Linguistic Pythagorean fuzzy numbers (LPFNs) are better tools for dealing with imprecision and vagueness. This article develops a new multiattribute group decision-making approach with LPFNs. The attribute values are LPFNs, and the information about the attribute weight is incomplete. Extended the notion of the traditional grey relational analysis (GRA) method, a new extension of the GRA method based on LPFN details is introduced. We develop a new distance measure and entropy measure for LPFNs. Moreover, a decision-making approach is proposed based on the traditional. GRA method and steps for solving LPFMAGDM problems with incompletely known weight information are given. The degree of grey relation between positive (PIS) and negative-ideal solutions (NIS) are determined. A relative relational degree is considered by calculating the degree of grey relation to the LPF-PIS and the LPF-NIS, respectively. Finally, an illustrative example is also given to show the application and effectiveness and compare the developed approach with existing methods.

The popularity of mutual funds, which are necessarily portfolios, has been drawing more attention from the people of India over the last three decades. In a mutual fund, one can invest his or her money in the securities of different sectors traded mainly in the stock exchange markets to get expected return bearing tolerable risks. A mutual fund other than the passive mutual funds is directed by an active fund manager. The performance of a mutual fund depends on the shares and securities of different companies it contains and the fund manager's performance also. Risk and return can be measured based on different criteria. Before investment, one should select such a mutual fund that can fulfill his or her anticipation as much as possible within the risk–return skeleton. Therefore the selection of a mutual fund is rigorously a multicriteria decision making. This paper has considered five open-ended, large-cap, direct, suspended sales mutual funds for the research work. In the first stage, we have shortlisted the more crucial criteria comparatively from a list of criteria with the help of the Fuzzy Analytic Hierarchy Process. In the second stage, we have applied the Pythagorean fuzzy Gray Relation Analysis approach to determine the weights of shortlisted criteria as well as the rank of those mutual funds. Finally, a comparison has been drawn between the present model and the Pythagorean fuzzy Interactive Multicriteria Decision-Making model, to show the effectiveness of the present model.

This article focuses on a group decision-making (GDM) approach based on the multiplicative consistency of linguistic preference relation (LPR) with experts' self-confidence and self-doubting (SC&SD) levels. To give their preferences, the experts use their knowledge of the experience according to their degree of SC&SD levels. First, we propose the concepts of multiplicative consistent LPR-SC&SD using the experts' general minimum self-confidence level and the maximum self-doubting level. We suggest then a consensus-building iterative process, that is, a consensus reaching process (CRP) algorithm to achieve multiplicative consistency of LPR-SC&SD according to identification and adjustment rules. A theorem is given for convergence of the CRP algorithm. In a GDM problem, social network analysis is studied for the experts to obtain their weight according to the degree of SC&SD. When we achieve the acceptable preferences of all the experts using the CRP algorithm of the multiplicative consistent LPR-SC&SD, then we aggregate all the preferences by the experts' weights. The aggregation of all preferences is also an LPR-SC&SD, known as the weight collective LPR-SC&SD. Finally, a case-by-case example and several comparative analyses are done with the current GDM processes to demonstrate the viability and applicability of the proposed GDM system.

In this paper, we introduce a new type of fuzzy set, called Pythagorean linguistic sets (PLSs), to address the preferred and nonpreferred degrees of linguistic variables. Moreover, it allows decision makers to offer effectively handle uncertain information more flexible than intuitionistic linguistic sets (ILSs) when one compares two alternatives in the process of decision making. Some of the fundamental operational laws, score, accuracy, and aggregation operators are defined, and their properties are investigated. Preference relation (PR) is a useful and efficient tool for decision making that only requires the decision makers to compare two alternatives at one time. Taking the advantages of PLSs and PRs, this paper also introduces Pythagorean linguistic preference relations (PLPRs) and studies their application. We propose an approach for group decision making using group recommendations based on consistency matrices and feedback mechanism. First, the proposed method constructs the collective consistency matrix, the weight collective PRs, and the group collective PRs. Then, it constructs a consensus relation for each expert and determines the group consensus degree (GCD) for all experts. If the GCD is smaller than a predefined threshold value, then a feedback mechanism is activated to update the PLPRs. Finally, after the GCD is greater than or equal to the predefined threshold value, we calculate the arithmetic mathematical average values of the updated group collective PR to select the most appropriate alternative.

The operations of t -norm (TN) and t -conorm (TCN), developed by Dombi, are generally known as Dombi operations, which have an advantage of flexibility within the working behavior of parameter. In this paper, we use Dombi operations to construct a few Q-rung orthopair fuzzy Dombi aggregation operators: Q-rung orthopair fuzzy Dombi weighted average operator, Q-rung orthopair fuzzy Dombi order weighted average operator, Q-rung orthopair fuzzy Dombi hybrid weighted average operator, Q-rung orthopair fuzzy Dombi weighted geometric operator, Q-rung orthopair fuzzy Dombi order weighted geometric operator, and Q-rung orthopair fuzzy Dombi hybrid weighted geometric operator. The different features of these proposed operators are reviewed. At that point, we have used these operators to build up a model to solve the multiple-attribute decision making issues under Q-rung orthopair fuzzy environment. Ultimately, a realistic instance is stated to substantiate the created model and to exhibit its applicability and viability.

The operations of -norm and -conorm, developed by Dombi, were generally known as Dombi operations, which may have a better expression of application if they are presented in a new form of flexibility within the general parameter. In this paper, we use Dombi operations to create a few Pythagorean fuzzy Dombi aggregation operators: Pythagorean fuzzy Dombi weighted average operator, Pythagorean fuzzy Dombi order weighted average operator, Pythagorean fuzzy Dombi hybrid weighted average operator, Pythagorean fuzzy Dombi weighted geometric operator, Pythagorean fuzzy Dombi order weighted geometric operator, and Pythagorean fuzzy Dombi hybrid weighted geometric operator. The distinguished feature of these proposed operators is examined. At that point, we have used these operators to build up a model to remedy the multiple attribute decision-making issues under Pythagorean fuzzy environment. Ultimately, a realistic instance is stated to substantiate the created model and to exhibit its applicability and viability.