Generalized Cubic Intuitionistic Fuzzy Aggregation Operators Using t-Norm Operations and Their Applications to Group Decision-Making Process

Decision algorithm for picture fuzzy sets and Aczel Alsina aggregation operators based on unknown degree of wights

Aggregation operators (AOs) are well-known and efficient mathematical tools that are utilized to overcome the impact of imprecise and vague information during the aggregation process. The theoretical concepts of Aczel Alsina aggregation expressions are an extension of triangular norms and become a hot research topic in the environment of the fuzzy framework. The power operators provide a smooth approximation and are used to mitigate the influence of redundant or insufficient information on the attributes or criteria. Some robust aggregation approaches are developed by combining two different theories, like power operators and Aczel Alsina aggregation tools. This article aims to explore the theory of picture fuzzy sets (PFSs), an extended version of fuzzy sets, and intuitionistic fuzzy sets. Some robust operations of Aczel Alsina aggregation tools are also present in light of the picture fuzzy environment. We established a class of new methodologies in the light of picture fuzzy information, including picture fuzzy Aczel Alsina power weighted average (PFAAPWA) and picture fuzzy Aczel Alsina power ordered weighted average (PFAAPOWA) operators. We also developed an appropriate approach like picture fuzzy Aczel Alsina power weighted geometric (PFAAPWG) and picture fuzzy Aczel Alsina power ordered weighted geometric (PFAAPOWG) operators. Notable properties and characteristics of proposed methodologies are also demonstrated. Our invented approaches not only aggregate complicated information but can clearly define interrelationships among several arguments. Moreover, we establish an algorithm for the multi-attribute group decision-making (MAGDM) problem to handle the impact of redundant and vague information on human opinions. Finally, we study an experimental case study to evaluate an appropriate optimal option from available options. To reveal consistency and effectiveness of developed approaches, influence study by changing various parametric values and comparative study by comparing results of existing approaches.

Development of hamming and hausdorff distance metrics for cubic intuitionistic fuzzy hypersoft set in cement storage quality control: Development and evaluation

Quality control is paramount in product manufacturing as it ensures consistent production to meet customer expectations, regulatory requirements and maintain a company's reputation and profitability. Distance measures within fuzzy sets serve as powerful tools for quality control, allowing for data comparison and identification of potential defects or outliers within a system. This study aims to develop a hybrid concept by combining a Cubic Intuitionistic Fuzzy Set (CIFS) with Soft Set (SS) and extending it to Cubic Intuitionistic Fuzzy Hypersoft Set (CIFHSS). CIFHSS enables handling multiple distinct attributes at the sub-attribute level within a cubic set environment. The concept includes operations like internal, partial internal, external, complement, direct sum, and product. Additionally, six distance metrics are defined within CIFHSS and applied to establish a quality control management system for industrial applications. The versatility of CIFHSS in quality control management stems from its ability to capture and model uncertainty, vagueness, and imprecision in data. This makes it an effective tool for decision-making, risk analysis, and process optimization across a wide range of industrial applications.

Multicriteria group decision making for COVID-19 testing facility based on picture cubic fuzzy aggregation information

The information aggregation of cubic fuzzy numbers and picture fuzzy numbers have played an important role in decision making. This paper introduces a novel approach to address the problem of testing facility of COVID-19 under picture cubic fuzzy environment. As the picture cubic fuzzy set is a generalized fuzzy structure to handle more uncertainty and ambiguity in decision making problems We discuss its various properties. Based on geometric aggregation operators and Hamacher operations, we introduce some Hamacher geometric aggregation operators under picture cubic fuzzy information. Namely, picture cubic fuzzy Hamacher weighted geometric aggregation operator, picture cubic fuzzy Hamacher hybrid geometric operator, picture cubic fuzzy Hamacher order weighted geometric aggregation operator. Discuss some properties of the defined operators. To verify the importance of the proposed operators, develop multicriteria group decision making (MCGDM) algorithm under picture cubic fuzzy environment and apply this strategy for the selection of an authentic laboratory for COVID-19 test. Further to validate the supremacy of our proposed operators, we present a comparative analysis with pre-existing aggregation operators. Results show that the proposed technique is more effective and suitable for MCGDM problems.

