Multi-attribute group decision-making with T-spherical fuzzy Dombi power Heronian mean-based aggregation operators

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.

In this paper, we investigate the multiple attribute decision making (MADM) problem based on the arithmetic and geometric aggregation operators with hesitant fuzzy linguistic information. Then, motivated by the ideal of traditional arithmetic and geometric operation, we have developed some aggregation operators for aggregating hesitant fuzzy linguistic information: hesitant fuzzy linguistic arithmetic aggregation operators, hesitant fuzzy linguistic geometric aggregation operators, hesitant fuzzy linguistic correlated aggregation operators, induced hesitant fuzzy linguistic aggregation operators, induced hesitant fuzzy linguistic correlated aggregation operators, hesitant fuzzy linguistic prioritized aggregation operators, hesitant fuzzy linguistic power aggregation operators. Then, we have utilized these operators to develop some approaches to solve the hesitant fuzzy linguistic multiple attribute decision making problems. Finally, a practical example is given to verify the developed approach.

In this paper, we investigate the multiple attribute decision making problem based on the arithmetic and geometric aggregation operators with interval valued hesitant fuzzy uncertain linguistic information. Then, motivated by the ideal of traditional arithmetic and geometric operation, we shall develop some aggregation operators for aggregating interval valued hesitant fuzzy uncertain linguistic information: interval valued hesitant fuzzy uncertain linguistic arithmetic aggregation operators, interval valued hesitant fuzzy uncertain linguistic geometric aggregation operators, interval valued hesitant fuzzy uncertain linguistic correlated aggregation operators, induced interval valued hesitant fuzzy uncertain linguistic aggregation operators, induced interval valued hesitant fuzzy uncertain linguistic correlated aggregation operators, interval valued hesitant fuzzy uncertain linguistic prioritized aggregation operators, interval valued hesitant fuzzy uncertain linguistic power aggregation operators. The prominent characteristic of these proposed operators are studied. Then, we shall utilize these operators to develop some approaches to solve the interval valued hesitant fuzzy uncertain linguistic multiple attribute decision making problems. Finally, a practical example is given to verify the developed approach and to demonstrate its practicality and effectiveness.

In this paper, we investigate the multiple attribute decision making problem based on the arithmetic and geometric aggregation operators with interval valued hesitant fuzzy uncertain linguistic information. Then, motivated by the ideal of traditional arithmetic and geometric operation, we shall develop some aggregation operators for aggregating interval valued hesitant fuzzy uncertain linguistic information: interval valued hesitant fuzzy uncertain linguistic arithmetic aggregation operators, interval valued hesitant fuzzy uncertain linguistic geometric aggregation operators, interval valued hesitant fuzzy uncertain linguistic correlated aggregation operators, induced interval valued hesitant fuzzy uncertain linguistic aggregation operators, induced interval valued hesitant fuzzy uncertain linguistic correlated aggregation operators, interval valued hesitant fuzzy uncertain linguistic prioritized aggregation operators, interval valued hesitant fuzzy uncertain linguistic power aggregation operators. The prominent characteristic of these proposed operators are studied. Then, we shall utilize these operators to develop some approaches to solve the interval valued hesitant fuzzy uncertain linguistic multiple attribute decision making problems. Finally, a practical example is given to verify the developed approach and to demonstrate its practicality and effectiveness.

In this paper, we investigate the multiple attribute decision making (MADM) problem based on the arithmetic, geometric aggregation operators and Hamacher operations with picture fuzzy information. Then, motivated by the ideal of traditional arithmetic, geometric aggregation operators and Hamacher operations, we have developed some aggregation operators for aggregating picture fuzzy information: picture fuzzy Hamacher aggregation operators, picture fuzzy Hamacher geometric aggregation operators, picture fuzzy Hamacher correlated aggregation operators, induced picture fuzzy Hamacher aggregation operators, induced picture fuzzy Hamacher correlated aggregation operators, picture fuzzy Hamacher prioritized aggregation operators, picture fuzzy Hamacher power aggregation operators. Then, we have utilized these operators to develop some approaches to solve the picture fuzzy multiple attribute decision making problems. Finally, a practical example for enterprise resource planning (ERP) system selection is given to verify the developed approach and to demonstrate its practicality and effectiveness.

