**1. Introduction**

The concept of fuzzy soft sets was popularized by Maji et al. [1], in the combination of fuzzy sets (Zadeh [2]) and soft sets (Molodtsov [3], Maji [4] and Ali [5]). To analyze the real-life problems, different types of uncertainties have been evaluated with fuzzy soft sets [6] and it has wide range of applications to deal with parameterizations and granularity. By virtue of robustness of fuzzy soft set theory in dealing with uncertain data, many researchers serve to integrate it with inductive learning techniques for better results. In recent past, fuzzy sets, soft sets and fuzzy soft sets are applied to evaluate vagueness in decision makings [7–18], algebraic structures [19,20], medical diagnosis [21] and differential equations [22]. Some hybrid models of fuzzy soft sets have been introduced and applied in several fields [23,24].

In 1986, Atanassov proposed the intuitionistic fuzzy set (IFS) [25], which appears as an inclusion of non-compatibility value with fuzzy set [2]. Every value of IFS is referred to a compatibility, a non-compatibility and a hesitancy, which assign it more dynamics in dealing with imprecise

information. The initial aggregation instruments [26,27] on IFSs were introduced by Atanassov and Xu, and then applied in a various fields. The geometric [28], and arithmetic aggregation operators [27] have been studied in diverse fields and especially in multi-attribute decision making (MADM) problems in financial management, medical diagnosis, business and engineering designs [29–32].

IFSs with soft sets, that is, intuitionistic fuzzy soft sets (IFSSs) [33], are very instrumental and more realistic tools for uncertainty than fuzzy soft sets. As the dual-memberships structure of IFS allow marking hesitancy factors, the use of IFSSs in inductive learning techniques accounts for the degree of imprecision by assigning grades of compatibility and non-compatibility. In an inclusive way, several decision-making problems have been considered using IFSSs; some attempts are hybrid with intervals [34], multi-attributes [35] and nonlinear-programming [36]. Garg et al. [37,38] popularized aggregation operators on IFSSs and considered related decision-making methods. Several strategies are used to overcome the challenges of granularity and vagueness. Despite there being the applicability of IFSSs in diverse fields, an opinion of an expert who implicitly exercises his assessments on parameters of an IFSS is needed. On this motivation, Agarwal et al [39], who popularized generalized intuitionistic fuzzy soft set (GIFSS) by including assessment of a moderator on parameters, thus validating and supporting the information. Thus, the accumulation of generalized parameter can reduce possibility of errors which are occur due to imprecise data.

Although the definition of GIFSS in [39] is useful to tackle imprecise data, some difficulties appear in several notions [40,41]. Altogether, the assertions in [39] have been pointed out and a novel definition of GIFSS was established by Feng et al. [42]. They presented several operations and developed related multi-attribute decision-making methods by introducing operators on GIFSSs. On this prospect, a practical application of GIFSS for design concept evaluation was proposed by Hayat et al. [43]. Even though GIFSSs are applicable in diverse fields, sometimes assessments of more than one prospectors are needed in various problems. Thus, we consider the problem of validation of the notion of group-based GIFSS (GGIFSS) [44,45], and introduce a novel definition of GGIFSS, which is the generalization of the notion of GIFSS in [42]. Further, some basic properties are validated and aggregation instruments are proposed to determine the industrial applicability of GGIFSSs. Usually, an accurate aggregation process recommends the nature of MCDM model, which aggregates interdependent information and behaves in a linear manner. The prospect of proposing group-based generalized weighted averaging and geometric operators (hereafter, GBGWA and GBGWG) is to contemplate the information together with the influence of mathematical operations on GGIFSSs. The advantages of the given framework are to contemplate the prospector's demands or experts' judgments in an incorporated way such that establishing more operators constitutes the design concept of the evaluation mechanism of GGIFSSs.The results presented in this paper can be studied in several fields, such as electrical engineering, industrial designs, and construction engineering, as estimation of risk factors in risk managemen<sup>t</sup> is a complex tasks.

The paper is organized as follows. Section 2 introduce basic concepts and notations. Section 3 clarify and redefine the notion of GGIFSS. Section 4 give operations on GGIFSSs, and introduce GBGWA(GBGWG) operators and related properties. Section 5 put forward the aggregation instruments of GGIFSSs into algorithm and discuss two different case studies. We present the comparison and benefits of method in Section 6. Advantages and superiorities are given in Section 7. Section 8 provide the conclusions of the paper.
