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The Covid-19 emergency condition is a critical issue for emergency decision support systems. Controlling the spread of Covid-19 in emergency circumstances throughout the global is a difficult task, hence the purpose of this research is to develop a non-linear diophantine fuzzy decision making mechanism for preventing and identifying Covid-19. Fundamentally, the article is divided into three sections in order to establish suitable and correct procedures to meet the circumstances of emergency decision-making. Firstly, we present a non-linear diophantine fuzzy set (non-LDFS), which is the generalisation of Pythagorean fuzzy set, q-rung orthopair fuzzy set, and linear diophantine fuzzy set, and explain their critical features. In addition, algebraic norms for non-LDFSs are constructed based on particular operational rules. In the second section, we use non-LDF averaging and geometric operator to aggregate expert judgements. The last section of this study consists of ranking in which MABAC (multi-attributive border approximation area comparison) method is used to handle the Covid-19 emergency circumstance using non-LDF information. Moreover, based on the presented methods, the numerical case-study of Covid-19 condition is presented as an application for emergency decision-making. The results shows the efficiency of our proposed techniques and give precise emergency strategies to resolve the worldwide ambiguity of Covid-19. [ABSTRACT FROM AUTHOR]

The goal of the present research work is to develop a new family of aggregation operators (AOs) under the fractional orthotriple fuzzy (FOF) information and apply them to MCDM problems. At the start, the Archimedean coupla and co-coupla are extended to handle FOF information, and some operational law for fractional orthotriple fuzzy numbers (FOFNs) based on extended Archimedean copula (EAC) and extended Archimedean co-copula (EACC) is presented. The fractional orthotriple fuzzy Banzhaf Choquet-Copula aggregation operator and fractional orthotriple fuzzy Banzhaf Choquet-Copula geometric operators are defined based on the proposed operational laws of FOFNs. In addition, the modified maximum deviation approach and the Banzhaf function model are created to objectively determine the fuzzy measure (FM) of criteria sets. Finally, based on the defined AOs, the appropriate decision-making procedures are developed. The proposed approaches can effectively overcome the FMs of criteria sets that are subjectively assigned by decision makers, as well as some decision-making problems in which the weights of the criteria are incomplete (completely) unknown, and there is a correlation between all criteria set. [ABSTRACT FROM AUTHOR]

The objectives of this paper are to define novel aggregation operators (AOs) for aggregating different complex spherical fuzzy numbers (CSFNs) under the influence of their membership grades. The uncertainties included in the information are dealt with in contemporary studies of the fuzzy set and its extensions by membership grades, which are a subset of real numbers that lose some relevant information and hence alter the decision results. The conversion to these complex spherical fuzzy sets addresses the classes' uncertainty, whose ranges differ from the specific subset of the complex subset of the unit disk. For this purpose, we defined new CSF power AOs. Some of the desirable properties of these operators have also been investigated. A multiattribute group decision-making (MAGDM) approach is implemented in the structure developed by the CSFNs on the basis of these operators. A numerical example concerning the selection of the best alternatives is given to demonstrate the effectiveness of the defined method and is tested by comparing its results with the various methods. [ABSTRACT FROM AUTHOR]

The main aim of the proposed work is to develop the new technique based on decision‐theoretical rough sets (DTRSs) and their applications in three‐way decision‐making problems. This study first develop a fractional fuzzy set (FFS) and their operations, the FFS is a more generalized and accurate tool for describing uncertainty in real‐life data information. A new form of decision technique for dealing with the issue of choice based on DTRSs is included in the three‐way decisions. The loss function of DTRSs is being used in the proposed decision method model. Initially, the idea of fractional fuzzy α‐covering (FF α‐covering), fractional fuzzy α–neighborhood (FF α–neighborhood) was introduced. Under the fractional fuzzy state, we integrated the loss function of DTRSs with covering‐based fractional fuzzy rough sets. Furthermore, we proposed and established performance characteristics for a new fractional fuzzy α‐covering decision‐theoretical rough sets model (FFCDTRSs). Then, according to the level of fractional fuzzy numbers (FFN's) positive and negative membership and related three‐way decision‐making, four methods to solve the expected loss expressed in the form of (FFNs) are described. We have developed a multicriteria decision algorithm (MCDM) based on FFCDTRS. Then an example is used to prove the feasibility of the four methods to solve the MCDM problem. Finally, the results of four distinct decision procedures with various loss functions are compared. The proposed three‐way decision‐making models are more accurate as compared with particular fuzzy sets. [ABSTRACT FROM AUTHOR]