Generalized Cubic Pythagorean Fuzzy Aggregation Operators and their Application to Multi-attribute Decision-Making Problems

Cubic Pythagorean fuzzy (CPF) set (CPFS) is a hybrid set that can hold much more information and can be used to describe both an interval-valued Pythagorean fuzzy set (IVPFS) and Pythagorean fuzzy set (PFS) at the same time to handle data uncertainties. Based on it, the present study is classified into three phases. The first phase is to modify the existing operational laws and aggregation operators (AOs) in the article presented by Abbas et al. (Journal of Intelligent & Fuzzy Systems, vol. 37, no. 1, pp. 1529–1544, (2019)). The main objective of improved operational laws is to eliminate the flows and ambiguities in existing AOs. Secondly, based on these laws, various AOs to aggregate the information are acquired along with their requisite properties and relations. Lastly, an approach for interpreting the multi-attribute decision-making (MCDM) problem based on the stated operators is given and illustrated with an example. Some of the existing models are used to perform a comprehensive comparative analysis to demonstrate their impacts.

Applications of complex picture fuzzy soft power aggregation operators in multi-attribute decision making

The major theme of this analysis is to suggest a new theory in the form of complex picture fuzzy soft (CPFS) information and to initiate their major algebraic laws, score value, and accuracy values. The mathematical form of the CPFS set includes three main functions, called supporting, abstinence, and supporting against terms with a prominent characteristic that the sum of the triplet will lie in the unit interval. Further, in the consideration of the power aggregation operator using generalized t-norm and t-conorm and CPFS information, we diagnosed the mathematical concept of CPFS power averaging (CPFSPA), CPFS weighted power averaging (CPFSWPA), CPFS ordered weighted power averaging (CPFSOWPA), CPFS power geometric (CPFSPG), CPFS weighted power geometric (CPFSWPG), CPFS ordered weighted power geometric (CPFSOWPG). Moreover, the major results and their particular investigation of the invented approaches are also deliberated. Additionally, in the consideration of diagnosed operators using CPFS information, we illustrated a MADM ("multi-attribute decision-making") tool to find the best option from the family of decisions. Finally, we have shown the supremacy and feasibility of the diagnosed operators with the help of sensitive analysis and geometrical representations.

Analysis and Applications of Bonferroni Mean Operators and TOPSIS Method in Complete Cubic Intuitionistic Complex Fuzzy Information Systems

This article manages vagueness, asymmetric data, and risk demonstrated in awkward information. The ambiguity is handled with the help of possibility and strategic decision-making theory. A MADM (multi-attribute decision-making) tool, the sub-part of the strategic decision theory, plays an important role in the circumstances of fuzzy data. The major influence of this analysis is to initiate the mathematical ideology of cubic intuitionistic complex fuzzy (CICF) information and its well-known properties such as algebraic laws, score values, and accuracy values. It is also to determine various inequalities for finding the relation between any two CICF numbers (CICFNs). Further, we know that the Bonferroni mean (BM) operator is more generalized than the simple averaging/geometric aggregation operators due to parameters involved in the mathematical form of BM operators. Keeping the supremacy and consistency of BM operators, the idea of CICF Bonferroni mean (CICFBM) and CICF weighted BM (CICFWBM) operators are diagnosed. We try to describe their well-known results and properties such as idempotency, monotonicity, commutativity, and boundedness with various specific cases. Further, we investigate three different sorts of decision-making procedures such as MADM tool, TOPSIS (Technique for order of preference by similarity to ideal solution) method using similarity measures, and TOPSIS method using aggregation operators to enhance the quality of the decision-making process. This analysis expressed how to make decisions when there is asymmetric data about companies. Finally, we compute the comparative analysis of the diagnostic approaches with various existing theories to demonstrate the feasibility and flexibility of the exposed work to try to illustrate with the help of geometrical expressions.

New concepts of domination in cubic graphs with application

The cubic set, introduced as a combination of a fuzzy set and an interval-valued fuzzy set, provided researchers with more flexibility than the previous two sets in dealing with complex and uncertain problems. Fuzzy graphs, based on this type of set, are among the emerging fuzzy graphs that have a great potential to model the surrounding phenomena. Consistent with the special role that cubic graphs play in decision-making and selecting superior options, dominating these graphs is of great importance and value. In this paper, we introduce the domination of the cubic graphs in terms of strong edges and examine their properties. In addition, we examine domination in terms of independent sets and since many of the phenomena surrounding us are hybrid, we also discuss the domination concept on its fuzzy operations. Finally, we present an application of this graph on the subject of domination.

