Set Theory and Logic


Neutrosophic Theory and its Applications, Collected Papers, Vol. 1

Authors: Florentin Smarandache

Neutrosophic Theory means Neutrosophy applied in many fields in order to solve problems related to indeterminacy. Neutrosophy considers every entity <A> together with its opposite or negation <antiA>, and with their spectrum of neutralities <neutA> in between them (i.e. entities supporting neither nor <antiA>). Where , which of course depends on <A>, can be indeterminacy, neutrality, tie (game), unknown, vagueness, contradiction, ignorance, incompleteness, imprecision, etc. Hence, in one hand, the Neutrosophic Theory is based on the triad <A>, <neutA>, and <antiA>. In the other hand, Neutrosophic Theory studies the indeterminacy in general, labelled as I, with I^n = I for n ≥ 1, and mI + nI = (m+n)I, in neutrosophic structures developed in algebra, geometry, topology etc. This volume contains 45 papers, written by the author alone or in collaboration with the following co-authors: Mumtaz Ali, Said Broumi, Sukanto Bhattacharya, Mamoni Dhar, Irfan Deli, Mincong Deng, Alexandru Gal, Valeri Kroumov, Pabitra Kumar Maji, Maikel Leyva- Vazquez, Feng Liu, Pinaki Majumdar, Munazza Naz, Karina Perez-Teruel, Rıdvan Sahin, A. A. Salama, Muhammad Shabir, Rajshekhar Sunderraman, Luige Vladareanu, Magdalena Vladila, Stefan Vladutescu, Haibin Wang, Hongnian Yu, Yan-Qing Zhang, about discounting of a neutrosophic mass in terms of reliability and respectively the importance of the source, evolution of sets from fuzzy set to neutrosophic set, classes of neutrosophic norm (n-norm) and neutrosophic conorm (n-conorm), applications of neutrosophic logic to physics, connections between extension logic and refined neutrosophic logic, approaches of neutrosophic logic to RABOT real time control, some applications of the neutrosophic logic to robotics, correlation coefficients of interval valued neutrosophic set, cosine similarity between interval valued neutrosophic sets, distance and similarity measures of interval neutrosophic soft sets, generalized interval neutrosophic soft sets and their operations, G-neutrosophic space, neutrosophic orbit, neutrosophic stabilizer, intuitionistic neutrosophic sets, intuitionistic neutrosophic soft sets, neutrosophic multi relation (NMR) defined on neutrosophic multisets, neutrosophic loops and biloops, neutrosophic N-loops and soft neutrosophic N-loops, operations on intuitionistic fuzzy soft sets, fuzzy soft matrix and new operations, such as fuzzy soft complement matrix and trace of fuzzy soft matrix based on reference function related properties, neutrosophic parameterized (NP) soft sets, NP-aggregation operator, and many more.

Comments: 480 Pages.

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[v1] 2014-12-09 20:21:48
[v2] 2015-01-30 13:43:13

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