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In this paper, we present four categories of covering-based intuitionistic hesitant fuzzy rough set (CIHFRS) models using intuitionistic hesitant fuzzy β -neighborhoods (IHF β -neighborhoods) and intuitionistic hesitant fuzzy complementary β -neighborhoods (IHFC β -neighborhoods. Through theoretical analysis of covering-based IHFRS models, we propose the intuitionistic hesitant fuzzy TOPSIS (IHF-TOPSIS) technique for order of preference by similarity to an ideal solution, addressing multicriteria decision-making (MCDM) challenges concerning the assessment of IHF data. A compelling example aptly showcases the suggested approach. Furthermore, we address MCDM problems regarding the assessment of IHF information based on CIHFRS models. Through comparison and analysis, it is evident that addressing MCDM problems by assessing IHF data using CIHFRS models proves more effective than utilizing intuitionistic fuzzy data with CIFRS models or hesitant fuzzy information with CHFRS models. IHFS emerges as a unique and superior tool for addressing real-world challenges. Additionally, covering-based rough sets (CRSs) have been successfully applied to decision problems due to their robust capability in handling unclear data. In this study, by combining CRSs with IHFS, four classes of CIFRS versions are established using IHF β -neighborhoods and IHFC β -neighborhoods. A corresponding approximation axiomatic system is developed for each. The roughness and precision degrees of CBIHFRS models are specifically talked about. The relationship among these four types of IHFRS versions and existing related versions is presented based on theoretical investigations. A method for MCDM problems through IHF information, namely, IHF-TOPSIS, is introduced to further demonstrate its effectiveness and applicability. By conducting a comparative study, the effectiveness of the suggested approach is evaluated. [ABSTRACT FROM AUTHOR]

This article uses the Aczel-Alsina t-norm and t-conorm to make several new linguistic interval-valued intuitionistic fuzzy aggregation operators. First, we devised some rules for how linguistic interval-valued intuitionistic fuzzy numbers should work. Then, using these rules as a guide, we created a set of operators, such as linguistic interval-valued intuitionistic fuzzy Aczel-Alsina weighted averaging (LIVIFAAWA) operator, linguistic interval-valued intuitionistic fuzzy Aczel-Alsina weighted geometric (LIVIFAAWG) operator, linguistic interval-valued intuitionistic fuzzy Aczel-Alsina ordered weighted averaging (LIVIFAAOWA) operator, linguistic interval-valued intuitionistic fuzzy Aczel-Alsina ordered weighted geometric (LIVIFAAOWG) operator, linguistic interval-valued intuitionistic fuzzy Aczel-Alsina hybrid weighted averaging (LIVIFAAHWA) operator and linguistic interval-valued intuitionistic fuzzy Aczel-Alsina hybrid weighted geometric (LIVIFAAHWG) operators are created. Several desirable qualities of the newly created operators are thoroughly studied. Moreover, a multi-criteria group decision-making (MCGDM) method is proposed based on the developed operators. The proposed operators are then applied to real-world decision-making situations to demonstrate their applicability and validity to the reader. Finally, the suggested model is contrasted with the currently employed method of operation. [ABSTRACT FROM AUTHOR]

Pythagorean Hesitant fuzzy set (PHFS) which permits the membership degree and non-membership degree of an element to a set represented by several possible values is deliberated as a powerful tool to express uncertain information in the process of multi-attribute decision making (MADM) problems. In this paper, we propose a novel approach based on TOPSIS method and the maximizing deviation method for solving MADM problems where the evaluation information provided by the decision makers (DMs) is expressed in form of Pythagorean hesitant fuzzy numbers and the information about attribute weights is incomplete. To determine the attribute weight we develop an optimization model based on maximizing deviation method. Finally we provide a practical decision-making problem to demonstrate the implementation process of the proposed method. [ABSTRACT FROM AUTHOR]

For multi-attribute group decision making (MAGDM) problem, there exist inter-dependent or interactive phenomena among criteria or preference of decision makers, therefor it is not suitable for us to aggregate them by conventional aggregation operators based on additive measures. In this paper based on fuzzy measures an interval-valued Pythagorean fuzzy Choquet integral geometric (IVPFCIG) operator is investigated for multiple criteria group decision making. First, some operational laws on interval-valued Pythagorean fuzzy numbers (IVPFNs) are introduced. Then an interval-valued Pythagorean fuzzy Choquet integral geometric (IVPFCIG) operator is proposed. Moreover, some of its properties are given and discussed in detail. Then Choquet integral-based distance between interval-valued Pythagorean fuzzy numbers is defined. Combining the IVPFCIG operator with Choquet integral-based distance, an extension of TOPSIS method is developed to deal with multi-attribute interval-valued Pythagorean fuzzy group decision making problems. Finally a numerical example is used to illustrate the developed procedures. [ABSTRACT FROM AUTHOR]