ABSTRACTFuzzy mathematical operations play an important role in the field of decision‐making. Decision‐making tools are being used in every field of life. Fuzzy operators are the building blocks for making a decision in the realm of uncertain information. The information is often in qualitative form which needs a qualitative approach for decision‐making rather than a quantitative one. The linguistic term sets are the mathematical tools to collect the qualitative data from experts of the fields and the conversion of linguistic data in the form linguistic intuitionistic fuzzy data is the more efficient and reliable for the process of decision making. The fuzzy aggregation operators are the best tools for the aggregation of uncertain and vague data. This work addresses a real‐world decision‐making problem of choosing the best diagnostic approach for the diagnosis of cardiovascular diseases by introducing a novel decision‐making technique with fuzzy aggregation operators in the domain of linguistic intuitionistic fuzzy (LIF) sets. Two new operators are used in this method: the Dynamic Linguistic Intuitionistic Fuzzy Dombi Weighted Averaging (DLIFDWA) operator and the Dynamic Linguistic Intuitionistic Fuzzy Dombi Weighted Geometric (DLIFDWG) operator. This work aims to identify an optimal technique for diagnosing cardiovascular illness using Dombi operations in the Linguistic Intuitionistic Fuzzy environment. The Dombi Operations are highly versatile and successful in addressing vagueness and uncertainty, making them crucial in our methodology. To demonstrate the effectiveness of the offered strategies, we have implemented the recommended operators for the selection of optimized diagnostic approach for cardiovascular diseases. This showcases the significance of these strategies in facilitating decision‐making. Ultimately, we perform a thorough analysis to showcase the reliability and uniformity of the produced procedures, comparing the provided operators with various current counterparts.

The focus of the interdisciplinary and scientific discipline of robotics is to design, maintain and use mechanical robotics. There exist many issues faced by the robotic industry but there are some factors that can cover these complexities effectively. Handling vague and imprecise data is a difficult task nowadays. So there is a need to define such kind of effective and valuable tool that can handle complex and vague data more dominantly. The evaluation based on distance from average solution (EDAS) method is a very useful tool that can handle complex data more effectively. The best alternative can be chosen based on distance from the average solution. The EDAS method is relatively simple to use and provide a quick evaluation of alternative based on multiple criteria. Yager t-norm and t-conorm are two fuzzy logic operators proposed by Yager. So based on the importance of Yager t-norm and t-conorm, initially, in this article, we have proposed the basic operative laws for intuitionistic fuzzy rough numbers. Based on these developed operational laws, we have developed some new intuitionistic fuzzy rough aggregation operators called intuitionistic fuzzy rough Yager average (weighted, ordered weighted, hybrid) aggregation operators and intuitionistic fuzzy rough Yager geometric (weighted, ordered weighted, hybrid) aggregation operators. Moreover, we have proposed the EDAS technique based on intuitionistic fuzzy rough Yager aggregation operators and used these notions for the selection of suitable factors that play a vital role in the robotic industry. Also, to show the effective use of these introduced notions, we have proposed an algorithm for the EDAS method based on intuitionistic fuzzy rough Yager aggregation operators along with a descriptive example. To show the superiority of the introduced work we have developed a comparative analysis.

The aggregation operators based on the Archimedean t-norm and t-conorm provide general operational rules for intuitionistic fuzzy numbers (IFNs), where they can generalize most of the existing aggregation operators. The Heronian mean (HM) considers interrelationships among attributes. Therefore, it is very necessary to extend the HM to IFNs for developing intuitionistic fuzzy HM operators based on the Archimedean t-norm and t-conorm. In this paper, we firstly discuss intuitionistic fuzzy operational rules based on the Archimedean t-norm and t-conorm. Then, we propose the intuitionistic fuzzy Archimedean Heronian aggregation (IFAHA) operator and the intuitionistic fuzzy weight Archimedean Heronian aggregation (IFWAHA) operator of IFNs. We also discuss some properties and some special cases of the proposed operators. The proposed IFAHA operator and the proposed IFWAHA operator of IFNs can be used for group decision making in intuitionistic fuzzy environments.

Archimedean t -conorm and t -norm provide the general operational rules for intuitionistic fuzzy numbers (IFNs). The aggregation operators based on them can generalize most of the existing aggregation operators. At the same time, the Heronian mean (HM) has a significant advantage of considering interrelationships between the attributes. Therefore, it is very necessary to extend the HM based on IFNs and to construct intuitionistic fuzzy HM operators based on the Archimedean t -conorm and t -norm. In this paper, we first discuss intuitionistic fuzzy operational rules based on the Archimedean t -conorm and t -norm. Then, we propose the intuitionistic fuzzy Archimedean Heronian aggregation (IFAHA) operator and the intuitionistic fuzzy weight Archimedean Heronian aggregation (IFWAHA) operator. We also further discuss some properties and some special cases of these new operators. Moreover, we also propose a new multiple attribute group decision making (MAGDM) method based on the proposed IFAHA operator and the proposed IFWAHA operator. Finally, we use an illustrative example to show the MAGDM processes and to illustrate the effectiveness of the developed method.

We present a new class of fuzzy aggregation operators that we call fuzzy triangular aggregation operators. To do so, we focus on the situation where the available information cannot be assessed with exact numbers and it is necessary to use another approach to assess uncertain or imprecise information such as fuzzy numbers. We also use the concept of triangular norms (t-norms and t-conorms) as pseudo-arithmetic operations. As a result, we get notably the fuzzy triangular weighted arithmetic (FTWA), the fuzzy triangular ordered weighted arithmetic (FTOWA), the fuzzy generalized triangular weighted arithmetic (FGTWA), the fuzzy generalized triangular ordered weighted arithmetic (FGTOWA), the fuzzy triangular weighted quasi-arithmetic (Quasi-FTWA), and the fuzzy triangular ordered weighted quasi-arithmetic (Quasi-FTOWA) operators. Main properties of these operators are discussed as well as their comparison with other existing ones. The fuzzy triangular aggregation operators not only cover a wide range of useful existing fuzzy aggregation operators but also provide new interesting cases. Finally, an illustrative example is also developed regarding the selection of strategies.

