Papers by Florentin Smarandache
In this paper, for the first time, we extend the Over/Under/Off Set/Logic/Probability used in unc... more In this paper, for the first time, we extend the Over/Under/Off Set/Logic/Probability used in uncertain theories (such as: fuzzy, neutrosophic and extensions) to the Over/Under/Off Mass that could be used in information fusion. The approach is exemplified in three scenarios: (1) wildfire evacuation and resource allocation with satellite, IoT, and social media; (2) coverage gaps where indeterminacy must be managed; and (3) security monitoring where contradictory or erroneous reports are discounted.
arXiv (Cornell University), 2006
In this book the authors probe into Vedic Mathematics (a concept that gained renown in the period... more In this book the authors probe into Vedic Mathematics (a concept that gained renown in the period of the religious fanatic and revivalist Hindutva rule in India): and explore whether it is really 'Vedic' in origin or 'Mathematics' in content. We analyzed this problem using fuzzy models like Fuzzy Cognitive Maps (FCM), Fuzzy Relational Maps (FRM) and the newly constructed fuzzy dynamical system (and its Neutrosophic analogue) that can analyze multi-experts opinion at a time using a single model. The issue of Vedic Mathematics involves religious politics, caste supremacy, apart from elementary arithmetic -- so we cannot use simple statistics for our analysis.
arXiv (Cornell University), Sep 20, 2020
This book has seven chapters. The first chapter is introductory in nature and it speaks about the... more This book has seven chapters. The first chapter is introductory in nature and it speaks about the migrant labourers. In chapter two we use Fuzzy Cognitive Maps to analyze the socio-economic problems of HIV/AIDS infected migrant labourers in rural areas of Tamil Nadu. In chapter three we analyze the role played by the government helping these migrant labourers with HIV/AIDS and factors of migration and their vulnerability in catching HIV/AIDS. For the first time Neutrosophic Cognitive Maps are used in the study of migrant labourers who have become HIV/AIDS victims. This study is done in Chapter IV. In chapter V we use Neutrosophic Relational Maps and we define some new neutrosophic tools like Combined Disjoint Block FRM, Combined Overlap NRM and linked NRM. We adopt these new techniques in the study and analysis of this problem. Chapter VI gives a very brief sketch of the life history of these 60 HIV/AIDS infected migrant labourers so that people from different social and cultural backgrounds follow our analysis. The last chapter gives suggestions and conclusions based on our study. This book has 8 appendices. The Appendix 1 is the questionnaire used in interviewing these migrant labourers. The questionnaire was formatted with the help of Dr. K. Kandasamy. Appendix 2 gives the table of these 60 migrant labourers. Appendix 3 to 8 gives the C programs used in finding the resultant vector for any given state vector using the dynamical system. Appendix 9 deals with Neutrosophic logic. We have included a list of further reading. We deeply acknowledge the TNSACS for its financial support and encouragement. We personally acknowledge the project director Mr. Deenabandu, I.A.S of TNSACS for his constant encouragement. We are indebted to Ms.Kama Kandasamy who had taken all pains to format, verify the equations and design the books. We deeply acknowledge the services of Dr.K.Kandasamy who had done a lot of background work and for formatting such a scientific linguistic questionnaire without which we would not have been in a position to get this data. We thank our research scholars Mr.Ganesan, Mr.Kanagamuthu and Mr.Narayanamurthy for taking the interviews. Our deep thanks are due to Meena Kandasamy who translated the Tamil interviews of these migrant labourers. We dedicate this book to the peoples and nations that are working to rehabilitate and support the poor men and women living with HIV/AIDS in the Third-World countries.
arXiv (Cornell University), Sep 1, 2003
arXiv (Cornell University), Aug 22, 2008
We extend Knuth's 16 Boolean binary logic operators to fuzzy logic and neutrosophic logic binary ... more We extend Knuth's 16 Boolean binary logic operators to fuzzy logic and neutrosophic logic binary operators. Then we generalize them to n-ary fuzzy logic and neutrosophic logic operators using the smarandache codification of the Venn diagram and a defined vector neutrosophic law. In such way, new operators in neutrosophic logic/set/probability are built.
