Fuzzy Multi-Criteria Decision Support System for the Best Anti-Aging Treatment Selection Process through Normal Wiggly Hesitant Fuzzy Sets

This socialized environment among educated and developed people causes themto focusmore on their appearance and health,which turns them towards medical-related treatments,leading us to discuss anti-aging treatment methods for each age group,particularly for urban people who are interested in this.Some anti-aging therapies are used to address the alterations brought on by aging in human life without the need for surgery or negative effects.Five anti-aging therapies such as microdermabrasion or dermabrasion,laser resurfacing anti-aging skin treatments,chemical peels,dermal fillers for aged skin,and botox injections are considered in this study.Based on the criteria of safety risk,investment cost,customer happiness,and side effects,the optimal alternative is picked.As a result,a NormalWiggly Hesitant Pythagorean Fuzzy Set(NWHPFS)is constructed and used in Multi-Criteria Decision-Making(MCDM)using traditional wavy mathematical approaches.The entropy approach is utilized to determine weight values,and the Normal Wiggly Hesitant Pythagorean-VlseKriterijumska Optimizacija I Kompromisno Resenje(NWHPF-VIKOR)method is utilized to rank alternatives using MCDM methodologies.Sensitivity analysis and comparative analysis were performed to ensure the robustness and reliability of the proposed method.The smart final choice will undoubtedly assist Decision Makers(DM)in making the right judgments,and the MCDM approach will undoubtedly assist individuals in understanding the medicine.

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.

Two-Sided Stable Matching Decision-Making Method Considering Matching Intention under a Hesitant Fuzzy Environment

In this paper,a stable two-sided matching(TSM)method considering the matching intention of agents under a hesitant fuzzy environment is proposed.The method uses a hesitant fuzzy element(HFE)as its basis.First,the HFE preference matrix is transformed into the normalized HFE preference matrix.On this basis,the distance and the projection of the normalized HFEs on positive and negative ideal solutions are calculated.Then,the normalized HFEs are transformed into agent satisfactions.Considering the stable matching constraints,a multiobjective programming model with the objective of maximizing the satisfactions of two-sided agents is constructed.Based on the agent satisfaction matrix,the matching intention matrix of two-sided agents is built.According to the agent satisfaction matrix and matching intention matrix,the comprehensive satisfaction matrix is set up.Furthermore,the multiobjective programming model based on satisfactions is transformed into a multiobjective programming model based on comprehensive satisfactions.Using the G-S algorithm,the multiobjective programming model based on comprehensive satisfactions is solved,and then the best TSM scheme is obtained.Finally,a terminal distribution example is used to verify the feasibility and effectiveness of the proposed method.

Novel Distance Measures on Hesitant Fuzzy Sets Based on Equal-Probability Transformation and Their Application in Decision Making on Intersection Traffic Control

The purpose of this study is to reduce the uncertainty in the calculation process on hesitant fuzzy sets(HFSs).The innovation of this study is to unify the cardinal numbers of hesitant fuzzy elements(HFEs)in a special way.Firstly,a probability density function is assigned for any given HFE.Thereafter,equal-probability transformation is introduced to transform HFEs with different cardinal numbers on the condition into the same probability density function.The characteristic of this transformation is that the higher the consistency of the membership degrees in HFEs,the higher the credibility of the mentioned membership degrees is,then,the bigger the probability density values for them are.According to this transformation technique,a set of novel distance measures on HFSs is provided.Finally,an illustrative example of intersection traffic control is introduced to show the usefulness of the given distance measures.The example also shows that this study is a good complement to operation theories on HFSs.

Fermatean Hesitant Fuzzy Prioritized Heronian Mean Operator and Its Application in Multi-Attribute Decision Making

In real life,incomplete information,inaccurate data,and the preferences of decision-makers during qualitative judgment would impact the process of decision-making.As a technical instrument that can successfully handle uncertain information,Fermatean fuzzy sets have recently been used to solve the multi-attribute decision-making(MADM)problems.This paper proposes a Fermatean hesitant fuzzy information aggregation method to address the problem of fusion where the membership,non-membership,and priority are considered simultaneously.Combining the Fermatean hesitant fuzzy sets with Heronian Mean operators,this paper proposes the Fermatean hesitant fuzzy Heronian mean(FHFHM)operator and the Fermatean hesitant fuzzyweighted Heronian mean(FHFWHM)operator.Then,considering the priority relationship between attributes is often easier to obtain than the weight of attributes,this paper defines a new Fermatean hesitant fuzzy prioritized Heronian mean operator(FHFPHM),and discusses its elegant properties such as idempotency,boundedness and monotonicity in detail.Later,for problems with unknown weights and the Fermatean hesitant fuzzy information,aMADM approach based on prioritized attributes is proposed,which can effectively depict the correlation between attributes and avoid the influence of subjective factors on the results.Finally,a numerical example of multi-sensor electronic surveillance is applied to verify the feasibility and validity of the method proposed in this paper.

