AN ALGEBRAIC APPROACH FOR REFINED NEUTROSOPHIC RANDOM VARIABLES
Abstract
In this article, we are going to extend the definition of literal neutrosophic random variables to literal refined neutrosophic random variables and we will study its new properties. We derive and present various concepts including refined neutrosophic probability distribution function in the continuous case, refined neutrosophic cumulative distribution function of continuous refined neutrosophic random variables, refined neutrosophic expected value, refined neutrosophic variance, refined neutrosophic standard deviation, refined neutrosophic mean deviation, refined neutrosophic rth quartiles, refined neutrosophic moments generating function, and refined neutrosophic characteristic function. Additionally, the paper includes many solved examples and applications. This paper opens the road to generalizing many concepts in neutrosophic probability theory specially neutrosophic reliability theory, neutrosophic stochastic processes, and neutrosophic queuing theory.
Keywords
Refined neutrosophic expected value, Refined neutrosophic variance, Refined standard neutrosophic deviation, Refined neutrosophic probability density function, Refined neutrosophic cumulative distribution
References
- [1] Smarandache F. Introduction to Neutrosophic Statistics. USA: Sitech & Education Publishing 2014; 3: 31-55.
- [2] Kandasamy WBV, Smarandache F. Neutrosophic Rings. Hexis, Phoenix, Arizona: Infinite Study 2006; 3: 7-20.
- [3] Kamaci H. Neutrosophic Cubic Hamacher Aggregation Operators and Their Applications in Decision Making. Neutrosophic Sets and Systems 2020; 33: 234-255.
- [4] Salama A, Sharaf Al-Din A, Abu Al-Qasim I, Alhabib R, Badran M. Introduction to Decision Making for Neutrosophic Environment Study on the Suez Canal Port. Egypt. Neutrosophic Sets and Systems 2020; 35: 22-44.
- [5] Anuradha J. Neutrosophic Fuzzy Hierarchical Clustering for Dengue Analysis in Sri Lanka. Neutrosophic Sets and Systems 2020; 31: 179-199.
- [6] Sahin R. Neutrosophic Hierarchical Clustering Algorithms. Neutrosophic Sets and Systems 2014; 2: 19-24.
- [7] Shahzadi G, Akram M, Saeid AB. An Application of Single-Valued Neutrosophic Sets in Medical Diagnosis. Neutrosophic Sets and Systems 2017; 18 (3): 80-88.
- [8] Ejaita OA, Asagba P. An Improved Framework for Diagnosing Confusable Diseases Using Neutrosophic Based Neural Network. Neutrosophic Sets and Systems 2017; 16: 28-34.
- [9] Chakraborty A, Banik B, Mondal SP, Alam S. Arithmetic and Geometric Operators of Pentagonal Neutrosophic Number and its Application in Mobile Communication Service Based MCGDM Problem. Neutrosophic Sets and Systems 2020; 32: 61-79.
- [10] Sahin M, Olgun N, Uluçay V, Kargın A, Smarandache F. A New Similarity Measure Based on Falsity Value between Single Valued Neutrosophic Sets Based on the Centroid Points of Transformed Single Valued Neutrosophic Numbers with Applications to Pattern Recognition, Neutrosophic Sets and Systems 2017; 15: 31-48.