitant Fuzzy Information Systems:Survey and Challenges

Three-way decision(T-WD)theory is about thinking,problem solving,and computing in threes.Behavioral decision making(BDM)focuses on effective,cognitive,and social processes employed by humans for choosing the optimal object,of which prospect theory and regret theory are two widely used tools.The hesitant fuzzy set(HFS)captures a series of uncertainties when it is difficult to specify precise fuzzy membership grades.Guided by the principles of three-way decisions as thinking in threes and integrating these three topics together,this paper reviews and examines advances in three-way behavioral decision making(TW-BDM)with hesitant fuzzy information systems(HFIS)from the perspective of the past,present,and future.First,we provide a brief historical account of the three topics and present basic formulations.Second,we summarize the latest development trends and examine a number of basic issues,such as one-sidedness of reference points and subjective randomness for result values,and then report the results of a comparative analysis of existing methods.Finally,we point out key challenges and future research directions.

A New Kind of Generalized Pythagorean Fuzzy Soft Set and Its Application in Decision-Making

The aim of this paper is to introduce the concept of a generalized Pythagorean fuzzy soft set(GPFSS),which is a combination of the generalized fuzzy soft sets and Pythagorean fuzzy sets.Several of important operations of GPFSS including complement,restricted union,and extended intersection are discussed.The basic properties of GPFSS are presented.Further,an algorithm of GPFSSs is given to solve the fuzzy soft decision-making.Finally,a comparative analysis between the GPFSS approach and some existing approaches is provided to show their reliability over them.

The Correlation Coefficient of Hesitancy Fuzzy Graphs in Decision Making

The hesitancy fuzzy graphs(HFGs),an extension of fuzzy graphs,are useful tools for dealing with ambiguity and uncertainty in issues involving decision-making(DM).This research implements a correlation coefficient measure(CCM)to assess the strength of the association between HFGs in this article since CCMs have a high capacity to process and interpret data.The CCM that is proposed between the HFGs has better qualities than the existing ones.It lowers restrictions on the hesitant fuzzy elements’length and may be used to establish whether the HFGs are connected negatively or favorably.Additionally,a CCMbased attribute DM approach is built into a hesitant fuzzy environment.This article suggests the use of weighted correlation coefficient measures(WCCMs)using the CCM concept to quantify the correlation between two HFGs.The decisionmaking problems of hesitancy fuzzy preference relations(HFPRs)are considered.This research proposes a new technique for assessing the relative weights of experts based on the uncertainty of HFPRs and the correlation coefficient degree of each HFPR.This paper determines the ranking order of all alternatives and the best one by using the CCMs between each option and the ideal choice.In the meantime,the appropriate example is given to demonstrate the viability of the new strategies.

Novel Decision Making Methodology under Pythagorean Probabilistic Hesitant Fuzzy Einstein Aggregation Information

This research proposes multicriteria decision-making(MCDM)-based real-time Mesenchymal stem cells(MSC)transfusion framework.The testing phase of the methodology denotes the ability to stick to plastic surfaces,the upregulation and downregulation of certain surface protein markers,and lastly,the ability to differentiate into various cell types.First,two scenarios of an enhanced dataset based on a medical perspective were created in the development phase to produce varying levels of emergency.Second,for real-timemonitoring ofCOVID-19 patients with different emergency levels(i.e.,mild,moderate,severe,and critical),an automated triage algorithmbased on a formal medical guideline is proposed,taking into account the improvement and deterioration procedures fromone level to the next.For this strategy,Einstein aggregation information under the Pythagorean probabilistic hesitant fuzzy environment(PyPHFE)is developed.Einstein operations on PyPHFE such as Einstein sum,product,scalar multiplication,and their properties are investigated.Then,several Pythagorean probabilistic hesitant fuzzy Einstein aggregation operators,namely the Pythagorean probabilistic hesitant fuzzy weighted average(PyPHFWA)operator,Pythagorean probabilistic hesitant fuzzy Einstein weighted geometric(PyPHFEWG)operator,Pythagorean probabilistic hesitant fuzzy Einstein ordered weighted average(PyPHFEOWA)operator,Pythagorean probabilistic hesitant fuzzy Einstein ordered weighted geometric(PyPHFEOWG)operator,Pythagorean probabilistic hesitant fuzzy Einstein hybrid average(PyPHFEHA)operator and Pythagorean probabilistic hesitant fuzzy Einstein hybrid geometric(PyPHFEHG)operator are investigated.All the above-mentioned operators are helpful in design the algorithm to tackle uncertainty in decision making problems.In last,a numerical case study of decision making is presented to demonstrate the applicability and validity of the proposed technique.Besides,the comparison of the existing and the proposed technique is established to show the effectiveness and validity of the established technique.

