T-Spherical Fuzzy Rough Interactive Power Heronian Mean Aggregation Operators for Multiple Attribute Group Decision-Making

In this article, to synthesize the merits of interaction operational laws (IOLs), rough numbers (RNs), power average (PA) and Heronian mean (HM), a new notion of T-spherical fuzzy rough numbers (T-SFRNs) is first introduced to describe the intention of group experts accurately and take the interaction between individual experts into account with complete and symmetric information. The distance measure and ordering rules of T-SFRNs are proposed, and the IOLs of T-SFRNs are extended. Next, the PA and HM are combined based on the IOLs of T-SFRNs, and the T-Spherical fuzzy rough interaction power Heronian mean operator and its weighted form are proposed. These aggregation operators can accurately express both individual and group uncertainty using T-SFRNs, capture the interaction among membership degree, abstinence degree and non-membership degree of T-SFRNs by employing IOLs, ensure the overall balance of variable values by the PA in the process of information fusion, and realize the interrelationship between attribute variables by the HM. Several properties and special cases of these aggregation operators are further presented and discussed. Subsequently, a new approach for dealing with T-spherical fuzzy multiple attribute group decision-making problems based on proposed aggregation operator is developed. Lastly, in order to validate the feasibility and reasonableness of the proposed approach, a numerical example is presented, and the superiorities of the proposed method are illustrated by describing a sensitivity analysis and a comparative analysis.

New distances for dual hesitant fuzzy sets and their application in clustering algorithm

Compared to hesitant fuzzy sets and intuitionistic fuzzy sets, dual hesitant fuzzy sets can model problems in the real world more comprehensively. Dual hesitant fuzzy sets explicitly show a set of membership degrees and a set of non-membership degrees, which also imply a set of important data: hesitant degrees.The traditional definition of distance between dual hesitant fuzzy sets only considers membership degree and non-membership degree, but hesitant degree should also be taken into account. To this end, using these three important data sets (membership degree, non-membership degree and hesitant degree), we first propose a variety of new distance measurements (the generalized normalized distance, generalized normalized Hausdorff distance and generalized normalized hybrid distance) for dual hesitant fuzzy sets in this paper, based on which the corresponding similarity measurements can be obtained. In these distance definitions, membership degree, non-membership-degree and hesitant degree are of equal importance. Second, we propose a clustering algorithm by using these distances in dual hesitant fuzzy information system. Finally, a numerical example is used to illustrate the performance and effectiveness of the clustering algorithm. Accordingly, the results of clustering in dual hesitant fuzzy information system are compared using the distance measurements mentioned in the paper, which verifies the utility and advantage of our proposed distances. Our work provides a new way to improve the performance of clustering algorithms in dual hesitant fuzzy information systems.

Research on Identification of Consumer Product Quality Safety Factors Based on Improved FCM Algorithm

In view of the shortcomings of FCM algorithm, the membership degree and the cluster category number are improved to perfect the FCM algorithm. The performance of the improved algorithm is verified by a case of consumer product quality as a data source, and the results show that with the improved algorithm, both clustering accuracy rate and F value are improved.

FUZZY LIMITS OF FUZZY FUNCTIONS

In this paper, we study the theory of fuzzy limit of fuzzy function depending on the Altai’s principle and using the representation theorem (resolution principle) to run the fuzzy arithmetic.The novelty underlying this theory is that we can provethe convergence of afuzzy function to its fuzzy limit through proving the convergence of its 𝛼-cuts’boundaries to their limits for the membership degree 0<𝛼𝑜<𝛼1≤𝛼≤1.

A method to solve strategy based decision making problems with logarithmic T-spherical fuzzy aggregation framework

T-Spherical fuzzy set (TSFS) is an improved extension in fuzzy set (FS) theory that takes into account four angles of the human judgment under uncertainty about a phenomenon that is membership degree (MD), abstinence degree (AD), non-membership degree (NMD), and refusal degree (RD). The purpose of this manuscript is to introduce and investigate logarithmic aggregation operators (LAOs) in the layout of TSFSs after observing the shortcomings of the previously existing AOs. First, we introduce the notions of logarithmic operations for T-spherical fuzzy numbers (TSFNs) and investigate some of their characteristics. The study is extended to develop T-spherical fuzzy (TSF) logarithmic AOs using the TSF logarithmic operations. The main theory includes the logarithmic TSF weighted averaging (LTSFWA) operator, and logarithmic TSF weighted geometric (LTSFWG) operator along with the conception of ordered weighted and hybrid AOs. An investigation about the validity of the logarithmic TSF AOs is established by using the induction method and examples are solved to examine the practicality of newly developed operators. Additionally, an algorithm for solving the problem of best production choice is developed using TSF information and logarithmic TSF AOs. An illustrative example is solved based on the proposed algorithm where the impact of the associated parameters is examined. We also did a comparative analysis to examine the advantages of the logarithmic TSF AOs.

