Related Experiment Video
Updated: Jun 28, 2025
Experimental Research Examining How People Can Cope with Uncertainty Through Soft Haptic Sensations
Published on: September 16, 2015
Interval-Valued Intuitionistic Fuzzy Soft Rough Approximation Operators and Their Applications in Decision Making
Anjan Mukherjee1, Abhik Mukherjee2
1Department of Mathematics, Tripura University, Suryamaninagar, Agartala, 799022 India.
Abstract:
It has been found that fuzzy sets, rough sets and soft sets are closely related concepts. Many complicated problems in economics, engineering, social sciences, medical science and many other fields involve uncertain data. These problems, which one comes in real life, cannot be solved using classical mathematical methods. There are several well-known theories to describe uncertainty, for instance, fuzzy set theory, rough set theory, and other mathematical tools. But all of these theories have their inherit difficulties as pointed out by D. Molodtsov. In 1999, D. Molodtsov introduced the concept of soft sets, which can be seen as a new mathematical tool for dealing with uncertainties. The concept of rough sets, proposed by Z. Pawlak as a framework for the construction of approximations of concepts. It is a formal tool for modeling and processing insufficient and incomplete information. Zhou and Wu first proposed the concept of intuitionistic fuzzy rough sets (IFrough sets). The aim of this paper is to introduce the concept of interval-valued intuitionistic fuzzy soft rough sets (IVIFS rough sets). We also investigate some properties of IVIFS rough approximation operators. Some basic operations and properties are studied. Lastly applications have been shown in decision making problems.
Related Concept Videos
01:37Reason and Intuition
01:28Accuracy, limits, and approximation
Accuracy is defined as the closeness of the measured value to the true or actual value. In engineering mechanics, repeated measurements are taken during theoretical or experimental analyses to ensure that the result is precise and accurate.
The accuracy of any solution is based on the...
01:09Decision Making: P-value Method
First, a specific claim about the population parameter is proposed. The claim is based on the research question and is stated in a simple form. Further, an opposing statement to the claim is also stated. These statements can act as null and alternative hypotheses: a null hypothesis would be a neutral statement while the alternative hypothesis can...
01:03Prediction Intervals
However, the point estimate is most likely not the exact value of the population parameter, but close to it. After calculating point estimates, we construct interval estimates, called confidence intervals or prediction intervals. This prediction interval comprises a range of values unlike the point estimate and is a better predictor of the observed sample value, y.
01:08The Availability Heuristic
01:21Linear Approximation in Time Domain
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...