Aggregation Operators for Decision Making Based on q-Rung Orthopair Fuzzy Hypersoft Sets:An Application in Real Estate Project

In this paper,a decision-making problem with a q-rung orthopair fuzzy hypersoft environment is developed,and two operators of ordered weighted average and induced ordered weighted average are developed.Several fundamental features are also derived.The induced ordered weighted average operator is essential in a q-ROFH environment as the induced ordered aggregation operators are special cases of the existing aggregation operators that already exist in q-ROFH environments.The main function of these operators is to help decision-makers gain a complete understanding of uncertain facts.The proposed aggregation operator is applied to a decision-making problem,with the aim of selecting the most promising real estate project for investment.

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.

Aggregation operators and CRITIC-VIKOR method for confidence complex q-rung orthopair normal fuzzy information and their applications

Supply chain management is an essential part of an organisation's sustainable programme.Understanding the concentration of natural environment,public,and economic influence and feasibility of your suppliers and purchasers is becoming progressively familiar as all industries are moving towards a massive sustainable potential.To handle such sort of developments in supply chain management the involvement of fuzzy settings and their generalisations is playing an important role.Keeping in mind this role,the aim of this study is to analyse the role and involvement of complex q-rung orthopair normal fuzzy(CQRONF)information in supply chain management.The major impact of this theory is to analyse the notion of confidence CQRONF weighted averaging,confidence CQRONF ordered weighted averaging,confidence CQRONF hybrid averaging,confidence CQRONF weighted geometric,confidence CQRONF ordered weighted geometric,confidence CQRONF hybrid geometric operators and try to diagnose various properties and results.Furthermore,with the help of the CRITIC and VIKOR models,we diagnosed the novel theory of the CQRONF-CRITIC-VIKOR model to check the sensitivity analysis of the initiated method.Moreover,in the availability of diagnosed operators,we constructed a multi-attribute decision-making tool for finding a beneficial sustainable supplier to handle complex dilemmas.Finally,the initiated operator's efficiency is proved by comparative analysis.

Novelty of Different Distance Approach for Multi-Criteria Decision-Making Challenges Using q-Rung Vague Sets

In this article,multiple attribute decision-making problems are solved using the vague normal set(VNS).It is possible to generalize the vague set(VS)and q-rung fuzzy set(FS)into the q-rung vague set(VS).A log q-rung normal vague weighted averaging(log q-rung NVWA),a log q-rung normal vague weighted geometric(log q-rung NVWG),a log generalized q-rung normal vague weighted averaging(log Gq-rung NVWA),and a log generalized q-rungnormal vagueweightedgeometric(logGq-rungNVWG)operator are discussed in this article.Adescription is provided of the scoring function,accuracy function and operational laws of the log q-rung VS.The algorithms underlying these functions are also described.A numerical example is provided to extend the Euclidean distance and the Humming distance.Additionally,idempotency,boundedness,commutativity,and monotonicity of the log q-rung VS are examined as they facilitate recognizing the optimal alternative more quickly and help clarify conceptualization.We chose five anemia patients with four types of symptoms including seizures,emotional shock or hysteria,brain cause,and high fever,who had either retrograde amnesia,anterograde amnesia,transient global amnesia,post-traumatic amnesia,or infantile amnesia.Natural numbers q are used to express the results of the models.To demonstrate the effectiveness and accuracy of the models we are investigating,we compare several existing models with those that have been developed.

A NovelMethod for Determining Tourism Carrying Capacity in a Decision-Making Context Using q−Rung Orthopair Fuzzy Hypersoft Environment

Tourism is a popular activity that allows individuals to escape their daily routines and explore new destinations for various reasons,including leisure,pleasure,or business.A recent study has proposed a unique mathematical concept called a q−Rung orthopair fuzzy hypersoft set(q−ROFHS)to enhance the formal representation of human thought processes and evaluate tourism carrying capacity.This approach can capture the imprecision and ambiguity often present in human perception.With the advanced mathematical tools in this field,the study has also incorporated the Einstein aggregation operator and score function into the q−ROFHS values to supportmultiattribute decision-making algorithms.By implementing this technique,effective plans can be developed for social and economic development while avoiding detrimental effects such as overcrowding or environmental damage caused by tourism.A case study of selected tourism carrying capacity will demonstrate the proposed methodology.