An approach for supplier selection problem based on picture cubic fuzzy aggregation operators

This article is an advanced approach to picture fuzzy set through the application of cubic set theory. For instance, we establish the idea of the picture cubic fuzzy sets (PCFSs) theory and define several operations for PCFS. Also, presented some weighted aggregation operators under picture cubic fuzzy information, so called picture cubic fuzzy weighted averaging (PCFWA) operator, picture cubic fuzzy order weighted averaging (PCFOWA) operator, picture cubic fuzzy weighted geometric (PCFWG) operator, and picture cubic fuzzy order weighted geometric (PCFOWG) operator. Further, we study their fundamental properties and showed the relationship among these aggregation operators. In order to determine the feasibility and practicality of the mentioned new technique, we developed multi-attribute group decision -making algorithm with picture cubic fuzzy environment. Further, the developed method applied to supply chain management and for implementation, consider numerical application of supply chain management. Compared the developed approach with other preexisting aggregation operators, and we concluded that the defined technique is better, reliable and effective.

Algorithm for solving the decision-making problems based on correlation coefficients under cubic intuitionistic fuzzy information: a case study in watershed hydrological system

Cubic intuitionistic fuzzy sets (CIFSs) are a powerful and relevant medium for expressing imprecise information to solve the decision-making problems. The conspicuous feature of their mathematical concept is that it considers simultaneously the hallmarks of both the intuitionistic fuzzy sets (IFSs) and interval-valued IFSs. The present paper is divided into two parts: (i) defining the correlation measures for the CIFSs; (ii) introducing the decision-making algorithm for the CIFS information. Furthermore, few of the fundamental properties of these measures are examined in detail. Based on this, we define a novel algorithm to solve the multi-criteria decision-making process and illustrate numerical examples related to watershed’s hydrological geographical areas, global recruitment problem and so on. A contrastive analysis with several existing studies is also administered to test the effectiveness and verify the proposed method.

Multiple attribute group decision-making based on cubic linguistic Pythagorean fuzzy sets and power Hamy mean

The linguistic Pythagorean fuzzy sets (LPFSs), which employ linguistic terms to express membership and non-membership degrees, can effectively deal with decision makers’ complicated evaluation values in the process of multiple attribute group decision-making (MAGDM). To improve the ability of LPFSs in depicting fuzzy information, this paper generalized LPFSs to cubic LPFSs (CLPFSs) and studied CLPFSs-based MAGDM method. First, the definition, operational rules, comparison method and distance measure of CLPFSs are investigated. The CLPFSs fully adsorb the advantages of LPFSs and cubic fuzzy sets and hence they are suitable and flexible to depict attribute values in fuzzy and complicated decision-making environments. Second, based on the extension of power Hamy mean operator in CLPFSs, the cubic linguistic Pythagorean fuzzy power average operator, the cubic linguistic Pythagorean fuzzy power Hamy mean operator as well as their weighted forms were introduced. These aggregation operators can effectively and comprehensively aggregate attribute values in MAGDM problems. Besides, some important properties of these operators were studied. Finally, we presented a new MAGDM method based on CLPFSs and their aggregation operators. Illustrative examples and comparative analysis are provided to show the effectiveness and advantages of our proposed decision-making method.

Multi-attribute group decision-making process based on possibility degree and operators for intuitionistic multiplicative set

This paper aims to present a novel multiple attribute group decision-making process under the intuitionistic multiplicative preference set environment. In it, Saaty’s 1/9-9 scale is used to express the imprecise information which is asymmetrical distribution about 1. To achieve it, the present work is divided into three folds. First, a concept of connection number-based intuitionistic multiplicative set (CN-IMS) is formulated by considering three degrees namely “identity”, “contrary”, and “discrepancy” of the set and study their features. Second, to rank the given number, we define a novel possibility degree measure which compute the degree of possibility within the given objects. Finally, several aggregation operators on the pairs of the given numbers are designed and investigated their fundamental inequalities and relations. To explain the presented measures and operators, a group decision-making approach is promoted to solve the problems with uncertain information and illustrated with several examples. The advantages, comparative, as well as perfection analysis of the proposed framework are furnished to confirm the approach.