Computer Science and Information Technology, 2013
Intuitionistic Neutrosophic soft set theory proposed by S.Broumi and F. Samarandache , has been r... more Intuitionistic Neutrosophic soft set theory proposed by S.Broumi and F. Samarandache , has been regarded as an effective mathematical tool to deal with uncertainties. In this paper new operations on intuitionistic neutrosophic soft sets have been introduced . Some results relating to the properties of these operations have been established. Moreover ,we illustrate their interconnections between each other.
This book has seven chapters. The first chapter is introductory in nature and it speaks about the... more This book has seven chapters. The first chapter is introductory in nature and it speaks about the migrant labourers. In chapter two we use Fuzzy Cognitive Maps to analyze the socio-economic problems of HIV/AIDS infected migrant labourers in rural areas of Tamil Nadu. In chapter three we analyze the role played by the government helping these migrant labourers with HIV/AIDS and factors of migration and their vulnerability in catching HIV/AIDS. For the first time Neutrosophic Cognitive Maps are used in the study of migrant labourers who have become HIV/AIDS victims. This study is done in Chapter IV. In chapter V we use Neutrosophic Relational Maps and we define some new neutrosophic tools like Combined Disjoint Block FRM, Combined Overlap NRM and linked NRM. We adopt these new techniques in the study and analysis of this problem. Chapter VI gives a very brief sketch of the life history of these 60 HIV/AIDS infected migrant labourers so that people from different social and cultural backgrounds follow our analysis. The last chapter gives suggestions and conclusions based on our study. This book has 8 appendices. The Appendix 1 is the questionnaire used in interviewing these migrant labourers. The questionnaire was formatted with the help of Dr. K. Kandasamy. Appendix 2 gives the table of these 60 migrant labourers. Appendix 3 to 8 gives the C programs used in finding the resultant vector for any given state vector using the dynamical system. Appendix 9 deals with Neutrosophic logic. We have included a list of further reading. We deeply acknowledge the TNSACS for its financial support and encouragement. We personally acknowledge the project director Mr. Deenabandu, I.A.S of TNSACS for his constant encouragement. We are indebted to Ms.Kama Kandasamy who had taken all pains to format, verify the equations and design the books. We deeply acknowledge the services of Dr.K.Kandasamy who had done a lot of background work and for formatting such a scientific linguistic questionnaire without which we would not have been in a position to get this data. We thank our research scholars Mr.Ganesan, Mr.Kanagamuthu and Mr.Narayanamurthy for taking the interviews. Our deep thanks are due to Meena Kandasamy who translated the Tamil interviews of these migrant labourers. We dedicate this book to the peoples and nations that are working to rehabilitate and support the poor men and women living with HIV/AIDS in the Third-World countries.
We express our sincere thanks to Kama Kandasamy for her help in the layout and Meena for cover-de... more We express our sincere thanks to Kama Kandasamy for her help in the layout and Meena for cover-design of the book. The authors express their whole-hearted gratefulness to Dr.K.Kandasamy whose invaluable support and help, and patient proofreading contributed to a great extent to the making of this book.
