Chapter 6: Computation with Z-Numbers
The following sections are included:
Z-number, Z-information
The arithmetic with continuous Z-numbers
State-of-the-art
General procedure of computation with Z-numbers
A general approach suggested by L. Zadeh
The suggested approach
Operations on continuous Z-numbers
Addition of continuous Z-numbers
Standard subtraction of continuous Z-numbers
Multiplication of continuous Z-numbers
Standard division of continuous Z-numbers
Square of a continuous Z-number
Square root of a continuous Z-number
Minimum and maximum of continuous Z-numbers
The arithmetic of discrete Z-numbers
Discrete Z-numbers
Addition of discrete Z-numbers
Standard subtraction of discrete Z-numbers
Multiplication of discrete Z-numbers
Standard division of discrete Z-numbers
Power of a discrete Z-number
Square of a discrete Z-number
Square root of a discrete Z-number
Z-numbers valued functions
Methodology for construction of functions of Z-numbers
Basic properties of functions of Z-numbers
Reasoning with Z-information
State-of-the-art
Fuzzy and Z-number-valued If-Then rules
Approximate reasoning with Z-rules
Linear interpolation-based reasoning with Z-rules
Ranking of Z-numbers
State-of-the-art
Ranking of Z-numbers
Aggregation of Z-information
State-of-the-art
Aggregation operators for Z-numbers based information
Z-arithmetic mean
Z-geometric mean
Z-weighted arithmetic mean
Z-T-norm and Z-T-conorm operators
Z-ordered weighted averaging operators
Z-numbers and type-2 fuzzy sets: A representation result
Z-numbers and type-2 fuzzy sets
Data processing to Z-numbers and type-2 fuzzy set
