The Spherical q-Linear Diophantine Fuzzy Multiple-Criteria Group Decision-Making Based on Differential Measure

Spherical q-linearDiophantine fuzzy sets(Sq-LDFSs)provedmore effective for handling uncertainty and vagueness in multi-criteria decision-making(MADM).It does not only cover the data in two variable parameters but is also beneficial for three parametric data.By Pythagorean fuzzy sets,the difference is calculated only between two parameters(membership and non-membership).According to human thoughts,fuzzy data can be found in three parameters(membership uncertainty,and non-membership).So,to make a compromise decision,comparing Sq-LDFSs is essential.Existing measures of different fuzzy sets do,however,can have several flaws that can lead to counterintuitive results.For instance,they treat any increase or decrease in the membership degree as the same as the non-membership degree because the uncertainty does not change,even though each parameter has a different implication.In the Sq-LDFSs comparison,this research develops the differentialmeasure(DFM).Themain goal of the DFM is to cover the unfair arguments that come from treating different types of FSs opposing criteria equally.Due to their relative positions in the attribute space and the similarity of their membership and non-membership degrees,two Sq-LDFSs formthis preference connectionwhen the uncertainty remains same in both sets.According to the degree of superiority or inferiority,two Sq-LDFSs are shown as identical,equivalent,superior,or inferior over one another.The suggested DFM’s fundamental characteristics are provided.Based on the newly developed DFM,a unique approach tomultiple criterion group decision-making is offered.Our suggestedmethod verifies the novel way of calculating the expert weights for Sq-LDFSS as in PFSs.Our proposed technique in three parameters is applied to evaluate solid-state drives and choose the optimum photovoltaic cell in two applications by taking uncertainty parameter zero.The method’s applicability and validity shown by the findings are contrasted with those obtained using various other existing approaches.To assess its stability and usefulness,a sensitivity analysis is done.

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.

An Integrated Bipolar Picture Fuzzy Decision Driven System to Scrutinize Food Waste Treatment Technology through Assorted Factor Analysis

Food Waste(FW)is a pressing environmental concern that affects every country globally.About one-third of the food that is produced ends up as waste,contributing to the carbon footprint.Hence,the FW must be properly treated to reduce environmental pollution.This study evaluates a few available Food Waste Treatment(FWT)technologies,such as anaerobic digestion,composting,landfill,and incineration,which are widely used.A Bipolar Picture Fuzzy Set(BPFS)is proposed to deal with the ambiguity and uncertainty that arise when converting a real-world problem to a mathematical model.A novel Criteria Importance Through Intercriteria Correlation-Stable Preference Ordering Towards Ideal Solution(CRITIC-SPOTIS)approach is developed to objectively analyze FWT selection based on thirteen criteria covering the industry’s technical,environmental,and entrepreneurial aspects.The CRITIC method is used for the objective analysis of the importance of each criterion in FWT selection.The SPOTIS method is adopted to rank the alternative hassle-free,following the criteria.The proposed model offers a rank reversal-free model,i.e.,the rank of the alternatives remains unaffected even after the addition or removal of an alternative.In addition,comparative and sensitivity analyses are performed to ensure the reliability and robustness of the proposed model and to validate the proposed result.

Some convergence theorems of fuzzy concave integral on fuzzyσ-algebra

In this paper,we consider the extension of the concave integral from classical crispσ-algebra to fuzzyσ-algebra of fuzzy sets.Firstly,the concept of fuzzy concave integral on a fuzzy set is introduced.Secondly,some important properties of such integral are discussed.Finally,various kinds of convergence theorems of a sequence of fuzzy concave integrals are proved.

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.