Strategic Renewable Energy Resource Selection Using a Fuzzy Decision-Making Method

Renewable energy is created by renewable natural resources such as geothermal heat,sunlight,tides,rain,and wind.Energy resources are vital for all countries in terms of their economies and politics.As a result,selecting the optimal option for any country is critical in terms of energy investments.Every country is nowadays planning to increase the share of renewable energy in their universal energy sources as a result of global warming.In the present work,the authors suggest fuzzy multi-characteristic decision-making approaches for renew-able energy source selection,and fuzzy set theory is a valuable methodology for dealing with uncertainty in the presence of incomplete or ambiguous data.This study employed a hybrid method for order of preference by resemblance to an ideal solution based on fuzzy analytical network process-technique,which agrees with professional assessment scores to be linguistic phrases,fuzzy numbers,or crisp numbers.The hybrid methodology is based on fuzzy set ideologies,which calculate alternatives in accordance with professional functional requirements using objective or subjective characteristics.The best-suited renewable energy alternative is discovered using the approach presented.

Governance of artificial intelligence applications in a business audit via a fusion fuzzy multiple rule‑based decision‑making model

A broad range of companies around the world has welcomed artificial intelligence(AI)technology in daily practices because it provides decision-makers with comprehensive and intuitive messages about their operations and assists them in formulating appropriate strategies without any hysteresis.This research identifies the essential components of AI applications under an internal audit framework and provides an appropriate direction of strategies,which relate to setting up a priority on alternatives with multiple dimensions/criteria involvement that need to further consider the interconnected and intertwined relationships among them so as to reach a suitable judgment.To obtain this goal and inspired by a model ensemble,we introduce an innovative fuzzy multiple rule-based decision making framework that integrates soft computing,fuzzy set theory,and a multi-attribute decision making algorithm.The results display that the order of priority in improvement—(A)AI application strategy,(B)AI governance,(D)the human factor,and(C)data infrastructure and data quality—is based on the magnitude of their impact.This dynamically enhances the implementation of an AI-driven internal audit framework as well as responds to the strong rise of the big data environment.Highlights Artificial intelligence(AI)promotes the sustainability development of audit tasks.A fuzzy MRDM model extracts key factors from large amounts of data.Fuzzy decision-making trial and evaluation laboratory analysis accounts for dependence and feedback among factors.An effective framework of AI-driven business audit is proposed in which“AI cognition of senior executives”is the most important criterion.

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.

A Blind Spot in the Reframing of a Universe of Possibles: Towards a Suitable Model for Decision-Making Theory and A.I.

Bayesian inference model is an optimal processing of incomplete information that, more than other models, better captures the way in which any decision-maker learns and updates his degree of rational beliefs about possible states of nature, in order to make a better judgment while taking new evidence into account. Such a scientific model proposed for the general theory of decision-making, like all others in general, whether in statistics, economics, operations research, A.I., data science or applied mathematics, regardless of whether they are time-dependent, have in common a theoretical basis that is axiomatized by relying on related concepts of a universe of possibles, especially the so-called universe (or the world), the state of nature (or the state of the world), when formulated explicitly. The issue of where to stand as an observer or a decision-maker to reframe such a universe of possibles together with a partition structure of knowledge (i.e. semantic formalisms), including a copy of itself as it was initially while generalizing it, is not addressed. Memory being the substratum, whether human or artificial, wherein everything stands, to date, even the theoretical possibility of such an operation of self-inclusion is prohibited by pure mathematics. We make this blind spot come to light through a counter-example (namely Archimedes’ Eureka experiment) and explore novel theoretical foundations, fitting better with a quantum form than with fuzzy modeling, to deal with more than a reference universe of possibles. This could open up a new path of investigation for the general theory of decision-making, as well as for Artificial Intelligence, often considered as the science of the imitation of human abilities, while being also the science of knowledge representation and the science of concept formation and reasoning.

