लक्ष्य निर्धारित कर सम्यकत्व के लिए पुरुषार्थ करेंगे तो मोक्ष का मार्ग मिलेगा- पूज्य श्री अतिशयमुनिजी म.सा.
लक्ष्य निर्धारित कर सम्यकत्व के लिए पुरुषार्थ करेंगे तो मोक्ष का मार्ग मिलेगा- पूज्य श्री अतिशयमुनिजी म.सा.
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P1 | Equality of two fuzzy sets | Fuzzy set A is considered equal to a fuzzy set BIF AND ONLY IF (iff) mA (x) = mB (x) |
P2 | Inclusion of one set into another set | Fuzzy set AÌ X is included ~ in (is a subset of) another fuzzy set, BÌX ~IF AND ONLY IF (iff) mA(x) £mB(x) " xÎ X |
Example: Consider X = {1, 2, 3}and A = 0.3/1 + 0.5/2 + 1/3 B = 0.5/1 + 0.55/2 + 1/3 Then A is a subset of B | ||
P3 | Cardinality of a fuzzy set | Cardinality of a non-fuzzy set, Z, is the number of elements in Z. BUT the cardinality of a fuzzy set A, the so-called SIGMA COUNT, expressed as a SUM of the values of the membership function of A, mA(x)Card A = mA(x1) + ….. +mA(xn) n = SmA(x1) i=1 |
EXAMPLE Card A = 1.8 Card B = 1.85 | ||
P4 | An empty fuzzy set | A fuzzy set A is empty IF AND ONLY IF mA(x) = 0, " xÎ X |
P5 | a -cuts or a -level sets of a fuzzy set | An a -cut or a -level set of a fuzzy set A Ì X is an ~ ORDINARY SET AaÌ X, ~ such that Aa ={xÎ X; mA(x)³a } 0£a£ 1 Decomposition A=Sa Aa 0£a£ 1 |
Example: A=0.3/1 + 0.5/2 + 1/3 X = {1, 2, 3} Then A0.5 = {2, 3} A0.1 = {1, 2, 3} A1 = {3} |
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