Business Blockchain Suitability Determinants: Decision-Making through an Intuitionistic Fuzzy Method

Blockchain is one of the innovative and disruptive technologies that has a wide range of applications in multiple industries beyond cryptocurrency.The widespread adoption of blockchain technology in various industries has shown its potential to solve challenging business problems,as well as the possibility to create new business models which can increase a firm’s competitiveness.Due to the novelty of the technology,whereby many companies are still exploring potential use cases,and considering the complexity of blockchain technology,which may require huge changes to a company’s existing systems and processes,it is important for companies to carefully evaluate suitable use cases and determine if blockchain technology is the best solution for their specific needs.This research aims to provide an evaluation framework that determines the important dimensions of blockchain suitability assessment by identifying the key determinants of suitable use cases in a business context.In this paper,a novel approach that utilizes both qualitative(Delphi method)and quantitative(fuzzy set theory)methods has been proposed to objectively account for the uncertainty associated with data collection and the vagueness of subjective judgments.This work started by scanning available literature to identify major suitability dimensions and collected a range of criteria,indicators,and factors that had been previously identified for related purposes.Expert opinions were then gathered using a questionnaire to rank the importance and relevance of these elements to suitability decisions.Subsequently,the data were analyzed and we proceeded to integrate multi-criteria group decision-making(MCGDM)and intuitionistic fuzzy set(IFS)theory.The findings demonstrated a high level of agreement among experts,with the model being extremely sensitive to variances in expert assessments.Furthermore,the results helped to refine and select the most relevant suitability determinants under three important dimensions:functional suitability of the use case,organizational applicability,and ecosystem readiness.

Multi-Attribute Group Decision-Making Method under Spherical Fuzzy Bipolar Soft Expert Framework with Its Application

Spherical fuzzy soft expert set(SFSES)theory blends the perks of spherical fuzzy sets and group decision-making into a unified approach.It allows solutions to highly complicated uncertainties and ambiguities under the unbiased supervision and group decision-making of multiple experts.However,SFSES theory has some deficiencies such as the inability to interpret and portray the bipolarity of decision-parameters.This work highlights and overcomes these limitations by introducing the novel spherical fuzzy bipolar soft expert sets(SFBSESs)as a powerful hybridization of spherical fuzzy set theory with bipolar soft expert sets(BSESs).Followed by the development of certain set-theoretic operations and properties of the proposed model,important problems,including the selection of non-powered dam(NPD)sites for hydropower conversion are discussed and solved under the proposed approach.These problems mainly focus on the need for an efficient tool capable of considering the bipolarity of parameters,complicated ambiguities,and multiple opinions.Supporting the new approach by a detailed comparative analysis,it is concluded that the proposed model is more comprehensive and reliable for multi-attribute group decisionmaking(MAGDM)than the previous tools,particularly considering the bipolarity of parameters under SFSES environment.

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.

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.

The Laplacian Energy of Hesitancy Fuzzy Graphs in Decision-Making Problems

Decision-making(DM)is a process in which several persons concur-rently engage,examine the problems,evaluate potential alternatives,and select an appropriate option to the problem.Technique for determining order preference by similarity to the ideal solution(TOPSIS)is an established DM process.The objective of this report happens to broaden the approach of TOPSIS to solve the DM issues designed with Hesitancy fuzzy data,in which evaluation evidence given by the experts on possible solutions is presents as Hesitancy fuzzy decision matrices,each of which is defined by Hesitancy fuzzy numbers.Findings:we represent analytical results,such as designing a satellite communication network and assessing reservoir operation methods,to demonstrate that our suggested thoughts may be used in DM.Aim:We studied a new testing method for the arti-ficial communication system to give proof of the future construction of satellite earth stations.We aim to identify the best one from the different testing places.We are alsofinding the best operation schemes in the reservoir.In this article,we present the concepts of Laplacian energy(LE)in Hesitancy fuzzy graphs(HFGs),the weight function of LE of HFGs,and the TOPSIS method technique is used to produce the hesitancy fuzzy weighted-average(HFWA).Also,consider practical examples to illustrate the applicability of thefinest design of satellite communication systems and also evaluation of reservoir schemes.

Proportion Integration Differentiation(PID)Control Strategy of Belt Sander Based on Fuzzy Algorithm

Aiming at solving the problems of response lag and lack of precision and stability in constant grinding force control of industrial robot belts,a constant force control strategy combining fuzzy control and proportion integration differentiation(PID)was proposed by analyzing the signal transmission process and the dynamic characteristics of the grinding mechanism.The simulation results showed that compared with the classical PID control strategy,the system adjustment time was shortened by 98.7%,the overshoot was reduced by 5.1%,and the control error was 0.2%-0.5%when the system was stabilized.The optimized fuzzy control system had fast adjustment speeds,precise force control and stability.The experimental analysis of the surface morphology of the machined blade was carried out by the industrial robot abrasive grinding mechanism,and the correctness of the theoretical analysis and the effectiveness of the control strategy were verified.