T-spherical fuzzy power aggregation operators and their applications in multi-attribute decision making

The paper aims to present the concept of power aggregation operators for the T-spherical fuzzy sets (T-SFSs). T-SFS is a powerful concept, with four membership functions denoting membership, abstinence, non-membership and refusal degree, to deal with the uncertain information as compared to other existing fuzzy sets. On the other hand, the relationship between the different pairs of the attributes are well recorded in terms of power operators. Thus, keeping these advantages of T-SFSs and power operator, the objective of this work is to define several weighted averaging and geometric power aggregation operators. The stated operators named as T-spherical fuzzy weighted, ordered weighted, hybrid averaging and geometric operators for the collection of the T-SFSs. The various properties and the special cases of them are also derived. Further, the consequences of proposed new power aggregation operators are studied in view of some constraints. Finally, a multiple attribute decision making algorithm, based on the proposed operators, is established to solve the problems with uncertain information and illustrate with numerical examples. A comparative study, superiority analysis and discussion of the proposed approach are furnished to confirm the approach.

Multi-attribute group decision-making for online education live platform selection based on linguistic intuitionistic cubic fuzzy aggregation operators

The purpose of this study is to propose a multi-attribute group decision-making (MAGDM) method for online education live platform selection based on proposed novel aggregation operators (AOs) under linguistic intuitionistic cubic fuzzy set (LICFS). First, the Archimedean copula and co-copula are extended to handle linguistic intuitionistic cubic fuzzy information (LICFI) and the operational law of linguistic intuitionistic cubic fuzzy variables (LICFVs) based on extended copula (EC) and extended co-copula (ECC) are given. In addition, linguistic intuitionistic cubic fuzzy copula weighted average (LICFCWA) operator and linguistic intuitionistic cubic fuzzy copula weighted geometric (LICFCWG) operator are proposed based on EC and ECC under LICFI; meanwhile, some special forms of LICFCWA and LICFCWG have been obtained by different types generators of ECs and ECCs. Third, a novel MAGDM approach based on proposed LICFCWA (LICFCWG) is constructed to solve the selection problem of the online education live platform in the period of the COVID-19, and a detailed parameter analysis was carried out. Fourthly, LICFS will degenerate into linguistic intuitionistic fuzzy set and intuitionistic cubic fuzzy set, respectively, in different cases. Finally, some comparisons are carried out with other existing proposed MAGDM approaches. By comparing different types of experiments, the effectiveness and flexibility of the proposed approach are also showed.

Evaluation of Enterprise Production Based on Spherical Cubic Hamacher Aggregation Operators

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.

A novel approach of linguistic intuitionistic cubic hesitant variables and their application in decision making

In this paper, we proposed the notion of linguistic intuitionistic cubic hesitant variables and defined some aggregation operators to deal with uncertainties in the form of linguistic intuitionistic cubic hesitant variables (LICHVs). LICHVs operators have more flexibility due to the general fuzzy set. We developed a series of aggregation operators, namely linguistic intuitionistic cubic hesitant variable averaging and linguistic intuitionistic cubic hesitant variable geometric aggregation operators. The distinguished feature of the developed operators is discussed. At that point, we used the developed operators to design a model to solve multi-criteria decision making issues with linguistic intuitionistic cubic hesitant variables. Further, the proposed method applied to explosion incident occurred in a chemical factory. We also proved that our developed model is practical and gives the decision makers more mathematical insight during the decision making on their options. Finally, a systematic comparison is conducted with other existent methods to show the advantage of our developed method.

Analysis of Decision Support System Based on 2-Tuple Spherical Fuzzy Linguistic Aggregation Information

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.

Analysis of Robot Selection Based on 2-Tuple Picture Fuzzy Linguistic Aggregation Operators

The aim of this article is to propose the 2-tuple picture fuzzy linguistic aggregation operators and a decision-making model to deal with uncertainties in the form of 2-tuple picture fuzzy linguistic sets; 2-tuple picture fuzzy linguistic operators have more flexibility than general fuzzy set. We proposed a number of aggregation operators, namely, 2-TPFLWA, 2-TPFLOWA, 2-TPFLHA, 2-TPFLWG, 2-TPFLOWG, and 2-TPFLHG operators. The distinguished feature of the developed operators are studied. At that point, we used these operators to design a model to deal with multiple attribute decision-making issues under the 2-tuple picture fuzzy linguistic information. Then, a practical application of robot selection by manufacturing unit is given to prove the introduced technique and to show its practicability and effectiveness. Besides this, a systematic comparison analysis with other existent approaches is conducted to reveal the advantage of our developed method. Results indicate that the proposed method is suitable and effective for decision-making problems.

