**1. Introduction**

The multiple attribute decision-making (MADM) technique is a widely used method in solving real-world problems, in which a variety of attributes are involved to consider from finite feasible alternatives according to the evaluated attributes' evaluation or preference information given by multiple decision-makers. Clearly, fuzziness and vagueness are inevitably integrated into the MADM process due to the vagueness and uncertainty of evaluated objects and the ambiguous nature of human thinking. Intuitionistic fuzzy set (IFS), initially developed by Atanassov [1], has proven to be a powerful and useful tool for processing complex-type information in day-to-day life. The IFS is described by a membership degree (0 ≤ *μ* ≤ 1) and a non-membership degree (0 ≤ *v* ≤ 1) that satisfies the condition *μ*2 + *v*2 ≤ 1. To date, various MADM methods related to IFS have appeared in well-known publications and conferences. Several authors have conducted valuable scientific investigations and literature reviews on the development of IFS from different viewpoints [2–4].

As one of the important aspects of fuzzy theory, the distance measured between IFSs has received continuous attention for decades in both the theory and application areas. Existing IFS distance measures are mostly investigated from the weighted averaging perspective [5–8]. Recently, Zeng and Su [9] proposed a new intuitionistic fuzzy distance measure from the ordered weighted viewpoint, namely the intuitionistic fuzzy ordered weighted distance (IFOWD) operator, whose prominent feature is that it can incorporate a decision-maker's attitudinal characters into the MADM process. Later, by combining the weighted average and IFOWD methods, Zeng and Xiao [10] developed the intuitionistic ordered weighted averaging-weighted average distance (IFOWAWAD) operator and explored its usefulness in solving MADM problems. More recently, motivated by the induced ordered weighted averaging distance (IOWAD) measure [11], Zeng et al. [12] proposed the intuitionistic fuzzy induced ordered weighted averaging distance (IFIOWAD) measure that enables us to consider the complex attitude of decision-makers using order-induced variables. The essence of the IFIOWAD as well as the IOWAD operator is to enable the decision-makers to incorporate their complex attitude into the aggregation process, using the order-induced variables on the ordered arguments. Thus, the interests of the decision-makers are taken into account during the decision-making process. Although it is a relatively new MADM approach, the induced aggregation distance operator has been successfully applied in various fields of research. Recent literature contains a number of extensions and subsequent applications in MADM problems, as listed in Table 1.

**Table 1.** Induced aggregation distance methodology in multiple attribute decision-making (MADM) problems.


It is clearly shown in previous reviews that the existing induced aggregation distance methods, such as the IFIOWAD operator, are popular techniques that have been applied successfully in many real-world problems. However, one can observe that the above-mentioned induced aggregated distances share a similar problem that must be solved: their order-inducing variables are not involved in the actual aggregation of results. As a consequence of this, the results obtained by these distance operators cannot account for the variation derived from a change of the order-inducing variables. The latter issue is especially important whenever variation degrees of property regarding alternative-attribution pairs, such as confidence, consistency or importance, are represented in terms of order-inducing variables and need to be considered. To circumvent this defect, this paper develops a revised induced aggregated distance measure between IFSs, termed as an intuitionistic fuzzy weighted induced ordered weighted averaging distance (IFWIOWAD) operator that takes into account the intrinsic variations in the order-inducing variables during the aggregation process. Further, to enrich the theory and application of the developed IFWIOWAD operator, we propose an intuitionistic weighted induced ordered weighted averaging weighted average distance (IFWIOWAWAD) operator that can integrate the weighted average approach with the IFWIOWAD measure. Therefore, it can address the complex attitude of experts and the importance of attributes in the decision-making framework.

The rest of this paper is structured as follows. In Section 2, some definitions of the IFS and induced aggregation distance operators are reviewed. Section 3 presents the IFWIOWAD operator and explores its main properties. Section 4 develops the IFWIOWAWAD operator, based on which a MADM model is represented in Section 5. An example concerning investment selection is presented in Section 6. In the final section, we summarize the paper's main results.
