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A multicriteria intuitionistic fuzzy group decision-making method 359

Aggregation of individual information. Summarize and aggregate the
importance of each criterion and evaluation of each project from different
decision-makers. The judgment information of single decision-maker is col-
lected into the judgment criteria of group decision-makers. (2) Calculation
of the criteria weights. Different criteria have different influences on the
projects’ evaluation. This difference is expressed by the weight of the cri-
teria. (3) Evaluation and selection of the alternatives. Applying the group
multicriteria decision-making methods to evaluate different objectives.
The optimal project will be selected according to certain judgment
principles.
In the group decision-making process, there are ubiquitous uncertainties
of the objectives. Managing and modeling of uncertain information are vital
for the acquisition of desirable solutions. To overcome this issue, fuzzy sets
are introduced in a way to help linguistic variables be expressed appropri-
ately (Zadeh, 1965). The fuzzy set uses the membership degree as a single
index which reflects the state of support or opposition attitude of the
decision-makers to the different objectives. It extends the eigenfunctions
of the membership degree from integer 0 and 1 to the closed interval [0,
1]. The fuzzy set breaks through the logic shackles in conventional analysis
methods and opens up a new field for decision-makers to deal with fuzzy
information. However, with the development of decision-making theory
and fuzzy set method, it is found that it will be difficult to accurately describe
the uncertainty of objectives by simply relying on fuzzy sets. This is because
the fuzzy set only involves the membership degree, but neglects the hesita-
tion and the indeterminacy often involved in decision-making. To fully
reflect the characteristics of affirmation, negation, and hesitation of human
cognitive performance, the intuitionistic fuzzy set (IFS) was proposed by
Atanassov (1986) and Atanassov and Gargov (1989). IFS is characterized
by a membership function, a nonmembership function, and a hesitancy
(indeterminacy) function. Compared with conventional fuzzy set, IFS has
a better ability to accurately describe the natural attributes of objectives.
Thus this method has gradually become the hotspot in the research area
of fuzzy mathematics and decision-making for recent 30 years (Mardani
et al., 2015), and has been widely used to describe the imprecise, vague,
or uncertain preferences of the decision-makers in decision-making process
(Xu and Zhao, 2016).
In the following research, the theory of IFS has been continuously
improved. The development of IFS accelerates the application in solving
the real-word problems. Recent applications of intuitionistic multicriteria