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.

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.

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.

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.

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.

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.

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.

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.

Multi-criteria group decision making with fuzzy data:an extension of the VIKOR method

The VIKOR method is a multi-criteria decision making aid, which employs linear normalization to offer compromise solu- tions and has been successfully applied to various group decision making problems. However, the conventional VIKOR techniques used to integrate group judgments and the information loss arising from defuzzification are problematic and distort final outcomes. An improved integration method, which is optimization-based, is proposed. And it can handle fuzzy criteria values and weights. The precondition for accurately defuzzifying triangular fuzzy num- bers is identified. Several effective defuzzification procedures are proposed to improve the extant VIKOR, and a comprehensive evaluation framework is offered to aid multi-criteria group decision making. Finally, a numerical example is provided to illustrate the practicability of the proposed method.

Fuzzy multi-criteria decision-making approach with incomplete information based on evidential reasoning

The weights of criteria are incompletely known and the criteria values are incomplete and uncertain or even default in some fuzzy multi-criteria decision-making problems.For those problems,an approach based on evidential reasoning is proposed,in which the criteria values are integrated on the basis of analytical algorithm of evidential reasoning,and then nonlinear programming models of each alternative are developed with the incomplete information on weights.The genetic algorithm is employed to solve the models,producing the weights and the utility interval of each alternative,and the ranking of the whole set of alternatives can be attained.Finally,an example shows the effectiveness of the method.

Tri-Intersectional Model of Leadership by Values:A Fuzzy Multi-Criteria Decision Making Open Technology Assessment System

Purpose-Nowadays successful organizations need to be masters at leadership by values to play in a constantly changing and transforming environment.But how can leaders and organizations effectively convene strategic and culture development based on values?This paper presents the Tri-Intersectional Model of Leadership by Values(TMLV)in which leaders and organizations can integrate a sustainable strategy,as well as a culture and value-based management system that simultaneously leverages human,financial,and social resources.With its three essential axes of values(economic-pragmatic,emotional-development,and ethical-social)at their intersection points,it allows leaders to focus on the strategy linkages:innovation-intersection between the economic-pragmatic values axis and the emotional-development values axis-allows them to develop sustainable innovations;survival-intersection between the economic-pragmatic values axis and the ethical-social values axis-enhances their organization’s survival;finally,sensibility-intersection between the economic-pragmatic values axis and the ethical-social values axis-makes them more humane and more socially-responsible.The application of the TMLV,using the Fuzzy Multi-Criteria Decision Making Open Technology Assessment System,can be a great inspiration for stimulating and working with values in organizations,as well as allowing leaders to develop a values-based,high-involvement,and performance-oriented culture.Methodology/Approach-This research considers empirical data analysis of the 37 case studies of the EU-InnovatE project(http//www.euinnovate.com)-a pioneering initiative to align innovation values to integrate the end user into the process of innovation and entrepreneurship related to a sustainable lifestyle and the green economy in Europe-using a fuzzy multiple-criteria decision making method and open technologies system,such as server-side PHP language,MariaDB Database,fork of MYSQL Database Management System,and JavaScript libraries to perform operation directly on the user’s browser.Findings-The application of the TMLV model,considering empirical analysis of the extracted values from the case studies,using the Fuzzy Multi-Criteria Decision Making Open Technology Assessment System,can be a great inspiration for stimulating and working with values in João organizations,as well as allowing leaders to develop suitable strategies and interventions for shaping a sustainable high-performance culture.Research implications-This research can be a starting point for further research to assess the effectiveness of the leadership model based on a decision-making open technology system in any given organization,as well as to invite researchers who have positive passion about working with values to participate in the improvement of this tool.Originality/value-The Tri-Intersectional Model of Leadership by Values using the Fuzzy Multi-Criteria Decision Making Open Technology Assessment System is presented as an evolution in leadership models that may be used to fuel innovation,survival,and a sensibility strategic focus that is necessary to optimize human and organizational performance and deliver effective solutions to the massive array of human,financial,and social problems we face today.