The triangular linguistic cubic fuzzy sets (TLCFSs) can express the fuzzy data easily and is also very useful in modeling of uncertain data in decision making (DM) problems. First of all, on the basis of Dombi t-norm and t-conorm (DTT), we propose novel operational rules of triangular linguistic cubic fuzzy numbers (TLCFNs). We propose some new aggregation operators of TLCFNs based on the newly developed operations, i.e., triangular linguistic cubic fuzzy Dombi weighted averaging (TLCFDWA), triangular linguistic cubic fuzzy Dombi weighted geometric (TLCFDWG), triangular linguistic cubic fuzzy Dombi order weighted averaging (TLCFDOWA), triangular linguistic cubic fuzzy Dombi order weighted geometric (TLCFDOWG), triangular linguistic cubic fuzzy Dombi hybrid weighted averaging (TLCFDHWA), and triangular linguistic cubic fuzzy Dombi hybrid weighted geometric (TLCFDHWG) operators. Furthermore, a new method is proposed with the help of the proposed operators to solve the decision making problem. Finally, a numerical example is provided to illustrate the effectiveness of the new method. Comparative analysis is used to demonstrate the proposed method's superiority. [ABSTRACT FROM AUTHOR]

In this study, we highlight the errors in Sections 2.3, 2.4, 3, and 4 in the article by Fahmi et al. (J Ambient Intell Human Comput (2020). https://doi.org/10.1007/s12652-020-02272-9) by counter definitions and theorems. We find that the definition of cubic Pythagorean fuzzy set (CPFS) (Definition 2.3.1) and operational laws (Definition 2.3.2) violates the rules to consider the membership and nonmembership functions, and then, we redefined the corrected definition and their operations for CPFS. Furthermore, we redefine the concept of cubic Pythagorean linguistic fuzzy set (CPLFS) and their basic operational laws. In addition, we find that Sections 3 and 4 (consist of a list of Maclaurin symmetric mean (MSM) and dual MSM aggregation operators) are invalid, and then, we redefined the list of updated MSM and dual MSM aggregation operators in correct way. Finally, we established the numerical application of the proposed improved algorithm using cubic Pythagorean linguistic fuzzy information to show the applicability and effectiveness of the proposed technique. [ABSTRACT FROM AUTHOR]

Information fusion of fuzzy numbers has played a vital role in the decision support systems under the environment of q-rung orthopair fuzzy set (q-ROFS), which is an effective extension of intuitionistic fuzzy set and fuzzy set. The goals of the present work are to build a family of new aggregation operators (AOs) under q-ROF environment and apply them to MADM problems. First, the extended Archimedean copula (EAC) and extended Archimedean co-copula (EACC) are proposed to handle q-ROF information; consequently, the operational law of q-ROFNs is defined based on EAC and EACC. In order to comprehensively consider the relationship between attributes, the q-rung orthopair fuzzy Banzhaf–Choquet-copula AOs ( B C C A q ) and q-rung orthopair fuzzy Banzhaf–Choquet-copula geometric operators ( B C C G q ) are introduced on the basis of the operation of q-rung orthopair fuzzy numbers (q-ROFNs); consequently, some special cases of B C C A q / B C C G q operators are investigated when the generators of copula take different functions which satisfy the condition of the generators of copulas. In addition, to determine the fuzzy measure (FM) of attribute sets objectively, the improved maximum deviation method and Banzhaf function model are built. Finally, the corresponding decision-making approaches are constructed based on the proposed AOs and proposed models. Proposed approaches can effectively address the some decision-making problems (DMPs), in which the weights of attributes are incompletely unknown (completely unknown), and the correlation also exists among all attribute sets. [ABSTRACT FROM AUTHOR]

Based on decision theory rough sets (DTRSs), three-way decisions (TWDs) provide a risk decision method for solving multi-attribute decision making (MADM) problems. The loss function matrix of DTRS is the basis of this method. In order to better solve the uncertainty and ambiguity of the decision problem, we introduce the q-rung orthopair fuzzy numbers (q-ROFNs) into the loss function. Firstly, we introduce concepts of q-rung orthopair fuzzy β-covering (q-ROF β-covering) and q-rung orthopair fuzzy β-neighborhood (q-ROF β-neighborhood). We combine covering-based q-rung orthopair fuzzy rough set (Cq-ROFRS) with the loss function matrix of DTRS in the q-rung orthopair fuzzy environment. Secondly, we propose a new model of q-ROF β-covering DTRSs (q-ROFCDTRSs) and elaborate its relevant properties. Then, by using membership and non-membership degrees of q-ROFNs, five methods for solving expected losses based on q-ROFNs are given and corresponding TWDs are also derived. On this basis, we present an algorithm based on q-ROFCDTRSs for MADM. Then, the feasibility of these five methods in solving the MADM problems is verified by an example. Finally, the sensitivity of each parameter and the stability and effectiveness of these five methods are compared and analyzed. [ABSTRACT FROM AUTHOR]

