52
B. Uzun et al.
∼ =
A = ˜
A
(20)
De Morgan’s Law:
The De Morgan’s laws was coined from Augustus De Morgan, a mathematician.
The law can be expressed as “the complement of two sets in Union having the same
intersection with the complements of the two sets in intersection. This law plays a
significant role in demonstrating redundancies and logical inconsistency. It states:
˜
A ∪ ˜
B = ˜
A ∩ ˜
B
(21)
˜
A ∩ ˜
B = ˜
A ∪ ˜
B
(22)
8.2.4 Membership Function
In the Fuzzy set, the membership function represents the weight of truth in the process
of valuation. In other words, the membership function is defined as the expression
set X and a real unit interval represented as 0,1. The membership degree of x ∈ ˜
A
can be denoted by μ ˜
A (x). If μ ˜
A (x) = 0, x is not a member of the fuzzy set (Fig. 8.1).
Lofti A. Zadeh perfectly expresses the membership features of the fuzzy sets in a
research, demonstrating the main features of the fuzzy sets. ‘The main properties of
membership description include:
• They form a distinct comparison in fuzziness
• The membership function use occurrences to solve real-life problems.
Fig. 8.1 A triangular fuzzy
set (Ozsahin et al. 2020)