Fuzzy Henstock-Kurzweil Triple Integral on a Type 1 Quasi-Fuzzy Parallelepipedal Domain

In this article, we propose by using the Hausdorff distance Simpson’s rule for the triple integral of a fuzzy-valued function and the error bound of this method, one of the variables of which is fuzzy. In addition, thin δ-fine partitions are introduced. The integration domain is a quasi-fuzzy parallelipiped. A numerical example is presented in order to show the application and the significance of the method.

APPROACH FOR FUZZY MULTI-ATTRIBUTE DECISION-MAKING WITH FUZZY COMPLEMENTARY PREFERENCE RELATION ON ALTERNATIVES

In presented fuzzy multi-attribute decision-making （FMADM） problems, the information about attribute weights is interval numbers and the decision maker （DM） has fuzzy complementary preference relation on alternatives. Firstly, the decision-making information based on the subjective preference information in the form of the fuzzy complementary judgment matrix is uniform by using a translation function. Then an objective programming model is established. Attribute weights are obtained by solving the model, thus the fuzzy overall values of alternatives are derived by using the additive weighting method. Secondly, the ranking approach of alternatives is proposed based on the degree of similarity between the fuzzy positive ideal solution of alternatives （FPISA） and the fuzzy overall values. The method can sufficiently utilize the objective information of alternatives and meet the subjective requirements of the DM as much as possible. It is easy to be operated and implemented on a computer. Finally, the proposed method is applied to the project evaluation in the venture investment.

Fuzzy multiple attribute decision-making model for synergic knowledge innovation in supply chain

The procedure of supply chain development is the process of continuously congregating knowledge and transforming knowledge.First,the precondition of synergic knowledge innovation in the supply chain is narrated.Then the characteristics of synergic knowledge innovation in the supply chain are analyzed,including complexity,accumulating and evolving process,and the cooperation of members and network integration.Due to the characteristics of multi-factors and uncertainties of the supply chain system,the fuzzy multi-attribution group decision-making model is introduced to solve the involved problem of synergic knowledge innovation in the supply chain.After elaborating on steps of using the fuzzy multiple attribute decision-making(MADM)model,the procedure of decision making for synergic knowledge innovation in the supply chain is explained from an example in the application of a fuzzy MADM model.The fuzzy MADM model,which amalgamates intuition and resolution decision-making can effectively improve the rationality of decision-making for synergic knowledge innovation in the supply chain.

A multi-enterprise quality function deployment paradigm with unstructured decision-making in linguistic contexts

This paper presents an operational framework of unstructured decision-making approach involving quality function deployment(QFD)in an uncertain linguistic context.Firstly,QFD is extended to the multi-enterprise paradigm in a real-world manufacturing environment.Secondly,hesitant fuzzy linguistic term sets(HFLTSs),which facilitate the management and handling of information equivocality,are designed to construct a house of quality(HoQ)in the product planning process.The technique of computing with words is applied to bridge the gap between mechanisms of the human brain and machine processes with fuzzy linguistic term sets.Thirdly,a multi-enterprise QFD pattern is formulated as an unstructured decision-making problem for alternative infrastructure project selection in a manufacturing organization.The inter-relationships of cooperative partners are directly matched with a back propagation neural network(BPNN)to construct the multi-enterprise manufacturing network.The resilience of the manufacturing organization is considered by formulating an outranking method on the basis of HFLTSs to decide on infrastructure project alternatives.Finally,a real-world example,namely,the prototype manufacturing of an automatic transmission for a vehicle,is provided to illustrate the effectiveness of the proposed decision-making approach.

Selection of the best initial orbital elements of satellite based on fuzzy integration evaluation method

The fuzzy integration evaluation method （FIEM） is studied in order to select the best orbital elements from the multi-group initial orbits determined by a satellite TT＆C （Tracking, Telemetry and Control） center with all kinds of data sources. By employing FIEM together with the experience of TT＆C experts, the index system to evaluate the selection of the best initial orbits is established after the data sources and orbit determination theories are studied. Besides, the concrete steps in employing the method are presented. Moreover, by taking the objects to be evaluated as evaluation experts, the problem of how to generate evaluation matrices is solved. Through practical application, the method to select the best initial orbital elements has been proved to be flexible and effective The originality of the method is to find a new evaluation criterion （comparing the actually tracked orbits） replacing the traditional one （comparing the nominal orbits） for selecting the best orbital elements.

