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Introduction
Published in John N. Mordeson, Davender S. Malik, Fuzzy Automata and Languages, 2002
John N. Mordeson, Davender S. Malik
If A and B are sets, we let A×B denote the Cartesian cross-product of A and B, i.e., A×B is the set of all ordered pairs (a,b), where a∈A and b∈B. We write An for the set of all ordered n-tuples of elements from A, where n∈N. We let P(X) denote the power set of a set X, i.e., P(X) is the set of all subsets of X.
Introduction to Sets and Relations
Published in Richard L. Shell, Ernest L. Hall, Handbook of Industrial Automation, 2000
Additional sets can be formed by using the elements of a given set. For instance, if A = {a, b, c}, the set whose elements are all the subsets of A, the power set P(A), is given by P(A)={0,{a},{b},{c},{a,b},{a,c},{b,c},{a,b,c}}
Discrete Mathematics
Published in Dan Zwillinger, CRC Standard Mathematical Tables and Formulas, 2018
for all sets A, B, C.Given the set X, the power set of X is {S|SsubseteqX}, the set of all subsets of X. The power set of X is written as as P(X) $ {\mathcal{P}}(X) $ or 2.
Discovery of effective infrequent sequences based on maximum probability path
Published in Connection Science, 2022
Ke Lu, Xianwen Fang, Na Fang, Esther Asare
is a finite active set. represents the power set on A, i.e. the set of all possible subsets of A. represents the set of all series on A. represents a sequence of length n, subsequence is a subset of sequence A. Empty sequence is marked as ε. The connection of sequence and is marked as . One occurrence of an activity forms an event e. And a sequence of events is the trace in the log. Event represents a multi-set of traces (Deshmukh et al., 2020).
Combining belief functions taking into consideration error in judgement
Published in International Journal of General Systems, 2020
Sunay P. Pai, Rajesh S. Prabhu Gaonkar
Let be the set containing N elements corresponding to N finite set of mutually exclusive and exhaustive hypothesis. This set is called as frame of discernment. The power set of is defined as the set which contains all the possible subsets A of and is represented by P(). The cardinality of this set is 2N, each representing the event “the object is possible in A”. where Ø denotes the empty set. Subsets containing only one element are called singletons. A Basic Probability Assignment (BPA) is a function from P() to [0, 1] defined by A → m(A) and which satisfies the following conditions:
Quasidifferentiabilities of the expectation functions of random quasidifferentiable functions
Published in Optimization, 2020
Sida Lin, Ming Huang, Zunquan Xia, Dan Li
Let be the set of subsets of , called power set of . A mapping is called multifunction and written as , which is called set-valued mapping in [7].