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Deep learning (DL), a branch of machine learning and artificial intelligence, is nowadays considered as a core technology. Due to its ability to learn from data, DL technology originated from artificial neural networks and has become a hot topic in the context of computing, it is widely applied in various application areas. However, building an appropriate DL model is a challenging task, due to the dynamic nature and variations in real-world problems and data. The aim of this work was to develope a new method for appropriate DL model selection using complex spherical fuzzy rough sets (CSFRSs). The connectivity of two or more complex spherical fuzzy rough numbers can be defined by using the Hamacher t-norm and t-conorm. Using the Hamacher operational laws with operational parameters provides exceptional flexibility in dealing with uncertainty in data. We define a series of Hamacher averaging and geometric aggregation operators for CSFRSs, as well as their fundamental properties, based on the Hamacher t-norm and t-conorm. Further we have developed the proposed aggregation operators and provide here a group decision-making approach for solving decision making problems. Finally, a comparative analysis with existing methods is given to demonstrate the peculiarity of our proposed method. [ABSTRACT FROM AUTHOR]

In daily life, the decision making problem is a complicated work related to uncertainties and vagueness. To overcome this vagueness and uncertainties, many fuzzy sets and theories have been presented by different scholars and researchers. EDAS (Evaluation based on distance from average solution) method plays a major role in decision-making problems. Especially, when multi-attribute group decision-making (MAGDM) problems have more conflicting attribute. In this paper, a new approach known as Spherical fuzzy rough-EDAS (SFR-EDAS) method is used to handle these uncertainties in the MAGDM problem. The aggregation operators have the ability to combine different sources of information, which plays an essential role in decision making (DM) problem. Keeping in view the increasing complexity of the DM problem, it will be useful to combine the aggregation operators with the fuzzy sets in solving DM problem. Therefore, an aggregation operator known as SFR-EDAS method is utilized. For this propounded some new averaging and geometric aggregation is investigated. Moreover, the essential and desirable properties with some particular cases are deliberated and discussed detail. To evaluate the emergency program, a MAGDM approach is used based on the new introduced operators. Later on, the viability and applicability the proposed method is certified by a detailed analysis with the other existing approaches. [ABSTRACT FROM AUTHOR]

The best mathematical tools for combining numerous inputs into a single result are aggregation operators. The aggregation operators work to combine all of the individual evaluation values provided in a uniform form, and they are very useful for evaluating the options provided in the decision-making process. To provide a larger space for decision makers, complex q -rung orthopair fuzzy rough sets can express their uncertain information. As a generalization of the algebraic operations, the Einstein t -norm and t -conorm, Hamacher operations have become significant in aggregation theory. The Hamacher aggregation operator's major characteristic is that it can capture the interrelationship between several input arguments. In this article, some Hamacher aggregation operators for complex q -rung orthopair fuzzy rough sets are presented. We define a complex q -rung orthopair fuzzy rough Hamacher operation laws and a new score function. In addition, we propose a serious of averaging aggregation operators for complex q -rung orthopair fuzzy rough set. We present the essential properties of these operators. We use the defined operators and modified EDAS (evaluation based on distance from average solution) method to propose an approach for solving a multicriteria decision making problem. To demonstrate the practicality and effectiveness of our propose model, we consider a numerical example of area selection for an arboretum. Finally, a comparison between the suggested approach with existing operators has been presented for authenticity and reliability. [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]

Spherical fuzzy sets have recently become more popular in various fields. It was proposed as a generalization of picture fuzzy sets and Pythagorean fuzzy sets in order to deal with uncertainty and fuzziness information. This paper presents a multi-attribute group decision making method based on novel sine aggregation operators to help decision makers choose the optimal alternative. Moreover, the well-known sine trigonometry function preserves the periodic and symmetric nature about the origin, and hence, it satisfies the decision makers preferences over the multi-time phase parameters. Keeping these features and the importance of the spherical fuzzy (SF) sets, the objective of this paper is to present some robust sine trigonometric (ST) operation laws for SF sets. Associated with these laws, we define some series of new aggregation operators (AOs) named as ST-weighted averaging and geometric operators to aggregate the spherical fuzzy information. Afterward, we present group decision making techniques to solve the multi-attribute group decision making problems based on proposed AOs and illustrate with a numerical example of an internet finance soft power evaluation problem to validate it. Also, we conduct some comparison analysis to study the reasonability and practicality of the proposed method. [ABSTRACT FROM AUTHOR]

