2 research outputs found
A Hypervolume Based Approach to Rank Intuitionistic Fuzzy Sets and Its Extension to Multi-criteria Decision Making Under Uncertainty
Ranking intuitionistic fuzzy sets with distance based ranking methods
requires to calculate the distance between intuitionistic fuzzy set and a
reference point which is known to have either maximum (positive ideal solution)
or minimum (negative ideal solution) value. These group of approaches assume
that as the distance of an intuitionistic fuzzy set to the reference point is
decreases, the similarity of intuitionistic fuzzy set with that point
increases. This is a misconception because an intuitionistic fuzzy set which
has the shortest distance to positive ideal solution does not have to be the
furthest from negative ideal solution for all circumstances when the distance
function is nonlinear. This paper gives a mathematical proof of why this
assumption is not valid for any of the non-linear distance functions and
suggests a hypervolume based ranking approach as an alternative to distance
based ranking. In addition, the suggested ranking approach is extended as a new
multicriteria decision making method, HyperVolume based ASsessment (HVAS). HVAS
is applied for multicriteria assessment of Turkey's energy alternatives.
Results are compared with three well known distance based multicriteria
decision making methods (TOPSIS, VIKOR, and CODAS).Comment: 8 pages, 3 figure
Improved Knowledge Measures for q-Rung Orthopair Fuzzy Sets
The q-rung orthopair fuzzy set (qROFS) defined by Yager is a generalization of Atanassov intuitionistic fuzzy set (IFS) and Pythagorean fuzzy sets (PyFSs). In this paper, we define the knowledge measure for qROFS by using the cosine inverse function. The information precision and information content are two facets of knowledge measure. Both facets of knowledge measure are considered. The properties of knowledge measure and their graphical explanations are discussed. An application of the knowledge measure in multi-attribute group decision-making (MAGDM) problem under the confidence level approach is given. A numerical example of the selection of renewable energy sources is discussed