1/1/2015 · Nowadays there is no arithmetic of Z-numbers suggested in the existing literature. Taking into account the fact that real problems are characterized by linguistic information which is, as a rule, described by a discrete set of meaningful linguistic terms, in our study we consider discrete Z-numbers.
Nowadays there is no arithmetic of Z-numbers suggested in the existing literature. Taking into account the fact that real problems are characterized by linguistic information which is, as a rule, described by a discrete set of meaningful linguistic terms, in our study we consider discrete Z-numbers.
A Z-number is an ordered pair Z = (A,B)Z= (A,B) of fuzzy numbers A and B used to describe a value of a random variable X, where A is an imprecise estimation of a value of X and B is an imprecise…
Arithmetic Operations . Continuous and Discrete Z-numbers: Discussion. A Z-number and a Z +-number. Addition of Discrete Z-numbers. Standard Subtraction of Discrete Z-numbers. Hukuhara Difference of Discrete Z-numbers. Multiplication of Discrete Z-numbers. Standard Division of Discrete Z-numbers. Power of a Discrete Z-number . Square of a …
Both discrete and continuous Z-numbers are pairs of discrete and continuous fuzzy numbers. … A. V.
Huseynov, O. H. 2017. An introduction to the arithmetic of Z-numbers by using horizontal membership functions. Procedia Computer Science, 120, 349-356. Zadeh, L. A. 2011. A note on Z-numbers. Information Sciences, 181(14): 2923–2932.
Definition 2.3 [4] A discrete Z-number is an ordered pair í µí± = (í µí°´, í µí°µ) where A is a discrete fuzzy number playing a role as a fuzzy constraint on values that a random …
The main critical problem that naturally arises in processing Z-numbers-based information is the computation with Z-numbers. Nowadays, there is no arithmetic of Z-numbers suggested in existing literature. This book is the first to present a comprehensive and self-contained theory of Z- arithmetic and its applications. … Operations on Discrete …
10/1/2020 · Discrete Z-Numbers . A discrete Z-number is defined as an ordered pair of discrete fuzzy numbers Z = A, B on X. Let X be a random variable, A and B are two discrete numbers, and ? A: a 1, a 2,.
a n ? [0, 1] and ? B: b 1, b 2,.
b n ? [0, 1] for the membership function of A and B, respectively, where a 1, a 2,.
a n ? R and b 1, b 2,.
b n ? [0, 1].
10/1/2018 · The suggested arithmetic of discrete Z-numbers includes basic arithmetic operations and important algebraic operations. In contrast to the other works devoted to Z-numbers [4] , [8] , [9] , [34] , [35] , [36] , [37] , [41] , [45] , [50] , [55] , [56] , [59] , the proposed approach allows dealing with Z-numbers directly without conversion to fuzzy numbers.
The letters R, Q, N, and Z refers to a set of numbers such that: R = real numbers includes all real number [-inf, inf] Q= rational numbers ( numbers written as ratio)