Due to the indeterminacy and uncertainty of the decision-makers (DM) in the complex decision making problems of daily life, evaluation and aggregation of the information usually becomes a complicated task. In literature many theories and fuzzy sets (FS) are presented for the evaluation of these decision tasks, but most of these theories and fuzzy sets have failed to explain the uncertainty and vagueness in the decision making issues. Therefore, we use complex intuitionistic fuzzy set (CIFS) instead of fuzzy set and intuitionistic fuzzy set (IFS). A new type of aggregation operation is also developed by the use of complex intuitionistic fuzzy numbers (CIFNs), their accuracy and the score functions are also discussed in detail. Moreover, we utilized the Maclaurin symmetric mean (MSM) operator, which have the ability to capture the relationship among multi-input arguments, as a result, CIF Maclarurin symmetric mean (CIFMSM) operator and CIF dual Maclaurin symmetric mean (CIFDMSM) operator are presented and their characteristics are discussed in detail. On the basis of these operators, a MAGDM method is presented for the solution of group decision making problems. Finally, the validation of the propounded approach is proved by evaluating a numerical example, and by the comparison with the previously researched results. [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 spherical fuzzy set (SFS) is one of the most important concepts to accommodate more uncertainties than the intuitionistic fuzzy set, Pythagorean fuzzy set, picture fuzzy set and hence its applications are more extensive. Keeping the feature and the importance of the SFS, the objective of this paper is to present some robust symmetric operational laws for SFSs. Associated with these laws, we define some series of new aggregation operators named as spherical fuzzy (SF) symmetric weighted averaging, SF ordered weighted averaging and SF hybrid weighted averaging operators to aggregate the SF information. Afterwards, we present a group decision making technique to solve the multi attribute group decision making (MAGDM) based on proposed symmetric aggregation operators and illustrate with a numerical example of renewable energy source selection as a real-life practical example to validate it. A comparative analysis is also conducted to show the superiorities of the proposed method. [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 paper, we introduce the notion of Einstein aggregation operators, such as the interval-valued Pythagorean fuzzy Einstein weighted averaging aggregation operator and the interval-valued Pythagorean fuzzy Einstein ordered weighted averaging aggregation operator. We also discuss some desirable properties, such as idempotency, boundedness, commutativity, and monotonicity. The main advantage of using the proposed operators is that these operators give a more complete view of the problem to the decision makers. These operators provide more accurate and precise results as compared the existing method. Finally, we apply these operators to deal with multiple-attribute group decision making under interval-valued Pythagorean fuzzy information. For this, we construct an algorithm for multiple-attribute group decision making. Lastly, we also construct a numerical example for multiple-attribute group decision making. [ABSTRACT FROM AUTHOR]

The aim of this paper is to propose the 2-tuple spherical fuzzy linguistic aggregation operators and a decision-making approach to deal with uncertainties in the form of 2-tuple spherical fuzzy linguistic sets. 2-tuple spherical fuzzy linguistic operators have more flexibility than general fuzzy set. We proposed a numbers of aggregation operators, namely 2-tuple spherical fuzzy linguistic weighted average, 2-tuple spherical fuzzy linguistic ordered weighted average, 2-tuple spherical fuzzy linguistic hybrid average, 2-tuple spherical fuzzy linguistic weighted geometric, 2-tuple spherical fuzzy linguistic ordered geometric, and 2-tuple spherical fuzzy linguistic hybrid geometric operators. The distinguishing feature of these proposed operators is studied. At that point, we have used these operators to design a model to deal with multiple attribute decision-making issues under the 2-tuple spherical fuzzy linguistic information. Then, a practical application for best company selection for feeds is given to prove the introduced technique and to show its practicability and effectiveness. Besides this, a systematic comparison analysis with other existent methods is conducted to reveal the advantage of our method. Results indicate that the proposed method is suitable and effective for decision making problems. [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]

The harmful waste products, beverages, chemical agents that are discharged or emitted by industrial processes are categorized as industrial waste (IW). IW is one of the most severe problems facing governments around the world due to its environmental effect and severity. So the aim of this paper is to develop a method for selecting industrial waste management technique (IWMT) for industry. Dombi Norms were commonly referred to as Dombi operations, but their applications might be better expressed if they are presented with a new level of flexibility within the general parameter. Dombi operations have not yet been applied in non-linear Diophantine fuzzy sets (N-LDFSs) in a suitable form. Therefore we apply the Dombi operators on complex N-LDFS (CN-LDFS) and develop a generalized area of research in decision making problems (DMPs). The majority of decision-making challenges in the actual world contain a wide range of elements that must be taken into account. Making decision under such circumstances can frequently be challenging. To deal with such complicated issues, we require multi-attribute group decision-making (MAGDM) techniques. The aims to discuss MAGDM issues, this paper will introduce a new COmbinative Distance-based ASsessment (CODAS) methodology. In this paper, we put forward three novel aggregation operators (AOs): complex non-linear Diophantine fuzzy Dombi weighted averaging (CN-LDFDWA), complex non-linear Diophantine fuzzy Dombi order weighted averaging (CN-LDFDOWA), and complex non-linear Diophantine fuzzy Dombi hybrid weighted averaging (CN-LDFDHWA). These operators are used in the operational parameter to help a successful solution of the problem. Due to the growing energy and material shortages, as well as to comply with environmental laws and regulations and to take advantage of disposal economics in the current context, industrial waste (IW) should be taken into consideration as one of the potential resources in the steel industry. Further, the proposed decision support model applied to solve a case study regarding to IWMT for Pakistan steel mill corporation (PSMC) under complex N-LDF Dombi operators. The proposed method is more effective and reliable for decision making (DM) model, as compared to the existing method. • We developed aggregation operators (AOs) for CN-LDF Dombi Norms to solve MAGDM issue. • We developed CN-LDFDWA AOs based on CODAS method with all unknown information. • An example regarding to the selection of best IW technique for PSMC is provided. • Comparison provided the feasibility of our work and results are discussed based on ranking. [ABSTRACT FROM AUTHOR]

