Abstract
The objective of this manuscript is to present a novel information measure for measuring the degree of fuzziness in intuitionistic fuzzy sets (IFSs). To achieve it, we define an ( R , S ) -norm-based information measure called the entropy to measure the degree of fuzziness of the set. Then, we prove that the proposed entropy measure is a valid measure and satisfies certain properties. An illustrative example related to a linguistic variable is given to demonstrate it. Then, we utilized it to propose two decision-making approaches to solve the multi-attribute decision-making (MADM) problem in the IFS environment by considering the attribute weights as either partially known or completely unknown. Finally, a practical example is provided to illustrate the decision-making process. The results corresponding to different pairs of ( R , S ) give different choices to the decision-maker to assess their results.
Highlights
Multi-attribute decision-making (MADM) problems are an important part of decision theory in which we choose the best one from the set of finite alternatives based on the collective information
In an attempt to address such problems and motivated by the characteristics of the intuitionistic fuzzy sets (IFSs) to describe the uncertainties in the data, this paper addresses a new entropy measure to quantify the degree of fuzziness of a set in the IFS environment
We propose an entropy measure based on the (R, S)-norm in the IFS environment
Summary
Multi-attribute decision-making (MADM) problems are an important part of decision theory in which we choose the best one from the set of finite alternatives based on the collective information. Garg [53] presented a generalized intuitionistic fuzzy entropy measure to determine the completely unknown attribute weight to solve the decision-making problems. In an attempt to address such problems and motivated by the characteristics of the IFSs to describe the uncertainties in the data, this paper addresses a new entropy measure to quantify the degree of fuzziness of a set in the IFS environment. The aim of this entropy is to determine the attribute weights under the characteristics of the attribute weights that they are either partially known or completely unknown.
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