The Pythagorean fuzzy number is a new tool for uncertainty and vagueness. It is a generalization of fuzzy numbers and intuitionistic fuzzy numbers. In this paper, we define some Einstein operations on Pythagorean trapezoidal fuzzy set and develop two averaging aggregation operators, which is an induced Pythagorean trapezoidal fuzzy Einstein ordered weighted averaging operator and an induced Pythagorean trapezoidal fuzzy Einstein hybrid averaging (I-PTFEHA) operator. We presented some new methods to deal with the multi-attribute group decision-making problems under the Pythagorean trapezoidal fuzzy environment. Finally, we used some practical examples to illustrate the validity and feasibility of the proposed methods by comparing with existing method. It shows that the proposed I-PTFEHA operator is much better and reliable than the existing one. [ABSTRACT FROM AUTHOR]

In this paper, we define aggregation operators for trapezoidal cubic linguistic fuzzy sets which includes generalized cubic linguistic fuzzy averaging (geometric) operator, generalized trapezoidal cubic linguistic fuzzy weighted averaging (GTrCLFWA) operator, generalized trapezoidal cubic linguistic fuzzy weighted geometric (GTrCFWG) operator, generalized trapezoidal cubic linguistic fuzzy ordered weighted average (GTrCLFOWA) operator, generalized trapezoidal cubic linguistic fuzzy ordered weighted geometric (GTrCLFOWG) operator, generalized trapezoidal cubic linguistic fuzzy hybrid averaging (GTrCLFHA) operator and generalized trapezoidal cubic linguistic fuzzy hybrid geometric (GTrCLFHG) operator. Furthermore, we relate these aggregation operators to develop an approach to multiple attribute group decision-making with trapezoidal cubic linguistic fuzzy information. Finally, a numerical example is providing to demonstrate the submission of the established approach. [ABSTRACT FROM AUTHOR]

The linguistic picture fuzzy set (LPFS) is an extension of the linguistic intuitionistic fuzzy set (LIFS), and can contain more information than the LIFS. In this paper, the degrees of positive, neutral and non-membership of PFSs are expressed in linguistic terms, which can more easily describe the uncertain and vague information existing in the real world. By combining the PFS and the linguistic term, we define the LPFS and propose operational rules for linguistic picture fuzzy numbers (LPFNs). We further propose weighted averaging and weighted geometric operators and discuss their properties. Additionally, we propose an approach to deal with a multiple-attribute group decision-making (MAGDM) problem based on the developed aggregation operators. Finally, we present an illustrative example to demonstrate the effectiveness and advantages of the developed method by comparing it with existing methods. In addition, our method can be utilized not only to solve problems with linguistic intuitionistic fuzzy numbers (LIFNs), but also to deal with problems with LPFNs, and is a generalization of a number of existing methods. [ABSTRACT FROM AUTHOR]

Trapezoidal cubic fuzzy numbers (TzCFNs) are an extraordinary cubic fuzzy set on a real number set. TzCFNs are useful for dealing with well-known quantities in decision data and decision making problems themselves. This paper is about multi-attribute group decision making problems in which the attribute values are stated with TzCFNs, which are solved by developing a new decision method based on power average operators of TzCFNs. The new operation laws for TzCFNs are given. Hereby, the power average operator of real numbers is extended to four kinds of power average operators of TzCFNs, involving the power average operator of TzCFNs, the weighted power average operator of TzCFNs, the power ordered weighted average operator of TzCFNs, and the power hybrid average operator of TzCFNs. In the proposed group decision method, the individual overall evaluation values of alternatives are generated by using the power average operator of TzCFNs. Applying the hybrid average operator of TzCFNs, the specific general evaluation standards of alternatives are then combined into the collective ones, which are used to rank the alternatives. The example analysis shows the practicality and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this study, we developed an approach to investigate multiple attribute group decision-making (MAGDM) problems, in which the attribute values take the form of Pythagorean fuzzy numbers whose information about attribute weights is incompletely known. First, the Pythagorean fuzzy Choquet integral geometric operator is utilized to aggregate the given decision information to obtain the overall preference value of each alternative by experts. In order to obtain the weight vector of the criteria, an optimization model based on the basic ideal of the traditional gray relational analysis method is established, and the calculation steps for solving Pythagorean fuzzy MAGDM problems with incompletely known weight information are given. The degree of gray relation between every alternative and positive-ideal solution and negative-ideal solution is calculated. Then, a relative relational degree is defined to determine the ranking order of all alternatives by calculating the degree of gray relation to both the positive-ideal solution and negative-ideal solution simultaneously. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness. [ABSTRACT FROM AUTHOR]

