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 Book Id: WPLBN0002097038 Subjects: Non Fiction, Education, Smarandache Collections Collections: Math, Literature, Education, Authors Community, Mathematics ► Abstract Full Text Search Details...also by Erhus Cniversity Press, dealt almost exclusively with some "basic" consequences of the Smarandache function. In this one, the universe of dis... ...y from the interest and excitement that can be generated by exploring the consequences of such a problem It is a well-known cliche among writers tha... ... some of these problems. In mathematics, one often does not know what the consequences of a statement are. Cnlike a novel however, there are no compl... ... n, where n is the smallest number such that m divides n'. and associated consequences has spawned many new branches of mathematics. A previous volu... ...t occur in n! 0 This function has many uses when dealing with some of the consequences of the Smarandache function Sen), most notably, the number of... ... prime, the Smarandache values would form the same 3 x 3 magic square. A logical extension of this problem places a restriction on the numbers. The...
 Book Id: WPLBN0002097105 ► Abstract Full Text Search Details...ant role in fuzzy relation equations. While the t-norm i may be interpreted as logical conjunction, the corresponding operation w i may be interpr... ... as logical conjunction, the corresponding operation w i may be interpreted as logical implication. The following basic properties 31 of w i ... ...practice. For example, in fuzzy reasoning [70], when the inference rule and the consequences are known, a problem to determine antecedents to be use... ...sible solutions according to some levels of plausibility is out of the scope of logical reasoning, strictly speaking. However one may for instance... ... 134 there are manifestations which are neither certain nor impossible and consequences of the presence of a given disorder d which are only po... ...n power of the model, we have to refine the non–fuzzy model in such a way that consequences (resp. manifestations) previously expressed as certain ... ...p. certainly absent) remain classified in the same way and where some possible consequences (resp. possibly present manifestations) are now allowed... ...ication, negation and a quantifier for generalization are used. As usual, those logical operators are characterized by the way they operate on the t... ... B ∧ t B ⊆ t A. (16) Introducing also the notation |= for (generalized) logical validity as in [28, 29] by |= A ≡ t A . ( 1 7 ) W...
 Book Id: WPLBN0002097100 ► Abstract Full Text Search Details...d terminal edges. For proof refer [11]. The following results are easy consequences of the above theorem. Result: [4]: Let G be any connecte... ... Machine Intelligence, 9 (1979) 149- 194. 75. Zhang, W.R., and S. Chen. A Logical Architecture for Cognitive Maps, Proceedings of the 2 nd IEEE ...
 Book Id: WPLBN0002097108 Subjects: Non Fiction, Education, Smarandache Collections ► Abstract Full Text Search Details...ant role in fuzzy relation equations. While the t-norm i may be interpreted as logical conjunction, the corresponding operation w i may be interpr... ... as logical conjunction, the corresponding operation w i may be interpreted as logical implication. The following basic properties 31 of w i ... ...practice. For example, in fuzzy reasoning [70], when the inference rule and the consequences are known, a problem to determine antecedents to be use... ...sible solutions according to some levels of plausibility is out of the scope of logical reasoning, strictly speaking. However one may for instance... ... 134 there are manifestations which are neither certain nor impossible and consequences of the presence of a given disorder d which are only po... ...n power of the model, we have to refine the non–fuzzy model in such a way that consequences (resp. manifestations) previously expressed as certain ... ...p. certainly absent) remain classified in the same way and where some possible consequences (resp. possibly present manifestations) are now allowed... ...ication, negation and a quantifier for generalization are used. As usual, those logical operators are characterized by the way they operate on the t... ... B ∧ t B ⊆ t A. (16) Introducing also the notation |= for (generalized) logical validity as in [28, 29] by |= A ≡ t A . ( 1 7 ) W...
 Book Id: WPLBN0002097117 Subjects: Non Fiction, Education, Smarandache Collections ► Abstract Full Text Search Details... related to Untouchability 114 3.3 Some facts about Untouchability and its Consequences even after 57 years of Independence 334 Chapter F... ...in order to understand the multi-dimensional facets of untouchability and its consequences, we have given relevant excerpts from the translation of ... ...Smarandache [55-59]. 23 DEFINITION 1.4.1: In the neutrosophic logic every logical variable x is described by an ordered triple x = (T, I, F) wh... ...sistent logic, which means contradictory sources of information about a same logical variable, proposition or event one has T + I + F > 1. Thu... ...temporary casteist atrocities to analyze the evils of untouchability and its consequences using Fuzzy Cognitive Maps (FCMs) and Neutrosophic Cognit... ...everal cases, those who dare to love across caste lines have to face the dire consequence of death. R 10 – Varnashrama Dharma It was the earl... ... of the Brahmin society must only be Chandalas. So, in this 150 situation, logically you cannot be faulted since you have a place and plenty of e... ...eech of Periyar, 19-12-1973] 3.3 Some facts about Untouchability and its Consequences even after 57 years of Independence Here we give some ... ... Nadu 1920-1940, Koodal Pubishers, Madurai, (1980). 375 34. Periyar Dasan, Logical Analysis of Atheistic Principles of Periyar, unpublished Ph.D ...
 Book Id: WPLBN0002097647 Subjects: Non-Fiction, Education, Smarandache Collections ► Abstract Full Text Search Details...se to the reader as the proof requires vitally only the definitions and a logical use of them. A recent paper [27] which studies strictly wild al... ...utative ring II. Proof: Left for the reader to verify as it is an easy consequence of the definition. THEOREM 4.2.2: Let R be a ring. If R is ...
 Book Id: WPLBN0002097101 Subjects: Non Fiction, Education, Smarandache Collections ► Abstract Full Text Search Details...trongly resemble neural networks, and they have powerful and far-reaching consequences as a mathematical tool for modeling complex systems. Prof. Ba... ... this stimulus input vector with FCM matrix, K.C. Lee et al [65] obtain a consequence vector as follows: (0, 0, 0, 0, 0.3, 0, – 0.3, 0.5) × FCM ma... ...3, 0, – 0.3, 0.5) × FCM matrix = (– 0.5, 0, 0.24, 0, – 0.08, 0, 0). The consequence vector may be interpreted such that changes in those three fact... ... vector can be organized into (0, 0, 0, – 0.1, 0.3, 0, – 0.3, .2). Then a consequence vector may be obtained as (– 0.15, .02, 0, – 0.24, 0, –0.12, 0... ...∩ M j ) ⊂ ( ~ Q j ∩ M j ). Here “⊂” stands for fuzzy set inclusion (logical implication). For brevity, fuzzy causal relationship is abbreviate... ...ity, fuzzy causal relationship is abbreviated as FCR in the following. Logical implication has an antecedent (or premise) and a consequent (or con... ...t (or premise) and a consequent (or conclusion). A typical example of the logical implication is “If A, then B”. In the logical implication, there a... ...quence: negation of A (or ¬ A). The FCR is more complicated than the logical implication. 1. Modus tollens does not hold in the FCR. “When mi... ...ble for relations between several concepts are indeterminate). 2. In a logical implication “If A, Then B”, we cannot draw inference in case when ...
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