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 Decision Making Based on Bipolar Picture Fuzzy Operators and New Distance Measures

This paper aims to introduce the novel concept of the bipolar picture fuzzy set(BPFS)as a hybrid structure of bipolar fuzzy set(BFS)and picture fuzzy set(PFS).BPFS is a new kind of fuzzy sets to deal with bipolarity(both positive and negative aspects)to each membership degree(belonging-ness),neutral membership(not decided),and non-membership degree(refusal).In this article,some basic properties of bipolar picture fuzzy sets(BPFSs)and their fundamental operations are introduced.The score function,accuracy function and certainty function are suggested to discuss the comparability of bipolar picture fuzzy numbers(BPFNs).Additionally,the concept of new distance measures of BPFSs is presented to discuss geometrical properties of BPFSs.In the context of BPFSs,certain aggregation operators(AOs)named as“bipolar picture fuzzy weighted geometric(BPFWG)operator,bipolar picture fuzzy ordered weighted geometric(BPFOWG)operator and bipolar picture fuzzy hybrid geometric(BPFHG)operator”are defined for information aggregation of BPFNs.Based on the proposed AOs,a new multicriteria decision-making(MCDM)approach is proposed to address uncertain real-life situations.Finally,a practical application of proposed methodology is also illustrated to discuss its feasibility and applicability.

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.

Linguistic Single-Valued Neutrosophic Power Aggregation Operators and Their Applications to Group Decision-Making Problems

Linguistic single-valued neutrosophic set(LSVNS)is a more reliable tool,which is designed to handle the uncertainties of the situations involving the qualitative data.In the present manuscript,we introduce some power aggregation operators(AOs)for the LSVNSs,whose purpose is to diminish the influence of inevitable arguments about the decision-making process.For it,first we develop some averaging power operators,namely,linguistic single-valued neutrosophic(LSVN)power averaging,weighted average,ordered weighted average,and hybrid averaging AOs along with their desirable properties.Further,we extend it to the geometric power AOs for LSVNSs.Based on the proposed work;an approach to solve the group decision-making problems is given along with the numerical example.Finally,a comparative study and the validity tests are present to discuss the reliability of the proposed operators.

Sine Trigonometry Operational Laws for Complex Neutrosophic Sets and Their Aggregation Operators in Material Selection

In this paper,sine trigonometry operational laws(ST-OLs)have been extended to neutrosophic sets(NSs)and the operations and functionality of these laws are studied.Then,extending these ST-OLs to complex neutrosophic sets(CNSs)forms the core of thiswork.Some of themathematical properties are proved based on ST-OLs.Fundamental operations and the distance measures between complex neutrosophic numbers(CNNs)based on the ST-OLs are discussed with numerical illustrations.Further the arithmetic and geometric aggregation operators are established and their properties are verified with numerical data.The general properties of the developed sine trigonometry weighted averaging/geometric aggregation operators for CNNs(ST-WAAO-CNN&ST-WGAO-CNN)are proved.A decision making technique based on these operators has been developed with the help of unsupervised criteria weighting approach called Entropy-ST-OLs-CNDM(complex neutrosophic decision making)method.A case study for material selection has been chosen to demonstrate the ST-OLs of CNDM method.To check the validity of the proposed method,entropy based complex neutrosophic CODAS approach with ST-OLs has been executed numerically and a comparative analysis with the discussion of their outcomes has been conducted.The proposed approach proves to be salient and effective for decision making with complex information.

Induced and heavy aggregation operators with distance measures

This paper introduces a new aggregation model by using induced and heavy aggregation operators in distances measures such as the Hamming distance.It is called the induced heavy ordered weighted averaging（OWA） distance（IHOWAD） operator.This paper studies some of its main properties and a wide range of particular cases such as the induced heavy OWA（IHOWA） operator,the induced OWA distance（IOWAD） operator and the heavy OWA distance（HOWAD） operator.This approach is generalized by using generalized and quasi-arithmetic means obtaining the induced generalized IHOWAD（IGHOWAD） operator and the Quasi-IHOWAD operator.An application of the new approach in a decision making problem regarding the selection of strategies is developed.