Now we give a simple illustration of a FRM, for more about FRMs please refer [130-132, 143, 144].... more Now we give a simple illustration of a FRM, for more about FRMs please refer [130-132, 143, 144]. Example 1.2.1: Let us consider the relationship between the teacher and the student. Suppose we take the domain space as the concepts belonging to the teacher say D 1 ,…, D 5 and the range space denote the concepts belonging to the student say R 1 , R 2 and R 3 . We describe the nodes D 1 ,…, D 5 and R 1 , R 2 and R 3 as follows: Domain Space D 1 -Teaching is good D 2 -Teaching is poor D 3 -Teaching is mediocre D 4 -Teacher is kind D 5 -Teacher is harsh [or rude] (We can have more concepts like teacher is non-reactive, unconcerned etc.) Range Space R 1 -Good Student R 2 -Bad Student
Now we illustrate this by examples before we proceed on to recall more properties about them. whe... more Now we illustrate this by examples before we proceed on to recall more properties about them. where G 1 = S 3 the symmetric group of degree 3 with 1 1 2 3 e 1 2 3 , the cyclic group of order 6, G 3 = Z 5 , the group under addition modulo 5 with e 3 = 0, G 4 = D 8 = {a, b | a 2 = b 8 = 1; bab = a}, the dihedral group of order 8, e 4 = 1 is the identity element of G 4 and G 5 = A 4 the alternating subgroup of S 4 with 4 these concepts mainly to define the new notion of linear nalgebra or n-linear algebra and n-vector spaces of type I. n, H i proper subgroup of G i is defined to be the proper n-subgroup of the ngroup G. If some of the H i = G i or H i = {e i } or H i = φ for some i, then H will not be called as proper n-subgroup but only as msubgroup of the n-group, m < n and m of the subgroups H j in G j are only proper and the rest are either {e j } or φ, 1 ≤ j ≤ n. We illustrate both these situations by the following example. be a 4-group where G 1 = S 4 , G 2 = Z 10 group under addition modulo 10, G 3 = D 12 the dihedral group with order 12 given by the set {a, b | a 2 = b 6 = 1, bab = a} and G 4 = Z the set of positive and negative integers with zero under +. Consider H = H 1 ∪ H 2 ∪ H 3 ∪ H 4 where H 1 = A 4 the alternating subgroup of S 4 , H 2 = {0, 2, 4, 6, 8} a subgroup of order 5 under addition modulo 10. H 3 = {1, b, b 2 , b 3 , b 4 , b 5 }; the subgroup of D 12 and H 4 = {2n | n ∈ Z} a subgroup of Z. Clearly H is a proper 4-subroup of the 4-group G.
Neutrosophic Sets and Systems, 2013
Smarandache (1995) defined the notion of neutrosophic sets, which is a generalization of Zadeh... more Smarandache (1995) defined the notion of neutrosophic sets, which is a generalization of Zadeh's fuzzy set and Atanassov's intuitionistic fuzzy set. In this paper, we first develop some similarity measures of neutrosophic sets. We will present a method to calculate the distance between neutrosophic sets (NS) on the basis of the Hausdorff distance. Then we will use this distance to generate a new similarity measure to calculate the degree of similarity between NS. Finally we will prove some properties of the proposed similarity measures.
In this paper, we firstly review the neutrosophic set, and then construct two new concepts called... more In this paper, we firstly review the neutrosophic set, and then construct two new concepts called neutrosophic implication of type 1 and of type 2 for neutrosophic sets. Furthermore, some of their basic properties and some results associated with the two neutrosophic
viXra, 2015
In the present paper we have discussed concerning Godel’s incompleteness theorem(s) and plausible... more In the present paper we have discussed concerning Godel’s incompleteness theorem(s) and plausible implications to artificial intelligence/life and human mind. Perhaps we should agree with Sullins III, that the value of this finding is not to discourage certain types of research in AL, but rather to help move us in a direction where we can more clearly define the results of that research. Godel’s incompleteness theorems have their own limitations, but so do Artificial Life (AL)/AI systems. Based on our experiences so far, human mind has incredible abilities to interact with other part of human body including heart, which makes it so difficult to simulate in AI/AL. However, it remains an open question to predict whether the future of AI including robotics science can bring this gap closer or not. In this regard, fuzzy logic and its generalization –neutrosophic logic- offer a way to improve significantly AI/AL research.[15]
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Papers by Florentin Smarandache