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.

Two-Sided Matching Decision Making with Multi-Attribute Probabilistic Hesitant Fuzzy Sets

In previous research on two-sided matching(TSM)decision,agents’preferences were often given in the form of exact values of ordinal numbers and linguistic phrase term sets.Nowdays,the matching agent cannot perform the exact evaluation in the TSM situations due to the great fuzziness of human thought and the complexity of reality.Probability hesitant fuzzy sets,however,have grown in popularity due to their advantages in communicating complex information.Therefore,this paper develops a TSM decision-making approach with multi-attribute probability hesitant fuzzy sets and unknown attribute weight information.The agent attribute weight vector should be obtained by using the maximum deviation method and Hamming distance.The probabilistic hesitancy fuzzy information matrix of each agent is then arranged to determine the comprehensive evaluation of two matching agent sets.The agent satisfaction degree is calculated using the technique for order preference by similarity to ideal solution(TOPSIS).Additionally,the multi-object programming technique is used to establish a TSM method with the objective of maximizing the agent satisfaction of two-sided agents,and the matching schemes are then established by solving the built model.The study concludes by providing a real-world supply-demand scenario to illustrate the effectiveness of the proposed method.The proposed method is more flexible than prior research since it expresses evaluation information using probability hesitating fuzzy sets and can be used in scenarios when attribute weight information is unclear.

Lanchester equation for cognitive domain using hesitant fuzzy linguistic terms sets

Intelligent wars can take place not only in the physical domain and information domain but also in the cognitive domain.The cognitive domain will become the key domain to win in the future intelligent war.A Lanchester equation considering cognitive domain is proposed to fit the development tendency intelligent wars in this paper.One party is considered to obtain the exponential enhancement advantage on combat forces in combat if it can gain an advantage in the cognitive domain over the other party according to the systemic advantage function.The operational effectiveness of the cognitive domain in war is considered to consist of a series of indicators.Hesitant fuzzy sets and linguistic term sets are powerful tools when evaluating indicators,hence the indicators are scored by experts using hesitant fuzzy linguistic terms sets here.A unique hesitant fuzzy hybrid arithmetical averaging operator is used to aggregate the evaluation.

A New Hesitant Fuzzy Multiple Attribute Decision Making Method with Unknown Weight Information

In this paper, we focus on a new approach based on new generalized hesitant fuzzy hybrid weighted aggregation operators, in which the evaluation information provided by decision makers is expressed in hesitant fuzzy elements (HFEs) and the information about attribute weights and aggregation-associated vector is unknown. More explicitly, some new generalized hesitant fuzzy hybrid weighted aggregation operators are proposed, such as the new generalized hesitant fuzzy hybrid weighted averaging (NGHFHWA) operator and the new generalized hesitant fuzzy hybrid weighted geometric (NGHFHWG) operator. Some desirable properties and the relationships between them are discussed. Then, a new algorithm for hesitant fuzzy multi-attribute decision making (HF-MADM) problems with unknown weight information is introduced. Further, a practical example is used to illustrate the detailed implementation process of the proposed approach. A sensitivity analysis of the decision results is analyzed with different parameters. Finally, comparative studies are given to verify the advantages of our method.

Hierarchical hesitant fuzzy K-means clustering algorithm

Due to the limitation and hesitation in one＇s knowledge, the membership degree of an element to a given set usually has a few different values, in which the conventional fuzzy sets are invalid. Hesitant fuzzy sets are a powerful tool to treat this case. The present paper focuses on investigating the clustering technique for hesitant fuzzy sets based on the K-means clustering algorithm which takes the results of hierarchical clustering as the initial clusters. Finally, two examples demonstrate the validity of our algorithm.

System portfolio selection based on GRA method under hesitant fuzzy environment

The hesitant fuzzy set(HFS) is an important tool to deal with uncertain and vague information.In equipment system portfolio selection, the index attribute of the equipment system may not be expressed by precise data;it is usually described by qualitative information and expressed as multiple possible values.We propose a method of equipment system portfolio selection under hesitant fuzzy environment.The hesitant fuzzy element(HFE) is used to describe the index and attribute values of the equipment system.The hesitation degree of HFEs measures the uncertainty of the criterion data of the equipment system.The hesitant fuzzy grey relational analysis(GRA) method is used to evaluate the score of the equipment system, and the improved HFE distance measure is used to fully consider the influence of hesitation degree on the grey correlation degree.Based on the score and hesitation degree of the equipment system,two portfolio selection models of the equipment system and an equipment system portfolio selection case is given to illustrate the application process and effectiveness of the method.