Aczel-Alsina Weighted Aggregation Operators of Simplified Neutrosophic Numbers and Its Application in Multiple Attribute Decision Making

The simplified neutrosophic number(SNN)can represent uncertain,imprecise,incomplete,and inconsistent information that exists in scientific,technological,and engineering fields.Hence,it is a useful tool for describing truth,falsity,and indeterminacy information in multiple attribute decision-making(MADM)problems.To suit decision makers’preference selection,the operational flexibility of aggregation operators shows its importance in dealing with the flexible decision-making problems in the SNN environment.To solve this problem,this paper develops the Aczel-Alsina aggregation operators of SNNs for MADM problems in view of the Aczel-Alsina operational flexibility.First,we define the Aczel-Alsina operations of SNNs.Then,the Aczel-Alsina aggregation operators of SNNs are presented based on the defined Aczel-Alsina operations of SNNs.Next,a MADM method is established using the proposed aggregation operators under the SNN environment.Lastly,an illustrative example about slope treatment scheme choices is provided to indicate the practicality and efficiency of the established method.By comparison with the existing relative MADM methods,the results show that the established MADM method can overcome the insufficiency of decision flexibility in the existing MADM methods and demonstrate the metric of flexible decision-making.

Linguistic Knowledge Representation in DPoS Consensus Scheme for Blockchain

The consensus scheme is an essential component in the real blockchain environment.The Delegated Proof of Stake(DPoS)is a competitive consensus scheme that can decrease energy costs,promote decentralization,and increase efficiency,respectively.However,how to study the knowledge representation of the collective voting information and then select delegates is a new open problem.To ensure the fairness and effectiveness of transactions in the blockchain,in this paper,we propose a novel fine-grained knowledge representation method,which improves the DPoS scheme based on the linguistic term set(LTS)and proportional hesitant fuzzy linguistic term set(PHFLTS).To this end,the symmetrical LTS is used in this study to express the fine-grained voting options that can be chosen to evaluate the blockchain nodes.PHFLTS is used to model the collective voting information on the voted blockchain nodes by aggregating the voting information from other blockchain nodes.To rank the blockchain nodes and then choose the delegate,a novel delegate selection algorithm is proposed based on the cumulative possibility degree.Finally,the numerical examples are used to demonstrate the implementation process of the proposed DPoS consensus algorithm and also its rationality.Moreover,the superiority of the proposed DPoS consensus algorithm is verified.The results show that the proposed DPoS consensus algorithm shows better performance than the existing DPoS consensus algorithms.

Analysis of TOPSIS techniques based on bipolar complex fuzzy N-soft setting and their applications in decision-making problems

A novel model termed a bipolar complex fuzzy N-soft set(BCFN-SS)is initiated for tackling information that involves positive and negative aspects,the second dimension,and parameterised grading simultaneously.The theory of BCFN-SS is the generalisation of two various theories,that is,bipolar complex fuzzy(BCF)and N-SS.The invented model of BCFN-SS helps decision-makers to cope with the genuine-life dilemmas containing BCF information along with parameterised grading at the same time.Further,various algebraic operations,including the usual type of union,intersection,complements,and a few others types,are invented.Certain primary operational laws for BCFNSS are also invented.Moreover,a technique for order preference by similarity to the ideal solution(TOPSIS)approach is devised in the setting of BCFN-SS for managing strategic decision-making(DM)dilemmas containing BCFN-SS information.Keeping in mind the usefulness and benefits of the TOPSIS approach,two various types of TOPSIS approaches in the environment of BCFN-SS are devised and then a numerical example for exposing the usefulness of the devised TOPSIS approach is interpreted.To disclose the prominence and benefits of the devised work,the devised approaches with numerous prevailing work are compared.

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.

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.

MCDM technique using single-valued neutrosophic trigonometric weighted aggregation operators

Motivated based on the trigonometric t-norm and t-conorm,the aims of this article are to present the trigonometric t-norm and t-conorm operational laws of SvNNs and then to propose the SvNN trigonometric weighted average and geometric aggregation operators for the modelling of a multiple criteria decision making(MCDM)technique in an inconsistent and indeterminate circumstance.To realize the aims,this paper first proposes the trigonometric t-norm and t-conorm operational laws of SvNNs,which contain the hybrid operations of the tangent and arctangent functions and the cotangent and inverse cotangent functions,and presents the SvNN trigonometric weighted average and geometric operators and their properties.Next,an MCDM technique is proposed in view of the presented two aggregation operators in the circumstance of SvNNs.In the end,an actual case of the choice issue of slope treatment schemes is provided to indicate the practicability and effectivity of the proposed MCDM technique.

