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.

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.