The aim of this paper is to define some new operation laws for the trapezoidal linguistic cubic fuzzy number and Hamming distance. Furthermore, we define and use the trapezoidal linguistic cubic fuzzy TOPSIS method to solve the multi criteria decision making (MCDM) method. The new ranking method for trapezoidal linguistic cubic fuzzy numbers (TrLCFNs) are used to rank the alternatives. Finally, an illustrative example is given to verify and prove the practicality and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

For the multi-attribute group decision-making problems where attribute values are the interval-valued Pythagorean fuzzy numbers, the group decision-making method based on induced Einstein averaging aggregation operators are developed. Firstly, induced interval-valued Pythagorean fuzzy Einstein ordered weighted averaging (I-IVPFEOWA) aggregation operator and induced interval-valued Pythagorean fuzzy Einstein hybrid weighted averaging (I-IVPFEHWA) aggregation operator, were proposed. Some general properties of these operators, such as idempotency, commutativity, monotonicity and boundedness, were discussed, and some special cases in these operators were analyzed. Furthermore, the method for multi-attribute group decision-making problems based on these operators was developed, and the operational progressions were explained in detail. These methods provide more general, more accurate and precise results as compared to the existing methods. Therefore these methods play a vital role in daily life problems. At the end of the paper the proposed operators have been applied to decision making problems to show the weight, practicality and effectiveness of the new approach. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Faced with the contradiction between economic growth and environmental pollution, to implement cleaner production has become a good choice for many mining companies in order to achieve sustainable development. This study aims to explore applicable decision-making methods to evaluate the cleaner production for gold mines. First, the CPFNs (cubic picture fuzzy numbers) are adopted to describe experts' assessment information under complicated fuzzy environment. Thereafter, the mean-squared deviation models are combined to obtain the comprehensive criteria weights. Meanwhile, a novel evaluation method, which integrates the ranking of CPFNs and distance measure, is proposed to judge the cleaner production level. Subsequently, according to the characteristics of gold mines, the evaluation criteria system of cleaner production is constructed. Finally, a case of evaluating the cleaner production performance for three gold mines is provided to explain the application of the proposed method. Besides this, a systematic comparison analysis with other existent methods is conducted to reveal the advantages of our method. Results indicate that the proposed method is suitable and effective for gold mines to evaluate their cleaner production performance and has important reference values for the cleaner production management and implementation. [ABSTRACT FROM AUTHOR]

The primary goal of this paper is to solve the investment problem based on linguistic picture decision making method under the linguistic triangular picture linguistic fuzzy environment. First to define the triangular picture linguistic fuzzy numbers. Further, we define operations on triangular picture linguistic fuzzy numbers and their aggregation operator namely, triangular picture fuzzy linguistic induce OWA (TPFLIOWA) and triangular picture fuzzy linguistic induce OWG (TPFLIOWG) operators. Multi-criteria group decision making method is developed based on TPFLIOWA and TPFLIOWG operators and solve the uncertainty in the investment problem. We study the applicability of the proposed decision making method under triangular picture linguistic fuzzy environment and construct a descriptive example of investment problem. We conclude from the comparison and sensitive analysis that the proposed decision making method is more effective and reliable than other existing models. [ABSTRACT FROM AUTHOR]

In this paper, we define some Einstein operations on trapezoidal cubic fuzzy set and develop three arithmetic averaging operators, that is trapezoidal cubic fuzzy Einstein weighted averaging (TrCFEWA) operator, trapezoidal cubic fuzzy Einstein ordered weighted averaging (TrCFEOWA) operator and trapezoidal cubic fuzzy Einstein hybrid weighted averaging (TrCFEHWA) operator, for aggregating trapezoidal cubic fuzzy information. The TrCFEHWA operator generalizes both the TrCFEWA and TrCFEOWA operators. Furthermore, we establish various properties of these operators and derive the relationship between the proposed operators and the exiting aggregation operators. We apply on the TrCFEHWA operator to multiple attribute decision making with trapezoidal cubic fuzzy information. Finally, a numerical example is providing to demonstrate the submission of the established approach. [ABSTRACT FROM AUTHOR]

In this paper, we describe the idea of trapezoidal cubic hesitant fuzzy number. We discuss some basic operational laws of trapezoidal cubic hesitant fuzzy number and hamming distance of trapezoidal cubic hesitant fuzzy numbers (TrCHFNs). We introduce the new concept of the trapezoidal cubic hesitant fuzzy TOPSIS method. Furthermore, we extend the classical trapezoidal cubic hesitant fuzzy TOPSIS method to solve the MCDM method based on the trapezoidal cubic hesitant fuzzy TOPSIS method. The new ranking method for TrCHFNs is used to rank the alternatives. Finally, an illustrative example is given to verify and prove the practicality and effectiveness of the proposed method. We compared the proposed method to the existing methods, which shows the trapezoidal cubic hesitant Fuzzy TOPSIS method is more flexible to deal uncertainties and fuzziness. The main advantage of these operators is that it is to provide more accurate and significant results. [ABSTRACT FROM AUTHOR]

