Related Experiment Video
Updated: Nov 27, 2025
08:12
A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
Published on: March 1, 2022
2.8K
Generalized Distance-Based Entropy and Dimension Root Entropy for Simplified Neutrosophic Sets
1Department of Electrical engineering and Automation, Shaoxing University, 508 Huancheng West Road, Shaoxing 312000, China.
Entropy (Basel, Switzerland)
|December 3, 2020
Summary
This study introduces new entropy measures for simplified neutrosophic sets (NSs) to quantify uncertainty. These novel measures, including generalized distance-based and dimension root entropy, are validated for decision-making applications.
Area of Science:
- Mathematics
- Information Theory
- Fuzzy Set Theory
Background:
- Simplified neutrosophic sets (NSs) offer a framework for handling uncertainty.
- Quantifying fuzziness in NSs is crucial for their practical application.
- Existing entropy measures may not fully capture the complexity of simplified NSs.
Purpose of the Study:
- To propose novel generalized distance-based entropy and dimension root entropy measures for simplified neutrosophic sets (NSs).
- To verify the properties and demonstrate the feasibility and rationality of the proposed entropy measures.
- To enrich the theory and measure approaches for simplified neutrosophic entropy.
Main Methods:
- Development of a generalized distance-based entropy measure for simplified NSs.
- Development of a dimension root entropy measure for simplified NSs.
- Verification of properties and comparison with existing measures using numerical and decision-making examples.
Main Results:
- The proposed generalized distance-based entropy and dimension root entropy measures for simplified NSs are presented.
- Properties of the new measures are verified, demonstrating their feasibility and rationality.
- A decision-making example confirms the effectiveness and reasonableness of the proposed entropy measures.
Conclusions:
- The study successfully introduces and validates new entropy measures for simplified neutrosophic sets.
- The proposed measures enhance the quantification of fuzziness in simplified NSs.
- This research contributes to the advancement of simplified neutrosophic entropy theory and its applications.
Related Concept Videos
02:39Entropy
33.7K
Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
33.7K
01:18Entropy
3.3K
The first law of thermodynamics is quantitatively formulated via an equation relating the internal energy of a system, the heat exchanged by it, and the work done on it. A quantitative formulation of the second law of thermodynamics leads to defining a state function, the entropy.
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
Consider an infinitesimal step in the expansion, which...
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
Consider an infinitesimal step in the expansion, which...
3.3K
02:05Entropy and Solvation
7.9K
The process of surrounding a solute with solvent is called solvation. It involves evenly distributing the solute within the solvent. The rule of thumb for determining a solvent for a given compound is that like dissolves like. A good solvent has molecular characteristics similar to those of the compound to be dissolved. For example, polar solutions dissolve polar solutes, and apolar solvents dissolve apolar solutes. A polar solvent is a solvent that has a high dielectric constant (ϵ...
7.9K
02:38Third Law of Thermodynamics
21.0K
A pure, perfectly crystalline solid possessing no kinetic energy (that is, at a temperature of absolute zero, 0 K) may be described by a single microstate, as its purity, perfect crystallinity,and complete lack of motion means there is but one possible location for each identical atom or molecule comprising the crystal (W = 1). According to the Boltzmann equation, the entropy of this system is zero.
21.0K
01:23Dimensional Analysis
1.7K
Dimensional analysis is a powerful tool that is used in physics and engineering to understand and predict the behavior of physical systems. The basic idea behind dimensional analysis is to express physical quantities in terms of fundamental dimensions such as the mass, length, and time. Derived dimensions like the velocity, acceleration, and force are derived from the combinations of these fundamental dimensions.
Dimensional analysis allows us to analyze and compare physical quantities on a...
Dimensional analysis allows us to analyze and compare physical quantities on a...
1.7K
02:19Dimensional Analysis
21.5K
The concept of dimension is important because every mathematical equation linking physical quantities must be dimensionally consistent, implying that mathematical equations must meet the following two rules. The first rule is that, in an equation, the expressions on each side of the equal sign must have the same dimensions. This is fairly intuitive since we can only add or subtract quantities of the same type (dimension). The second rule states that, in an equation, the arguments of any of the...
21.5K