Power Aggregation Operators and Similarity Measures Based on Improved Intuitionistic Hesitant Fuzzy Sets and their Applications to Multiple Attribute Decision Making

Intuitionistic hesitant fuzzy set(IHFS)is amixture of two separated notions called intuitionistic fuzzy set(IFS)and hesitant fuzzy set(HFS),as an important technique to cope with uncertain and awkward information in realistic decision issues.IHFS contains the grades of truth and falsity in the formof the subset of the unit interval.The notion of IHFS was defined by many scholars with different conditions,which contain several weaknesses.Here,keeping in view the problems of already defined IHFSs,we will define IHFS in another way so that it becomes compatible with other existing notions.To examine the interrelationship between any numbers of IHFSs,we combined the notions of power averaging(PA)operators and power geometric(PG)operators with IHFSs to present the idea of intuitionistic hesitant fuzzy PA(IHFPA)operators,intuitionistic hesitant fuzzy PG(IHFPG)operators,intuitionistic hesitant fuzzy power weighted average(IHFPWA)operators,intuitionistic hesitant fuzzy power ordered weighted average(IHFPOWA)operators,intuitionistic hesitant fuzzy power ordered weighted geometric(IHFPOWG)operators,intuitionistic hesitant fuzzy power hybrid average(IHFPHA)operators,intuitionistic hesitant fuzzy power hybrid geometric(IHFPHG)operators and examined as well their fundamental properties.Some special cases of the explored work are also discovered.Additionally,the similarity measures based on IHFSs are presented and their advantages are discussed along examples.Furthermore,we initiated a new approach to multiple attribute decision making(MADM)problem applying suggested operators and a mathematical model is solved to develop an approach and to establish its common sense and adequacy.Advantages,comparative analysis,and graphical representation of the presented work are elaborated to show the reliability and effectiveness of the presented works.

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.

Dynamic hesitant fuzzy linguistic group decision-making from a reliability perspective

A dynamic hesitant fuzzy linguistic group decisionmaking(DHFLGDM) problem is studied from the perspective of information reliability based on the theory of hesitant fuzzy linguistic term sets(HFLTSs). First, an approach is applied to transform the dynamic HFLTSs(DHFLTSs) into a set of proportional linguistic terms to eliminate the time dimension. Second, expert reliability is measured by considering both group similarity and degree of certainty, and an optimization method is employed to quantify the linguistic terms by maximizing the group similarity. Third, through computing the attribute stability as well as its reliability, a combination rule which considers both reliability and weight is proposed to aggregate the information, and then the aggregated grade values and degree of stability are used to make a selection. Finally,the application and feasibility of the proposed method are verified through a case study and method comparison.

A Novel Multi-Attribute Decision-Making Method Based on Probabilistic Hesitant Fuzzy Soft Set and Its Application

The probabilistic hesitant fuzzy multi-attribute group decision-making method introduces probability and hesitation into decision-making problems at the same time,which can improve the reliability and accuracy of decision-making results,and has become a research hotspots in recent years.However,there are still many problems,such as overly complex calculations and difficulty in obtaining probability data.Based on these,the paper proposes a multi-attribute group decision-making model based on probability hesitant fuzzy soft sets.Firstly,the definition of probabilistic hesitant fuzzy soft set is given.Then,based on soft set theory and probabilistic hesitant fuzzy set,the similarity measure of probabilistic hesitant fuzzy soft set is proposed,and the two measures are further combined.Finally,it is applied to the construction of multi-attribute group decision-making model,and the effectiveness and rationality of the model are verified by an example.The example shows that the new similarity calculation formula and algorithm model in this paper have higher accuracy,and the calculation process is more simple,it provides a feasible method for multi-attribute group decision making problems.