Pythagorean fuzzy sets (PFSs) and interval-valued Pythagorean fuzzy sets (IVPFSs) play a vital role in decision-making processes. In this paper based on PFS and IVPFS we introduce the concept of Cubic Pythagorean fuzzy set in which membership degree is an IVPFS and non-membership degree is a PFS. We define some basic operation of Cubic Pythagorean fuzzy numbers (CPFNs). We define score and accuracy functions to compare CPFNs. We also define distance between CPFNs. Based on the defined operations we develop Cubic Pythagorean fuzzy weighted averaging (CPFWA) operator and Cubic Pythagorean fuzzy weighted geometric (CPFWG) operator. We discuss some properties of the developed operators such as idempotancy, boundedness and monotonicity. Moreover, we give a multi-attribute decision making, to show the validity and effectiveness of the developed approach. Finally, we compare our approach with the existing methods. [ABSTRACT FROM AUTHOR]

In this paper, we describe the new idea of trapezoidal linguistic uncertain cubic fuzzy number. We discuss some basic operational laws of trapezoidal linguistic uncertain cubic fuzzy number and hamming distance of TrLUCFNs. We introduce the new concept of trapezoidal linguistic uncertain cubic fuzzy TOPSIS method. Furthermore, we extend the classical trapezoidal linguistic uncertain cubic fuzzy TOPSIS method to solve the MCDM method based on trapezoidal linguistic uncertain cubic fuzzy TOPSIS method. The new ranking method for TrLUCFNs is used to rank the alternatives. Finally, an illustrative example is given to verify and prove the practicality and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Pythagorean cubic fuzzy set, is an extension of the interval valued Pythagorean fuzzy set which relax the condition of the square sum of its membership and non-membership degree is less than or equal to one to supremum square sum of its membership and non-membership functions is less than one. Based on this information and by combining the idea of the confidence levels of each Pythagorean cubic fuzzy number, the proposed study investigated a new averaging and geometric operators, namely confidence Pythagorean cubic fuzzy weighted and geometric operators along with their order are presented. Some of their desired properties related to the new defined operators have been investigated. Under the given information, a multi criteria decision making process has been proposed with a numerical example for showing the effectiveness and validity of it. [ABSTRACT FROM AUTHOR]

The main objective of proposed work is to introduce a series of picture fuzzy weighted geometric aggregation operators by using t-norm and t-conorm. In this paper, we discussed generalized form of weighted geometric aggregation operator for picture fuzzy information. Further, the proposed geometric aggregation operators of picture fuzzy number are applied to multi-attribute group decision making problems. Also, we propose the TOPSIS method to aggregate the picture fuzzy information. To implement the proposed models, we provide some numerical applications of group decision making problems. Also compared with previous model, we conclude that the proposed technique is more effective and reliable. [ABSTRACT FROM AUTHOR]

The key objective of the present proposed work in this paper is introduced a new version of picture fuzzy set so called spherical fuzzy sets (SFS). spherical fuzzy set is a new extension of picture fuzzy sets and Pythagorean fuzzy sets. In spherical fuzzy sets, membership degrees are gratifying the condition 0 ⩽ P2 (x) + I2 (x) + N2 (x) ⩽1 instead of 0 ⩽ P (x) + I (x) + N (x) ⩽1 as is in picture fuzzy sets. In this paper, we investigate the basic operations of spherical fuzzy sets and discuss some related results. We extend operational laws to aggregation operators and introduce weighted averaging and weighted geometric aggregation operators based on spherical fuzzy number's. Further a multi attribute decision making method is developed and these aggregation operators are utilized. Finally, we constructed a numerical approach for implementation of proposed technique. [ABSTRACT FROM AUTHOR]

Spherical fuzzy sets (SFSs) are a new extension of Cuong's picture fuzzy sets (PFSs). In SFSs, membership degrees satisfy the condition 0≤P2(x)+I2(x)+N2(x)≤1 instead of 0≤P(x)+I(x)+N(x)≤1 as is in PFSs. In the present work, we extend different strict archimedean triangular norm and conorm to aggregate spherical fuzzy information. Firstly, we define the SFS and discuss some operational rules. Generalized spherical aggregation operators for spherical fuzzy numbers utilizing these strict Archimedean t‐norm and t‐conorm are proposed. Finally, based on these operators, a decision‐making method has been established for ranking the alternatives by utilizing a spherical fuzzy environment. The suggested technique has been demonstrated with a descriptive example for viewing their effectiveness as well as reliability. A test checking the reliability and validity has also been conducted for viewing the supremacy of the suggested technique. [ABSTRACT FROM AUTHOR]