Picture Hesitant Fuzzy Clustering Based on Generalized Picture Hesitant Fuzzy Distance Measures

Certain scholars have generalized the theory of fuzzy set, but the theory of picture hesitant fuzzy set (PHFS) has received massive attention from distinguished scholars. PHFS is the combination of picture fuzzy set (PFS) and hesitant fuzzy set (HFS) to cope with awkward and complicated information in real-life issues. The well-known characteristic of PHFS is that the sum of the maximum of the membership, abstinence, and non-membership degree is limited to the unit interval. This manuscript aims to develop some generalized picture hesitant distance measures (GPHDMs) as a generalization of generalized picture distance measures (GPDMs). The properties of developed distance measures are investigated, and the generalization of developed theory is proved with the help of some remarks and examples. A clustering problem is solved using GPHDMs and the results obtained are explored. Some advantages of the proposed work are discussed, and some concluding remarks based on the summary of the proposed work and as well as future directions, are added.

q-Rung orthopair fuzzy frank power point aggregation operators with new multi-parametric distance measures

The recently proposed q-rung orthopair fuzzy set (q-ROFS) whose main feature is that the qth power of membership degree (MD) and the qth power of non-membership degree (NMD) is equal to or less than 1, is a powerful tool to describe uncertainty. The major contribution of this paper lies to investigate power point average (PPA) aggregation operators with q-rung orthopair fuzzy information based on Frank t-conorm and t-norm. Since the existing power average (PA) operators all rely on the traditional distance measures to measure support degree between the input values, it cannot reflect decision makers’ attitude. In response, this paper introduces firstly a series of distance measures for q-rung orthopair fuzzy numbers (q-ROFNs) based on point operators, from which the corresponding support measures can be obtained. Secondly, based on the proposed point distance measures, new Frank power point average aggregation operators are proposed to aggregate q-rung orthopair fuzzy information. Finally, a novel multiple attribute decision making (MADM) technique is presented based on the proposed Frank power point average aggregation operators. The developed MADM method not only can get more objective information, but also avoid the influence of unduly high or low attribute values on the decision result, providing a new way for decision makers (DMs) under q-rung orthopair fuzzy environment.

Some Novel Geometric Aggregation Operators of Spherical Cubic Fuzzy Information with Application

Technology is quickly evolving and becoming part of our lives. Life has become better and easier due to the technologies. Although it has lots of benefits, it also brings serious risks and threats, known as cyberattacks, which are neutralized by cybersecurities. Since spherical fuzzy sets (SFSs) and interval-valued SFS (IVSFS) are an excellent tool in coping with uncertainty and fuzziness, the current study discusses the idea of spherical cubic FSs (SCFSs). These sets are characterized by three mappings known as membership degree, neutral degree, and nonmembership degree. Each of these degrees is spherical cubic fuzzy numbers (SCFNs) such that the summation of their squares does not exceed one. The score function and accuracy function are presented for the comparison of SCFNs. Moreover, the spherical cubic fuzzy weighted geometric (SCFWG) operators and SCF ordered weighted geometric (SCFOWG) operators are established for determining the distance between two SCFNs. Furthermore, some operational rules of the proposed operators are analyzed and multiattribute decision-making (MADM) approach based on these operators is presented. These methods are applied to make the best decision on the basis of risks factors as a numerical illustration. Additionally, the comparison of the proposed method with the existing methods is carried out; since the proposed methods and operators are the generalizations of existing methods, they provide more general, exact, and accurate results. Finally, for the legitimacy, practicality, and usefulness of the decision-making processes, a detailed illustration is given.

Evaluation of Tourism E-Commerce User Satisfaction

According to the UNWTO, within 4 to 5 years, the proportion of tourism e-commerce in e-commerce will reach 20%-25%. The purpose of this paper is to improve the inadequacy of tourism e-commerce in customer experience, to conduct customer e-commerce satisfaction surveys, and to draw customers' dissatisfaction with tourism e-commerce. The experimental results show that the overall customer satisfaction is 2.6128. According to the division of the scale vector, the overall satisfaction of the travel e-commerce customers is generally level. The first-level fuzzy comprehensive evaluation is 0.0967, 0.1696, 0.3366, 0.2469, 0.502. According to the principle of maximum membership degree, the evaluation grades of R3 and R5 in the first-level fuzzy comprehensive evaluation are “unsatisfactory,” that is, the tourism-supporting services and contract-performance services become the main factors affecting customer satisfaction. In order to improve customer satisfaction, the tourism e-commerce platform should strengthen the management of tourism-supporting services and contract-fulfillment services.

Medical diagnosis of nephrotic syndrome using m-polar spherical fuzzy sets

The aim of this paper is to introduce the notion of m-polar spherical fuzzy set (mPSFS) as a hybrid model of spherical fuzzy set (SFS) and m-polar fuzzy set (mPFS). The proposed model named as mPSFS is an efficient model to address multi-polarity in a spherical fuzzy environment. That is, an mPSFS assigns [Formula: see text] number of ordered triple of three independent grades (membership degree, neutral-membership degree and non-membership degree) against each alternative in the universe of discourse. The existing models, namely, mPFS and SFS, are the special cases of suggested hybrid mPSFS. In order to ensure the novelty of this robust extension, various operations on the m-polar spherical fuzzy sets (mPSFSs) are introduced with some brief illustrations to understand these concepts. A robust multi-criteria decision-making (MCDM) method is established by using new score function and accuracy function for m-polar spherical fuzzy numbers (mPSFNS). Additionally, the extensions of technique of order preference by similarity to ideal solution (TOPSIS) and gray relationship analysis (GRA) towards m-polar spherical fuzzy environment are proposed. Moreover, an application to nephrotic syndrome which may lead to kidney damage is analyzed by extensions TOPSIS and GRA. The proposed techniques and their algorithms provide a fruitful diagnosis procedure in the treatment of nephrotic syndrome. Lastly, we give a comparison analysis of the suggested models with some existing models as well.