Behavioral Decision-Making of Key Stakeholders in Public-Private Partnerships:A Hybrid Method and Benefit Distribution Study

Public-private partnerships(PPPs)have been used by governments around the world to procure and construct infrastructural amenities.It relies on private sector expertise and funding to achieve this lofty objective.However,given the uncertainties of project management,transparency,accountability,and expropriation,this phenomenon has gained tremendous attention in recent years due to the important role it plays in curbing infrastructural deficits globally.Interestingly,the reasonable benefit distribution scheme in a PPP project is related to the behavior decisionmaking of the government and social capital,aswell as the performance of the project.In this paper,the government and social capital which are the key stakeholders of PPP projects were selected as the research objects.Based on the fuzzy expected value model and game theory,a hybrid method was adopted in this research taking into account the different risk preferences of both public entities and private parties under the fuzzy demand environment.To alleviate the problem of insufficient utilization of social capital in a PPP project,this paper seeks to grasp the relationship that exists between the benefit distribution of stakeholders,their behavioral decision-making,and project performance,given that they impact the performance of both public entities and private parties,as well as assist in maximizing the overall utility of the project.Furthermore,four game models were constructed in this study,while the expected value and opportunity-constrained programming model for optimal decision-making were derived using alternate perspectives of both centralized decision-making and decentralized decision-making.Afterward,the optimal behavioral decision-making of public entities and private parties in four scenarios was discussed and thereafter compared,which led to an ensuing discussion on the benefit distribution system under centralized decision-making.Lastly,based on an example case,the influence of different confidence levels,price,and fuzzy uncertainties of PPP projects on the equilibrium strategy results of both parties were discussed,giving credence to the effectiveness of the hybrid method.The results indicate that adjusting different confidence levels yields different equilibriumpoints,and therefore signposts that social capital has a fair perception of opportunities,as well as identifies reciprocal preferences.Nevertheless,we find that an increase in the cost coefficient of the government and social capital does not inhibit the effort of both parties.Our results also indicate that a reasonable benefit distribution of PPP projects can assist them in realizing optimum Pareto improvements over time.The results provide us with very useful strategies and recommendations to improve the overall performance of PPP projects in China.

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.

Unique Solution of Integral Equations via Intuitionistic Extended Fuzzy b-Metric-Like Spaces

In this manuscript,our goal is to introduce the notion of intuitionistic extended fuzzy b-metric-like spaces.We establish some fixed point theorems in this setting.Also,we plot some graphs of an example of obtained result for better understanding.We use the concepts of continuous triangular norms and continuous triangular conorms in an intuitionistic fuzzy metric-like space.Triangular norms are used to generalize with the probability distribution of triangle inequality in metric space conditions.Triangular conorms are known as dual operations of triangular norms.The obtained results boost the approaches of existing ones in the literature and are supported by some examples and applications.

Integrated classification method of tight sandstone reservoir based on principal component analysise simulated annealing genetic algorithmefuzzy cluster means

In this research,an integrated classification method based on principal component analysis-simulated annealing genetic algorithm-fuzzy cluster means(PCA-SAGA-FCM)was proposed for the unsupervised classification of tight sandstone reservoirs which lack the prior information and core experiments.A variety of evaluation parameters were selected,including lithology characteristic parameters,poro-permeability quality characteristic parameters,engineering quality characteristic parameters,and pore structure characteristic parameters.The PCA was used to reduce the dimension of the evaluation pa-rameters,and the low-dimensional data was used as input.The unsupervised reservoir classification of tight sandstone reservoir was carried out by the SAGA-FCM,the characteristics of reservoir at different categories were analyzed and compared with the lithological profiles.The analysis results of numerical simulation and actual logging data show that:1)compared with FCM algorithm,SAGA-FCM has stronger stability and higher accuracy;2)the proposed method can cluster the reservoir flexibly and effectively according to the degree of membership;3)the results of reservoir integrated classification match well with the lithologic profle,which demonstrates the reliability of the classification method.