Multi-criteria group decision making based on Archimedean power partitioned Muirhead mean operators of q-rung orthopair fuzzy numbers

Two critical tasks in multi-criteria group decision making (MCGDM) are to describe criterion values and to aggregate the described information to generate a ranking of alternatives. A flexible and superior tool for the first task is q-rung orthopair fuzzy number (qROFN) and an effective tool for the second task is aggregation operator. So far, nearly thirty different aggregation operators of qROFNs have been presented. Each operator has its distinctive characteristics and can work well for specific purpose. However, there is not yet an operator which can provide desirable generality and flexibility in aggregating criterion values, dealing with the heterogeneous interrelationships among criteria, and reducing the influence of extreme criterion values. To provide such an aggregation operator, Muirhead mean operator, power average operator, partitioned average operator, and Archimedean T-norm and T-conorm operations are concurrently introduced into q-rung orthopair fuzzy sets, and an Archimedean power partitioned Muirhead mean operator of qROFNs and its weighted form are presented and a MCGDM method based on the weighted operator is proposed in this paper. The generalised expressions of the two operators are firstly defined. Their properties are explored and proved and their specific expressions are constructed. On the basis of the specific expressions, a method for solving the MCGDM problems based on qROFNs is then designed. Finally, the feasibility and effectiveness of the method is demonstrated via a numerical example, a set of experiments, and qualitative and quantitative comparisons.

A Quick Algorithm for Binary Discernibility Matrix Simplification using Deterministic Finite Automata

The binary discernibility matrix, originally introduced by Felix and Ushio, is a binary matrix representation for storing discernible attributes that can distinguish different objects in decision systems. It is an effective approach for feature selection, knowledge representation and uncertainty reasoning. An original binary discernibility matrix usually contains redundant objects and attributes. These redundant objects and attributes may deteriorate the performance of feature selection and knowledge acquisition. To overcome this shortcoming, row relations and column relations in a binary discernibility matrix are defined in this paper. To compare the relationships of different rows (columns) quickly, we construct deterministic finite automata for a binary discernibility matrix. On this basis, a quick algorithm for binary discernibility matrix simplification using deterministic finite automata (BDMSDFA) is proposed. We make a comparison of BDMR (an algorithm of binary discernibility matrix reduction), IBDMR (an improved algorithm of binary discernibility matrix reduction) and BDMSDFA. Finally, theoretical analyses and experimental results indicate that the algorithm of BDMSDFA is effective and efficient.

Algorithm for Probabilistic Dual Hesitant Fuzzy Multi-Criteria Decision-Making Based on Aggregation Operators With New Distance Measures

Probabilistic dual hesitant fuzzy set (PDHFS) is an enhanced version of a dual hesitant fuzzy set (DHFS) in which each membership and non-membership hesitant value is considered along with its occurrence probability. These assigned probabilities give more details about the level of agreeness or disagreeness. By emphasizing the advantages of the PDHFS and the aggregation operators, in this manuscript, we have proposed several weighted and ordered weighted averaging and geometric aggregation operators by using Einstein norm operations, where the preferences related to each object is taken in terms of probabilistic dual hesitant fuzzy elements. Several desirable properties and relations are also investigated in details. Also, we have proposed two distance measures and its based maximum deviation method to compute the weight vector of the different criteria. Finally, a multi-criteria group decision-making approach is constructed based on proposed operators and the presented algorithm is explained with the help of the numerical example. The reliability of the presented decision-making method is explored with the help of testing criteria and by comparing the results of the example with several prevailing studies.

Symmetric Triangular Interval Type-2 Intuitionistic Fuzzy Sets with Their Applications in Multi Criteria Decision Making

Type-2 intuitionistic fuzzy set (T2IFS) is a powerful and important extension of the classical fuzzy set, intuitionistic fuzzy set to measure the vagueness and uncertainty. In a practical decision-making process, there always occurs an inter-relationship among the multi-input arguments. To deal with this point, the motivation of the present paper is to develop some new interval type-2 (IT2) intuitionistic fuzzy aggregation operators which can consider the multi interaction between the input argument. To achieve it, we define a symmetric triangular interval T2IFS (TIT2IFS), its operations, Hamy mean (HM) operator to aggregate the preference of the symmetric TIT2IFS and then shows its applicability through a multi-criteria decision making (MCDM). Several enviable properties and particular cases together with following different parameter values of this operator are calculated in detail. At last a numerical illustration is to given to exemplify the practicability of the proposed technique and a comparative analysis is analyzed in detail.