This paper investigates the multiple attribute decision making (MADM) problems in which the attribute values take the form of hesitant intuitionistic fuzzy linguistic elements (HIFLEs). Firstly, motivated by the idea of hesitant fuzzy linguistic elements and intuitionistic fuzzy numbers, the concept, operational laws and comparison laws of HIFLEs are defined. Then, some aggregation operators are developed for aggregating the hesitant intuitionistic fuzzy linguistic information, such as hesitant intuitionistic fuzzy linguistic weighted aggregation operators, hesitant intuitionistic fuzzy linguistic ordered weighted aggregation operators and hesitant intuitionistic fuzzy linguistic hybrid aggregation operators. Some desirable properties of these operators and the relationships between them are discussed. Furthermore, the hesitant intuitionistic fuzzy linguistic set is extended to hesitant intuitionistic fuzzy uncertain linguistic set, and some hesitant intuitionistic fuzzy uncertain linguistic aggregation operators are developed. Based on the hesitant intuitionistic fuzzy linguistic weighted average (HIFLWA) operator, an approach to MADM is proposed under hesitant intuitionistic fuzzy linguistic environment. Finally, a practical example is given to illustrate the application of the proposed method and to demonstrate its practicality and effectiveness.

In this paper, we define various induced intuitionistic fuzzy aggregation operators, including induced intuitionistic fuzzy ordered weighted averaging (OWA) operator, induced intuitionistic fuzzy hybrid averaging (I-IFHA) operator, induced interval-valued intuitionistic fuzzy OWA operator, and induced interval-valued intuitionistic fuzzy hybrid averaging (I-IIFHA) operator. We also establish various properties of these operators. And then, an approach based on I-IFHA operator and intuitionistic fuzzy weighted averaging (WA) operator is developed to solve multi-attribute group decision-making (MAGDM) problems. In such problems, attribute weights and the decision makers' (DMs') weights are real numbers and attribute values provided by the DMs are intuitionistic fuzzy numbers (IFNs), and an approach based on I-IIFHA operator and interval-valued intuitionistic fuzzy WA operator is developed to solve MAGDM problems where the attribute values provided by the DMs are interval-valued IFNs. Furthermore, induced intuitionistic fuzzy hybrid geometric operator and induced interval-valued intuitionistic fuzzy hybrid geometric operator are proposed. Finally, a numerical example is presented to illustrate the developed approaches.

The picture fuzzy set is a generation of an intuitionistic fuzzy set. The aggregation operators are important tools in the process of information aggregation. Some aggregation operators for picture fuzzy sets have been proposed in previous papers, but some of them are defective for picture fuzzy multi-attribute decision making. In this paper, we introduce a transformation method for a picture fuzzy number and trapezoidal fuzzy number. Based on this method, we proposed a picture fuzzy multiplication operation and a picture fuzzy power operation. Moreover, we develop the picture fuzzy weighted geometric (PFWG) aggregation operator, the picture fuzzy ordered weighted geometric (PFOWG) aggregation operator and the picture fuzzy hybrid geometric (PFHG) aggregation operator. The related properties are also studied. Finally, we apply the proposed aggregation operators to multi-attribute decision making and pattern recognition.

Due to more advanced features of the picture fuzzy soft set and valuable characteristics of aggregation operators, in this article, we present the notion of picture fuzzy soft Bonferroni mean aggregation operators and weighted picture fuzzy soft Bonferroni mean aggregation operators. Moreover, some basic properties of these introduced aggregation operators have been given. As cancer is one of the most rapidly increasing diseases globally. But due to different kinds of cancer diseases, it is very difficult to say which type of cancer disease is increasing rapidly. So to reduce this difficulty in the medical field, we have applied our work to medical diagnosis problems to ensure that fuzzy ideas can also help in the medical field. Also, an algorithm along with a descriptive example is established that conforms to the authenticity of initiated work. Furthermore, a comparative analysis of the introduced work has been given to show how this work is more efficient and dominant than other existing theories.

In this paper, we propose some new aggregation operators which are based on the Choquet integral and Einstein operations. The operators not only consider the importance of the elements or their ordered positions, but also consider the interactions phenomena among the decision making criteria or their ordered positions. It is shown that the proposed operators generalize several intuitionistic fuzzy Einstein aggregation operators. Moreover, some of their properties are investigated. We also study the relationship between the proposed operators and the existing intuitionistic fuzzy Choquet aggregation operators. Furthermore, an approach based on intuitionistic fuzzy Einstein Choquet integral operators is presented for multiple attribute decision-making problem. Finally, a practical decision making problem involving the water resource management is given to illustrate the multiple attribute decision making process.