The aim of this paper is to investigate information aggregation methods under Pythagorean trapezoidal fuzzy environment. Some Einstein operational laws on Pythagorean trapezoidal fuzzy numbers are defined based on Einstein sum and Einstein product. Based on Einstein operations we define Pythagorean trapezoidal fuzzy Einstein weighted geometric (PTFEWG) operator, Pythagorean trapezoidal fuzzy Einstein ordered weighted geometric (PTFEOWG) operator and Pythagorean trapezoidal fuzzy Einstein hybrid geometric (PTFEHG) operator. Furthermore, we apply the proposed aggregation operators to deal with multiple attribute group decision making. In the last we construct a numerical example for multiple attribute group decision making problem and compare the result with existing method. [ABSTRACT FROM AUTHOR]

The aim of this paper is to define some new operation laws for the trapezoidal linguistic cubic fuzzy number and Hamming distance. Furthermore, we define and use the trapezoidal linguistic cubic fuzzy TOPSIS method to solve the multi criteria decision making (MCDM) method. The new ranking method for trapezoidal linguistic cubic fuzzy numbers (TrLCFNs) are used to rank the alternatives. Finally, an illustrative example is given to verify and prove the practicality and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the concept of multiple‐attribute group decision‐making (MAGDM) problems with interval‐valued Pythagorean fuzzy information is developed, in which the attribute values are interval‐valued Pythagorean fuzzy numbers and the information about the attribute weight is incomplete. Since the concept of interval‐valued Pythagorean fuzzy sets is the generalization of interval‐valued intuitionistic fuzzy set. Thus, due the this motivation in this paper, the concept of interval‐valued Pythagorean fuzzy Choquet integral average (IVPFCIA) operator is introduced by generalizing the concept of interval‐valued intuitionistic fuzzy Choquet integral average operator. To illustrate the developed operator, a numerical example is also investigated. Extended the concept of traditional GRA method, a new extension of GRA method based on interval‐valued Pythagorean fuzzy information is introduced. First, utilize IVPFCIA operator to aggregate all the interval‐valued Pythagorean fuzzy decision matrices. Then, an optimization model based on the basic ideal of traditional grey relational analysis (GRA) method is established, to get the weight vector of the attributes. Based on the traditional GRA method, calculation steps for solving interval‐valued Pythagorean fuzzy MAGDM problems with incompletely known weight information are given. The degree of grey relation between every alternative and positive‐ideal solution and negative‐ideal solution is calculated. To determine the ranking order of all alternatives, a relative relational degree is defined by calculating the degree of grey relation to both the positive‐ideal solution and negative ideal solution simultaneously. Finally, to illustrate the developed approach a numerical example is to demonstrate its practicality and effectiveness. [ABSTRACT FROM AUTHOR]

In this paper, we define some Einstein operations on cubic fuzzy set (CFS) and develop three arithmetic averaging operators, which are cubic fuzzy Einstein weighted averaging (CFEWA) operator, cubic fuzzy Einstein ordered weighted averaging (CFEOWA) operator and cubic fuzzy Einstein hybrid weighted averaging (CFEHWA) operator, for aggregating cubic fuzzy data. The CFEHWA operator generalises both the CFEWA and CFEOWA operators. Furthermore, we develop various properties of these operators and derive the relationship between the proposed operators and the exiting aggregation operators. We apply CFEHWA operator to multiple attribute decision-making with cubic fuzzy data. Finally, a numerical example is constructed to demonstrate the established approach. [ABSTRACT FROM AUTHOR]

For multi-attribute group decision making (MAGDM) problem, there exist inter-dependent or interactive phenomena among criteria or preference of decision makers, therefor it is not suitable for us to aggregate them by conventional aggregation operators based on additive measures. In this paper based on fuzzy measures an interval-valued Pythagorean fuzzy Choquet integral geometric (IVPFCIG) operator is investigated for multiple criteria group decision making. First, some operational laws on interval-valued Pythagorean fuzzy numbers (IVPFNs) are introduced. Then an interval-valued Pythagorean fuzzy Choquet integral geometric (IVPFCIG) operator is proposed. Moreover, some of its properties are given and discussed in detail. Then Choquet integral-based distance between interval-valued Pythagorean fuzzy numbers is defined. Combining the IVPFCIG operator with Choquet integral-based distance, an extension of TOPSIS method is developed to deal with multi-attribute interval-valued Pythagorean fuzzy group decision making problems. Finally a numerical example is used to illustrate the developed procedures. [ABSTRACT FROM AUTHOR]