The concept of interval-valued Pythagorean fuzzy (IVPF) sets is capable of handling imprecise and ambiguous information and managing complex uncertainty in real-world applications. The focus of our this paper is to introduce some generalized operators, such as the generalized interval-valued Pythagorean fuzzy Einstein weighted averaging (abbreviated as GIVPFEWA) operator, the generalized interval-valued Pythagorean fuzzy Einstein ordered weighted averaging (abbreviated as GIVPFEOWA) operator, and the generalized interval-valued Pythagorean fuzzy Einstein hybrid averaging (abbreviated as GIVPFEHA) operator along with their some general properties, such as idempotency, commutativity, monotonicity and boundedness. 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 as compared to the existing methods. 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. A systematic comparison between the existing work and the proposed work also has been given. [ABSTRACT FROM AUTHOR]

The information aggregation operator plays a key rule in the group decision making problems. The aim of this paper is to investigate the information aggregation operators method under the picture fuzzy environment with the help of Einstein norms operations. The picture fuzzy set is an extended version of the intuitionistic fuzzy set, which not only considers the degree of acceptance or rejection but also takes into the account of neutral degree during the analysis. Under these environments, some basic aggregation operators namely picture fuzzy Einstein weighted and Einstein ordered weighted operators are proposed in this paper. Some properties of these aggregation operators are discussed in detail. Further, a group decision making problem is illustrated and validated through a numerical example. A comparative analysis of the proposed and existing studies is performed to show the validity of the proposed operators. [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]

The novel concept of spherical fuzzy set consists of positive, neutral and negative membership grades which satisfy the conditions that the square sum of its membership grades is less than or equal to 1. In this paper, we investigate the family of novel similarity measures between spherical fuzzy sets based on cosine function by considering the positive, neutral, negative and refusal grades in SFSs. To implement the proposed similarity measures, we provide some numerical applications of decision-making problems. A comparative study of the proposed and existing similarity measures is established. The proposed method is more advance as compare to the previous all reflexive. [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]

On the basis of decision-theoretical rough sets (DTRSs), the three-way decisions give new model of decision approach for deal with the problem of decision. This proposed model of decision method is based on the loss function of DTRSs. First, the concept of fractional orthotriple fuzzy β -covering (FOF β -covering) and fractional orthotriple fuzzy β -neighborhood (FOF β -neighborhood) was introduced. We combined loss feature of DTRSs with covering-based fractional orthotriple fuzzy rough sets (CFOFSs) under the fractional orthotriple fuzzy condition. Secondly, we proposed a new FOF-covering decision-theoretical rough sets model (FOFCDTRSs) and developed related properties. Then, based on the grade of positive, neutral and negative membership of fractional orthotriple fuzzy numbers (FOFNs), five methods are established for addressing the expected loss expressed in the form of FOFNs and the corresponding three-way decisions are also derived. Based on this, we presented a FOFCDTRS-based algorithm for multi-criteria decision making (MCDM). Then, an example verifies the feasibility of the five methods for solving the MCDM problem. Finally, by comparing the results of the decisions of five methods with different loss functions. [ABSTRACT FROM AUTHOR]

The Pythagorean probabilistic hesitant fuzzy set (PyPHFS) is an effective, generalized and powerful tool for expressing fuzzy information. It can cover more complex and more hesitant fuzzy evaluation information. Therefore, based on the advantages of PyPHFSs, this paper presents a new extended fuzzy TOPSIS method for dealing with uncertainty in the form of PyPHFS in real life problems. The paper is divided into three main parts. Firstly, the novel Pythagorean probabilistic hesitant fuzzy entropy measure is established using generalized distance measure under PyPHFS information to find out the unknown weights information of the attributes. The second part consists of the algorithm sets of the TOPSIS technique under PyPHFS environment, where the weights of criteria are completely unknown. Finally, in order to verify the efficiency and superiority of the proposed method, this paper applies some practical examples of the selection of the most critical fog-haze influence factor and makes a detailed comparison with other existing methods. [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 aims of this study are to propose the linguistic picture fuzzy Dombi (LPFD) aggregation operators and decision-making approach to deal with uncertainties in the form of linguistic picture fuzzy sets. LPFD operators have more flexibility due to the general fuzzy set. Utilizing the Dombi operational rule, the series of Dombi aggregation operators were proposed, namely linguistic picture fuzzy Dombi arithmetic/geometric, ordered arithmetic/ordered geometric and Hybrid arithmetic/Hybrid geometric aggregation operators. The distinguished feature of these proposed operators is studied. At that point, we have used these Dombi operators to design a model to deal with multiple attribute decision-making (MADM) issues under linguistic picture fuzzy information. Finally, an illustrative example to evaluate the emerging technology enterprises is provided to demonstrate the effectiveness of the proposed approach, together with a sensitivity analysis and comparison analysis, proving that its results are feasible and credible. [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]