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The methodology of managing hesitancy situations is improving step by step with new basics and tools which have their specific characteristics. As a rule, aggregation operators can undoubtedly deal with the data in a definite way. Employing hesitant intuitionistic fuzzy linguistic term sets (HIFLTSs), the adaptability in creating assessment data under uncertainty can be accomplished to a bigger degree than either intuitionistic linguistic sets or hesitant fuzzy linguistic term sets do. In this view, this paper provides a multi-criteria group decision-making (MCGDM) method based on new aggregation operators for HIFLTSs and the proposed modified VIKOR method. Besides, some operational laws for HIFLTSs are studied with their important properties, which is followed by the definitions of some aggregation operators, including the hesitant intuitionistic fuzzy linguistic weighted averaging (HIFLWA) operator and the hesitant intuitionistic fuzzy linguistic weighted geometric (HIFLWG) operator. The hesitant intuitionistic fuzzy linguistic individual regret (HIFLIR) measure and hesitant intuitionistic fuzzy linguistic compromise (HIFLC) measure are established with the help of hesitant intuitionistic fuzzy group utility measure. After that, by using the proposed aggregation operators, we develop a modified VIKOR method in the context of HIFLTSs. The outcome of this research is ranking and selecting of best alternative with the help of modified VIKOR method based on aggregation operators for HIFLTSs. A numerical problem is provided to verify the proposed approach, and its accuracy and effectiveness have been demonstrated through the comparative analysis of the modified VIKOR method with the TOPSIS method for the selection of the best alternative. This research study showed that the proposed approach can describe the fuzziness and uncertainty of experts more relevantly and the ranking results calculated with the modified VIKOR method are effective and reliable. [ABSTRACT FROM AUTHOR]

The linguistic information can be expressed as a 2-tuple of a linguistic variable and a real number in an interval [ - 1 2 , 1 2) . The intuitionistic 2-tuple linguistic (I2TL) set accurately deals with the imprecise and unpredictable information in those decision-making problems where experts prefer the degree of membership and non-membership values in the form of 2-tuple. The existing approaches used for the aggregation operations of I2TL sets are extremely complicated. This work aims to develop new aggregation operations for I2TL sets using Einstein operations. We present intuitionistic 2-tuple linguistic Einstein weighted averaging (I2TLEWA), and intuitionistic 2-tuple linguistic Einstein weighted geometric (I2TLEWG) operators. We also discuss their properties and relationship between them. Moreover, we numerically test the feasibility and significance of our proposed operators by solving a multi-criteria group decision making (MCGDM) problem. Finally, we do a comparative analysis with another method to give insights on our designed operators for I2TL sets. [ABSTRACT FROM AUTHOR]

This paper attempts to develop an outranking method based on intuitionistic 2-tuple fuzzy linguistic information and apply it to multi-criteria group decision-making problems. The theory of intuitionistic 2-tuple fuzzy linguistic elements (I2FLEs) is useful for modeling impressions and quantifying the ambiguous nature of subjective judgments in a convenient manner. The family of ELECTRE methods is well known and widely used outranking method, but it has not been investigated within the intuitionistic 2-tuple fuzzy linguistic environment. ELECTRE uses the concept of an outranking relationship. Therefore, the directional Hausdorff distance, which uses I2FLEs, is proposed and the outranking relations are subsequently defined using this distance. Furthermore, using the proposed score and accuracy functions of I2FLEs, this paper also develops an outranking method based on intuitionistic fuzzy support function, intuitionistic fuzzy risk function, intuitionistic fuzzy credibility function, and the net outranking flow index similar to the PROMETHEE method. An illustrative example is given to demonstrate the practicality and effectiveness of the developed approaches. Finally, a comparative discussion of two decision-making methods is conducted to demonstrate the advantages of the proposed method over the other. [ABSTRACT FROM AUTHOR]

Actual existing multi-criteria decision-making (MCDM) methods yield results that may be questionable and unreliable. These methods very often ignore the issue of uncertainty and rank reversal paradox, which are fundamental and important challenges of MCDM methods. In response to these challenges, the Characteristic Objects Method (COMET) was developed. Despite it being immune to the rank reversal paradox, classical COMET is not designed for uncertain, decisional problems. In this paper, we propose to extend COMET using hesitant fuzzy set (HFS) theory. Hesitant fuzzy set theory is a powerful tool to express the uncertainty that derives from an expert comparing characteristic objects and identifying membership functions for each criterion domain. We present the theoretical foundations and principles of COMET, and we provide an illustrative example to show how COMET handles uncertain decision problems both practically and effectively. [ABSTRACT FROM AUTHOR]

An outranking method is developed within the environment of hesitant intuitionistic fuzzy linguistic term sets (HIFLTSs), where the membership degree and the non-membership degree of the element are subsets of linguistic term set. The directional Hausdorff distance, which uses HIFLTSs, is proposed, and the dominance relations are subsequently defined using this distance. Moreover, some interesting characteristics of the proposed directional Hausdorff distance are further discussed in detail. In this context, a collective decision matrix is obtained in the form of hesitant intuitionistic fuzzy linguistic elements and analyzes the collective data by using proposed ELECTRE-based outranking method. The linguistic scale functions are employed in this paper to conduct the transformation between qualitative information and quantitative data. Furthermore, based on the proposed method, we also investigate the ranking of the alternatives based on a new proposed definition of HIFLTS. The feasibility and applicability of the proposed method are illustrated with an example, and a comparative analysis is performed with other approaches to validate the effectiveness of the proposed methodology. [ABSTRACT FROM AUTHOR]