The motivation behind this artifact is to inspect the strategy to various multiple attribute group decision making with triangular cubic fuzzy numbers, part of operational laws of triangular cubic fuzzy numbers are connected. We concentrate the group decision making problems in which everything the data gave over the chiefs is conveyed as choice structure anywhere the greater part of the components remain described by triangular cubic fuzzy numbers and the data roughly property weights are known. We first utilize the triangular cubic fuzzy hybrid aggregation (TCFHA) administrator to total all individual fuzzy choice structure provide by the decision makers into the aggregate cubic fuzzy decision matrix. Besides, we expend weighted normal rating technique and score function to give a way to deal with positioning the certain choices and choosing the furthermost appealing unique. At last we offer an expressive example. [ABSTRACT FROM AUTHOR]

Pythagorean fuzzy sets (PFSs), hesitant fuzzy sets (HFSs) and intuitionistic hesitant fuzzy sets (IHFSs) have attracted more and more scholars' attention due to their powerfulness in expressing vagueness and uncertainty. Intuitionistic hesitant fuzzy set satisfies the condition that the sum of its membership's degrees is less than or equal to one. However, there may be a situation where the decision maker may provide the degree of membership and nonmembership of a particular attribute in such a way that their sum is greater than 1. To overcome this shortcoming, in this paper we introduce the concept of Pythagorean hesitant fuzzy set (PHFS) which is the generalization of intuitionistic hesitant fuzzy set under the restriction that the square sum of its membership degrees is less than or equal to 1. We discuss some properties of PHFS. We define score and accuracy degree of the Pythagorean hesitant fuzzy numbers (PHFNs) for comparison in Pythagorean hesitant fuzzy numbers. Also in decision making with PHFSs, aggregation operators play a very important role since they can be used to synthesize multidimensional evaluation values represented as Pythagorean hesitant fuzzy valued into collective values. We develop distance measure between PHFNs. Under PHFS environments, we develop aggregation operators namely, Pythagorean hesitant fuzzy weighted averaging (PHFWA), Pythagorean hesitant fuzzy weighted geometric (PHFWG). We develop the maximizing deviation method for solvingMADMproblems, in which the evaluation information provided by the decision maker is expressed in Pythagorean hesitant fuzzy numbers and the information about attribute weights is incomplete. The main advantage of these operators is that it is to provide more accurate and precious results. Furthermore, we developed these operators are applied to decision-making problems in which experts provide their preferences in the Pythagorean hesitant fuzzy environment to show the validity, practicality and effectiveness of the new approach. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of triangular cubic fuzzy numbers. We discuss some basic operational laws of triangular cubic fuzzy numbers and then develop triangular cubic fuzzy weighted average (TCFWA) operator. We also define crisp weighted possibility means of TCFNs and hamming distance between TCFNs. Furthermore, we extend the classical VIKOR method to solve the MCDM method based on triangular cubic fuzzy numbers. The new ranking method for TCFNs is used to rank the alternatives. Finally, an illustrative example is given to verify and demonstrate the practicality and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this article, we combine the concept of a bipolar fuzzy set and a soft set. We introduce the notion of bipolar fuzzy soft set and study fundamental properties. We study basic operations on bipolar fuzzy soft set. We define extended union, intersection of two bipolar fuzzy soft set. We also give an application of bipolar fuzzy soft set into decision making problem. We give a general algorithm to solve decision making problems by using bipolar fuzzy soft set. [ABSTRACT FROM AUTHOR]

In the age of the information-based economy and the rapid advancements of data schemes, business management has been faced with extraordinary difficulties and has entered into a reasonable period where the board's conventional enterprise execution assessment centers around the interests of investors. Speculators accept money-related information as their basis and focus on the investigation of material fascination, and in the event of the off chance that they do not, they cannot confirm the next economy period. In this way, enterprise execution reflects the interests of investors and business strategists for the needs of partners, which is significant for the forthcoming rivalry. Given that, the collection of data is a significant research tool that has lately been considered by researchers for data examination. In this paper, we have established multi-criteria decision-making methods for the assessment of business execution with spherical fuzzy information. We have applied Hamacher aggregation operators such as the spherical cubic fuzzy Hamacher weighted averaging (SCFHWA) operator, the spherical cubic fuzzy Hamacher ordered weighted averaging (SCFHOWA) operator, the spherical cubic fuzzy Hamacher hybrid averaging (SCFHHA) operator, the spherical cubic fuzzy Hamacher weighted geometric (SCFHWG) operator, the spherical cubic fuzzy Hamacher ordered weighted geometric (SCFHOWG) operator, and the spherical cubic fuzzy Hamacher hybrid geometric (SCFHHG) operator for the appraisal of the best choice of enterprise. We ultimately defend the proposed approach with the existing strategies for possibility and adequacy. [ABSTRACT FROM AUTHOR]