Prospect Theory Based Hesitant Fuzzy Multi-Criteria Decision Making for Low Sulphur Fuel of Maritime Transportation

The environmental impact of maritime transport has now become a relevant issue in sustainable policy formulation and has attracted increasing interest from academia.For the sustainable development of maritime transport,International Maritime Organization stipulates that the sulfur content of ship emissions will reach 0.5 from 2020.With the approaching of the stipulated implementation date,shipowners need to adopt scientific methods to make decision on low sulfur fuel.In this study,we applied a prospect theory based hesitant fuzzy multi-criteria decision-making model to obtain the optimal decision of low Sulphur marine fuel.For this purpose,the hesitant fuzzy decision matrix is established to collect expert opinions,the maximizing deviation method is adopted to determine criteria weights.According to calculate the Euclidean distance from the reference points,we obtain the comprehensive prospect values of alternatives.Lastly,a case study is carried out to illustrate the significance and effectiveness of the proposed methodology.The innovation of this study is that it is the first-time adopting prospect theory and hesitate fuzzy sets to multi-criteria decision making for low Sulphur marine fuel,which provides an effective decision model for shipping companies under Low Sulphur regulations,and can also be extended to other industries.

Multi-Criteria Fuzzy-Based Decision Making Algorithm to Optimize the VHO Performance in Hetnets

Despite the seemingly exponential growth of mobile and wireless communication,this same technology aims to offer uninterrupted access to different wireless systems like Radio Communication,Bluetooth,and Wi-Fi to achieve better network connection which in turn gives the best quality of service(QoS).Many analysts have established many handover decision systems(HDS)to enable assured continuous mobility between various radio access technologies.Unbrokenmobility is one of themost significant problems considered in wireless communication networks.Each application needs a distinct QoS,so the network choice may shift appropriately.To achieve this objective and to choose the finest networks,it is important to select a best decision making algorithm that chooses the most effective network for every application that the user requires,dependent on QoS measures.Therefore,the main goal of the proposed system is to provide an enhanced vertical handover(VHO)decision making programby using aMulti-CriteriaFuzzy-Based algorithm to choose the best network.Enhanced Multi-Criteria algorithms and a Fuzzy-Based algorithm is implemented successfully for optimal network selection and also to minimize the probability of false handover.Furthermore,a double packet buffer is utilized to decrease the packet loss by 1.5%and to reduce the number of handovers up to 50%compared to the existing systems.In addition,the network setup has an optimized mobilitymanagement system to supervise the movement of the mobile nodes.

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.

Fuzzy data envelopment analysis approach based on sample decision making units

The conventional data envelopment analysis （DEA） measures the relative efficiencies of a set of decision making units with exact values of inputs and outputs. In real-world prob- lems, however, inputs and outputs typically have some levels of fuzziness. To analyze a decision making unit （DMU） with fuzzy input/output data, previous studies provided the fuzzy DEA model and proposed an associated evaluating approach. Nonetheless, numerous deficiencies must still be improved, including the α- cut approaches, types of fuzzy numbers, and ranking techniques. Moreover, a fuzzy sample DMU still cannot be evaluated for the Fuzzy DEA model. Therefore, this paper proposes a fuzzy DEA model based on sample decision making unit （FSDEA）. Five eval- uation approaches and the related algorithm and ranking methods are provided to test the fuzzy sample DMU of the FSDEA model. A numerical experiment is used to demonstrate and compare the results with those obtained using alternative approaches.

Novel combinatorial algorithm for the problems of fuzzy grey multi-attribute group decision making

To study the fuzzy and grey information in the problems of multi-attribute group decision making, the basic concepts of both fuzzy grey numbers and grey interval numbers are given firstly, then a new model of fuzzy grey multi-attribute group decision making based on the theories of fuzzy mathematics and grey system is presented. Furthermore, the grey interval relative degree and deviation degree is defined, and both the optimistic algorithm of the grey interval relational degree and the algorithm of deviation degree minimization for solving this new model are also given. Finally, a decision making example to demonstrate the feasibility and rationality of this new method is given, and the results by using these two algorithms are uniform.

Extension of TOPSIS for fuzzy multi-attribute decision making problem based on experimental analysis

This paper is concerned with a technique for order performance by similarity to ideal solution（TOPSIS） method for fuzzy multi-attribute decision making,in which the information about attribute weights is partly known and the attribute values take form of triangular fuzzy numbers.Considering the fact that the triangular fuzzy TOPSIS results yielded by different distance measures are different from others,a comparative analysis of triangular fuzzy TOPSIS ranking from each distance measure is illustrated with discussion on standard deviation.By applying the most reasonable distance,the deviation degrees between attribute values are measured.A linear programming model based on the maximal deviation of weighted attribute values is established to obtain the attribute weights.Therefore,alternatives are ranked by using TOPSIS method.Finally,a numerical example is given to show the feasibility and effectiveness of the method.

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.