Solving Multi-Objective Linear Programming Problem by Statistical Averaging Method with the Help of Fuzzy Programming Method

A multi-objective linear programming problem is made from fuzzy linear programming problem. It is due the fact that it is used fuzzy programming method during the solution. The Multi objective linear programming problem can be converted into the single objective function by various methods as Chandra Sen’s method, weighted sum method, ranking function method, statistical averaging method. In this paper, Chandra Sen’s method and statistical averaging method both are used here for making single objective function from multi-objective function. Two multi-objective programming problems are solved to verify the result. One is numerical example and the other is real life example. Then the problems are solved by ordinary simplex method and fuzzy programming method. It can be seen that fuzzy programming method gives better optimal values than the ordinary simplex method.

A decision support system for satellite layout integrating multi-objective optimization and multi-attribute decision making

A decision support system, including a multi-objective optimization framework and a multi-attribute decision making approach is proposed for satellite equipment layout. Firstly, given three objectives (to minimize the C.G. offset, the cross moments of inertia and the space debris impact risk), we develop a threedimensional layout optimization model. Unlike most of the previous works just focusing on mass characteristics of the system, a space debris impact risk index is developed. Secondly, we develop an efficient optimization framework for the integration of computer-aided design (CAD) software as well as the optimization algorithm to obtain the Pareto front of the layout optimization problem. Thirdly, after obtaining the candidate solutions, we present a multi-attribute decision making approach, which integrates the smart Pareto filter and the correlation coefficient and standard deviation (CCSD) method to select the best tradeoff solutions on the optimal Pareto fronts. Finally, the framework and the decision making approach are applied to a case study of a satellite platform.

Multiple attribute decision making method based on trapezoid fuzzy linguistic variables

The problem of multiple attribute decision making under fuzzy linguistic environments, in which decision makers can only provide their preferences （attribute values）in the form of trapezoid fuzzy linguistic variables（TFLV）, is studied. The formula of the degree of possibility between two TFLVs is defined, and some of its characteristics are studied. Based on the degree of possibility of fuzzy linguistic variables, an approach to ranking the decision alternatives in multiple attribute decision making with TFLV is developed. The trapezoid fuzzy linguistic weighted averaging （TFLWA） operator method is utilized to aggregate the decision information, and then all the alternatives are ranked by comparing the degree of possibility of TFLV. The method can carry out linguistic computation processes easily without loss of linguistic information, and thus makes the decision results reasonable and effective. Finally, the implementation process of the proposed method is illustrated and analyzed by a practical example.

Land Evaluation Method Based on Decision Tree Produced by C4.5 and Fuzzy Decision

[Objective]The aim was to overcome the shortage of being difficult to build land evaluation model when the impact factors had continuous value in the traditional land evaluation process,as well as to improve the intelligibility of the land evaluation knowledge.[Method] The land evaluation method combining classification rule extracted by C4.5 algorithm with fuzzy decision was proposed in this study.[Result] The result of Second General Soil Survey of Guangdong Province had demonstrated that the method was convenient to extract classification rules,and by using only 100 rules,quantity correct rate 86.67% and area correct rate 84.80% of land evaluation could be obtained.[Conclusions] The use of C4.5 algorithm to obtain the rules,combined with fuzzy decision algorithm to build classifiers had got satisfactory results,which provided a practical algorithm for the land evaluation.

Forest use suitability:Towards decision-making-oriented sustainable management of forest ecosystem services

Management of forest lands considering multi-functional approaches is the basis to sustain or enhance the provi-sion of specific benefits,while minimizing negative impacts to the environment.Defining a desired management itinerary to a forest depends on a variety of factors,including the forest type,its ecological characteristics,and the social and economic needs of local communities.A strategic assessment of the forest use suitability(FUS)(namely productive,protective,conservation-oriented,social and multi-functional)at regional level,based on the provision of forest ecosystem services and trade-offs between FUS alternatives,can be used to develop management strategies that are tailored to the specific needs and conditions of the forest.The present study assesses the provision of multiple forest ecosystem services and employs a decision model to identify the FUS that sup-ports the most present and productive ecosystem services in each stand in Catalonia.For this purpose,we apply the latest version of the Ecosystem Management Decision Support(EMDS)system,a spatially oriented decision support system that provides accurate results for multi-criteria management.We evaluate 32 metrics and 12 as-sociated ecosystem services indicators to represent the spatial reality of the region.According to the results,the dominant primary use suitability is social,followed by protective and productive.Nevertheless,final assignment of uses is not straightforward and requires an exhaustive analysis of trade-offs between all alternative options,in many cases identifying flexible outcomes,and increasing the representativeness of multi-functional use.The assignment of forest use suitability aims to significantly improve the definition of the most adequate management strategy to be applied.