For the multiple attribute group decision-making problems where attribute values are the interval-valued Pythagorean fuzzy numbers, the group decision-making method based on generalized Einstein geometric aggregation operators is developed. First, induced generalized interval-valued Pythagorean fuzzy Einstein ordered weighted geometric (I-GIVPFEOWG) aggregation operator and induced generalized interval-valued Pythagorean fuzzy Einstein hybrid weighted geometric (I-GIVPFEHWG) aggregation operator, were proposed. Some general properties of these operators, such as idempotency, commutativity, monotonicity, and boundedness, were discussed, and some special cases in these operators were analyzed. Furthermore, the method for multiple attribute group decision-making problems based on these operators was developed, and the operational processes were illustrated in detail. The main advantage of using the proposed methods and operators is that these operators and methods give a more complete view of the problem to the decision makers. These methods provide more general, more accurate, and precise results. Therefore, these methods play a vital role in real-world problems. Finally the proposed operators have been applied to decision-making problems to show the validity, practicality, and effectiveness of the new approach. [ABSTRACT FROM AUTHOR]

The aim of this paper is to investigate the information aggregation methods under interval-valued Pythagorean trapezoidal fuzzy environment. Some Einstein operational laws on Pythagorean trapezoidal fuzzy numbers are defined based on Einstein sum and Einstein product. We define interval-valued Pythagorean trapezoidal fuzzy aggregation operators, induced interval-valued Pythagorean trapezoidal fuzzy Einstein ordered weighted averaging (I-IVTFEOWA) operator and induced interval-valued Pythagorean trapezoidal fuzzy Einstein hybrid averaging (I-IVPTFEHA) operator. We discuss some basic properties of the proposed operator, including idempotency, commutativity and monotonicity. We construct an algorithm for multiple-attribute group decision-making problem, and apply the proposed aggregation operator to deal with multiple-attribute group decision-making. Finally, we construct a numerical example for multiple-attribute group decision-making. [ABSTRACT FROM AUTHOR]

This paper aims to resolve the issue of the ranking of the fuzzy numbers in decision analysis, artificial intelligence, and optimization. In the literature, many ideas have been established for the ranking of the fuzzy numbers, and those ideas have some restrictions and limitations. We propose a method based on spherical fuzzy numbers (SFNs) for ranking to overcome the existing restrictions. Further, we investigate the basic properties of SFNs, compare the idea of spherical fuzzy set with the picture fuzzy set, and establish some distance operators, namely spherical fuzzy distance-weighted averaging (SFDWA), spherical fuzzy distance order-weighted averaging (SFDOWA), and spherical fuzzy distance order-weighted average weighted averaging (SFDOWA WA) operators with the attribute weights' information incompletely described. Further, we design an algorithm to solve decision analysis problems. Finally, to validate the usage and applicability of the established procedure, we assume the child development influence environmental factors problem as a practical application. [ABSTRACT FROM AUTHOR]

The objective of this study was to create a logarithmic decision-making approach to deal with uncertainty in the form of a picture fuzzy set. Firstly, we define the logarithmic picture fuzzy number and define the basic operations. As a generalization of the sets, the picture fuzzy set provides a more profitable method to express the uncertainties in the data to deal with decision making problems. Picture fuzzy aggregation operators have a vital role in fuzzy decision-making problems. In this study, we propose a series of logarithmic aggregation operators: logarithmic picture fuzzy weighted averaging/geometric and logarithmic picture fuzzy ordered weighted averaging/geometric aggregation operators and characterized their desirable properties. Finally, a novel algorithm technique was developed to solve multi-attribute decision making (MADM) problems with picture fuzzy information. To show the superiority and the validity of the proposed aggregation operations, we compared it with the existing method, and concluded from the comparison and sensitivity analysis that our proposed technique is more effective and reliable. [ABSTRACT FROM AUTHOR]

The key objective of the proposed work in this paper is to introduce a generalized form of linguistic picture fuzzy set, so-called linguistic spherical fuzzy set (LSFS), combining the notion of linguistic fuzzy set and spherical fuzzy set. In LSFS we deal with the vague and defective information in decision making. LSFS is characterized by linguistic positive, linguistic neutral and linguistic negative membership degree which satisfies the conditions that the square sum of its linguistic membership degrees is less than or equal to 1. In this paper, we investigate the basic operations of linguistic spherical fuzzy sets and discuss some related results. We extend operational laws of aggregation operators and propose linguistic spherical fuzzy weighted averaging and geometric operators based on spherical fuzzy numbers. Further, the proposed aggregation operators of linguistic spherical fuzzy number are applied to multi-attribute group decision-making problems. To implement the proposed models, we provide some numerical applications of group decision-making problems. In addition, compared with the previous model, we conclude that the proposed technique is more effective and reliable. [ABSTRACT FROM AUTHOR]