Pythagorean probabilistic hesitant triangular fuzzy aggregation operators with applications in multiple attribute decision making

As a generalization of fuzzy set,hesitant probabilistic fuzzy set and pythagorean triangular fuzzy set have their own unique advantages in describing decision information.As modern socioeconomic decision-making problems are becoming more and more complex,it also becomes more and more difficult to appropriately depict decision makers’cognitive information in decision-making process.In order to describe the decision information more comprehensively,we define a pythagorean probabilistic hesitant triangular fuzzy set(PPHTFS)by combining the pythagorean triangular fuzzy set and the probabilistic hesitant fuzzy set.Firstly,the basic operation and scoring function of the pythagorean probabilistic hesitant triangular fuzzy element(PPHTFE)are proposed,and the comparison rule of two PPHTFEs is given.Then,some pythagorean probabilistic hesitant triangular fuzzy aggregation operators are developed,and their properties are also studied.Finally,a multi-attribute decision-making(MADM)model is constructed based on the proposed operators under the pythagorean probabilistic hesitant triangular fuzzy information,and an illustration example is given to demonstrate the practicability and validity of the proposed decision-making method.

Multi-attribute Group Decision-making Based on Hesitant Bipolar-valued Fuzzy Information and Social Network

Fuzzy sets have undergone several expansions and generalisations in the literature,including Atanasov’s intuitionistic fuzzy sets,type 2 fuzzy sets,and fuzzy multisets,to name a few.They can be regarded as fuzzy multisets from a formal standpoint;nevertheless,their interpretation differs from the two other approaches to fuzzy multisets that are currently available.Hesitating fuzzy sets(HFS)are very useful if consultants have hesitation in dealing with group decision-making problems between several possible memberships.However,these possible memberships can be not only crisp values in[0,1],but also interval values during a practical evaluation process.Hesitant bipolar valued fuzzy set(HBVFS)is a generalization of HFS.This paper aims to introduce a general framework of multi-attribute group decision-making using social network.We propose two types of decision-making processes:Type-1 decision-making process and Type-2 decision-making process.In the Type-1 decision-making process,the experts’original opinion is proces for thefinal ranking of alternatives.In Type-2 decision making processs,there are two major aspects we consider.First,consistency tests and checking of consensus models are given for detecting that the judgments are logically rational.Otherwise,the framework demands(partial)decision-makers to review their assessments.Second,the coherence and consensus of several HBVFSs are established forfinal ranking of alternatives.The proposed framework is clarified by an example of software packages selection of a university.

Analysis of migraine in mutlicellular organism based on trapezoidal neutrosophic cubic hesitant fuzzy TOPSIS method

In this paper,we define a new idea of trapezoidal neutrosophic cubic hesitant fuzzy number based on migraine diseases.We define and the migraine diseases on trapezoidal neutrosophic cubic hesitant fuzzy number and operational laws of trapezoidal neutrosophic cubic hesitant fuzzy number and hamming distance of TrNCHFNs.The new concept of trapezoidal neutrosophic cubic hesitant fuzzy TOPSIS method is introduced.Furthermore,we extend MCDM method based on the trapezoidal neutrosophic cubic hesitant fuzzy TOPSIS method.Finally,an illustrative example is given to verify and demonstrate the practicality and effectiveness of the proposed method.

New type of cancer patients based on triangular cubic hesitant fuzzy TOPSIS method

In this paper,we define the new idea of triangular cubic hesitant fuzzy number(TCHFN).We discuss some basic operational laws of triangular cubic hesitant fuzzy number and hamming distance of TCHFNs.We introduce the new concept of triangular cubic hes­itant TOPSIS method.Furthermore,we extend the classical cubic hesitant the tech­nique for order of preference by similarity to ideal solution(TOPSIS)method to solve the Multi-Criteria decision-making(MCDM)method based on triangular cubic hesitant TOPSIS method.The new ranking method for TCHFNs is used to rank the alternatives.Finally,an illustrative example is given to verify and demonstrate the practicality and effectiveness of the proposed method.

DUAL HESITANT FUZZY INFORMATION AGGREGATION WITH EINSTEIN T-CONORM AND T-NORM

Dual hesitant fuzzy set （DHFS） is a new generalization of fuzzy set （FS） consisting of two parts （i.e., the membership hesitancy function and the non-membership hesitancy fimction）, which confronts several different possible values indicating the epistemic degrees whether certainty or uncertainty. It encompasses fuzzy set （FS）, intuitionistic fuzzy set （IFS）, and hesitant fuzzy set （HFS） so that it can handle uncertain information more flexibly in the process of decision making. In this paper, we propose some new operations on dual hesitant fuzzy sets based on Einstein t-eonorm and t-norm, study their properties and relationships and then give some dual hesitant fuzzy aggregation operators, which can be considered as the generalizations of some existing ones under fuzzy, intuitionistic fuzzy and hesitant fuzzy environments. Finally, a decision making algorithm under dual hesitant fuzzy environment is given based on the proposed aggregation operators and a numerical example is used to demonstrate the effectiveness of the method.