Intuitionistic fuzzy hierarchical clustering algorithms

Intuitionistic fuzzy set （IFS） is a set of 2-tuple arguments, each of which is characterized by a membership degree and a nonmembership degree. The generalized form of IFS is interval-valued intuitionistic fuzzy set （IVIFS）, whose components are intervals rather than exact numbers. IFSs and IVIFSs have been found to be very useful to describe vagueness and uncertainty. However, it seems that little attention has been focused on the clustering analysis of IFSs and IVIFSs. An intuitionistic fuzzy hierarchical algorithm is introduced for clustering IFSs, which is based on the traditional hierarchical clustering procedure, the intuitionistic fuzzy aggregation operator, and the basic distance measures between IFSs： the Hamming distance, normalized Hamming, weighted Hamming, the Euclidean distance, the normalized Euclidean distance, and the weighted Euclidean distance. Subsequently, the algorithm is extended for clustering IVIFSs. Finally the algorithm and its extended form are applied to the classifications of building materials and enterprises respectively.

Spherical Linear Diophantine Fuzzy Sets with Modeling Uncertainties in MCDM

The existing concepts of picture fuzzy sets(PFS),spherical fuzzy sets(SFSs),T-spherical fuzzy sets(T-SFSs)and neutrosophic sets(NSs)have numerous applications in decision-making problems,but they have various strict limitations for their satisfaction,dissatisfaction,abstain or refusal grades.To relax these strict constraints,we introduce the concept of spherical linearDiophantine fuzzy sets(SLDFSs)with the inclusion of reference or control parameters.A SLDFSwith parameterizations process is very helpful formodeling uncertainties in themulti-criteria decisionmaking(MCDM)process.SLDFSs can classify a physical systemwith the help of reference parameters.We discuss various real-life applications of SLDFSs towards digital image processing,network systems,vote casting,electrical engineering,medication,and selection of optimal choice.We show some drawbacks of operations of picture fuzzy sets and their corresponding aggregation operators.Some new operations on picture fuzzy sets are also introduced.Some fundamental operations on SLDFSs and different types of score functions of spherical linear Diophantine fuzzy numbers(SLDFNs)are proposed.New aggregation operators named spherical linear Diophantine fuzzy weighted geometric aggregation(SLDFWGA)and spherical linear Diophantine fuzzy weighted average aggregation(SLDFWAA)operators are developed for a robust MCDM approach.An application of the proposed methodology with SLDF information is illustrated.The comparison analysis of the final ranking is also given to demonstrate the validity,feasibility,and efficiency of the proposed MCDM approach.

A Novel Green Supplier Selection Method Based on the Interval Type-2 Fuzzy Prioritized Choquet Bonferroni Means

In view of the environment competencies,selecting the optimal green supplier is one of the crucial issues for enterprises,and multi-criteria decision-making(MCDM)methodologies can more easily solve this green supplier selection(GSS)problem.In addition,prioritized aggregation(PA)operator can focus on the prioritization relationship over the criteria,Choquet integral(CI)operator can fully take account of the importance of criteria and the interactions among them,and Bonferroni mean(BM)operator can capture the interrelationships of criteria.However,most existing researches cannot simultaneously consider the interactions,interrelationships and prioritizations over the criteria,which are involved in the GSS process.Moreover,the interval type-2 fuzzy set(IT2FS)is a more effective tool to represent the fuzziness.Therefore,based on the advantages of PA,CI,BM and IT2FS,in this paper,the interval type-2 fuzzy prioritized Choquet normalized weighted BM operators with fuzzy measure and generalized prioritized measure are proposed,and some properties are discussed.Then,a novel MCDM approach for GSS based upon the presented operators is developed,and detailed decision steps are given.Finally,the applicability and practicability of the proposed methodology are demonstrated by its application in the shared-bike GSS and by comparisons with other methods.The advantages of the proposed method are that it can consider interactions,interrelationships and prioritizations over the criteria simultaneously.