Intuitionistic hesitant linguistic sets and their application in multi-criteria decision-making problems

Abstract

In practice, the use of linguistic information is flexible and definite due to the complexity of problems, and therefore the linguistic models have been widely studied and applied to solve multi-criteria decision-making (MCDM) problems under uncertainty. In this paper, intuitionistic hesitant linguistic sets (IHLSs) are defined on the basis of intuitionistic linguistic sets (ILSs) and hesitant fuzzy linguistic sets (HFLSs). As an evaluation value of one reference object, an intuitionistic hesitant linguistic number (IHLN) contains a linguistic term, a set of membership degrees and a set of non-membership degrees. There can be a consensus on the linguistic term and then decision makers can express their opinions on membership or non-membership degrees depending on their preferences. Therefore, by means of IHLSs, the flexibility in generating evaluation information under uncertainty can be achieved to a larger extent than either ILSs or HFLSs do. Besides, the basic operations and comparison method of IHLNs are studied, which is followed by the definitions of several aggregation operators, including the intuitionistic hesitant linguistic hybrid averaging (IHLHA) operator, the intuitionistic hesitant linguistic hybrid geometric (IHLHG) operator and the corresponding generalized operators. Using these operators, an approach to MCDM problems with intuitionistic hesitant linguistic information is proposed. Finally, an illustrative example is provided to verify the proposed approach and its accuracy and effectiveness have been demonstrated through the comparative analysis with ILSs and HFLSs.

Decision support model with Pythagorean fuzzy preference relations and its application in financial early warnings

“…In group decision-making (GDM) problems, DMs usually need to give a precise preference for a group of options using pairwise comparisons to express their preferred information and construct a preference relation judgment matrix [1][2][3]. Obviously, there are many methods to support decision-making [4][5][6]. Nevertheless, in many GDM problems, DMs may be challenging to depict their preference with a precise number.…”

A New Method to Support Decision-Making in an Uncertain Environment Based on Normalized Interval-Valued Triangular Fuzzy Numbers and COMET Technique

“…For decision-making, different techniques are used, and a general assessment of alternatives is preferred for the MCDM problems. MCDM helps to make best possible decision by following different approaches in fuzzy environments such as triangular fuzzy numbers (TFNs) [10][11][12][13], hesitant fuzzy numbers [14][15][16][17], trapezoidal fuzzy numbers [18], generalized fuzzy numbers (GFNs) [19,20], interval-valued triangular fuzzy numbers (IVTFNs) [12,21], intuitionistic fuzzy numbers [22,23] and linguistic fuzzy sets [24][25][26]. With the inception of the new techniques in MCDM to achieve optimal solution, many methods like TOPSIS (The Technique for Order of Preference by Similarity to Ideal solution) [27][28][29], AHP (Analytic Hierarchy Process) [30][31][32][33], ANP (Analytic Network Process) [34][35][36], COMET (Characteristics Object Method) [33,[37][38][39][40][41] etc.…”

A measure of probabilistic hesitant I‐fuzzy sets and decision makings for strategy choice

“…Due to that decision-maker (DM) is often unable to evaluate exactly the data and information during the uncertain and complex real-life situations, a large number of fuzzy decision-making problems have been researched. Currently, many conceptions have been extended into different contexts, such as intuitionistic fuzzy set/number (IFS/IFN), 1,2 fuzzy preference relation, [3][4][5] hesitant fuzzy set (HFS), [6][7][8][9] and probabilistic linguistic term set. 10 Most of these studies are based on fuzzy sets 11 and IFSs, 1 which means that the uncertainty is described with the membership degree, or with both membership degree and nonmembership degree.…”