Author
I. M. Hanafy
Other affiliations: Suez Canal University
Bio: I. M. Hanafy is an academic researcher from Port Said University. The author has contributed to research in topics: Topological space & Fuzzy logic. The author has an hindex of 9, co-authored 26 publications receiving 327 citations. Previous affiliations of I. M. Hanafy include Suez Canal University.
Papers
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01 Jan 2012
TL;DR: The purpose of this paper is to introduce a new type of data called the neutrosophic data, and obtain several properties, and discussed the relationship between neutrosophile sets and others.
Abstract: Neutrosophy has been introduced by Smarandache [3, 4] as a new branch of philosophy. Salama et al. [5] in 2012 introduced and studied the operations on neutrosophic sets. The purpose of this paper is to introduce a new type of data called the neutrosophic data. After given the fundamental definitions of neutrosophic set operations due to Salama [5], we obtain several properties, and discussed the relationship between neutrosophic sets and others. Finally, we discuss and derived a fomula for correlation coefficient, defined on the domain of neutrosophic sets.
109 citations
DOI•
01 Jan 2013
TL;DR: In this article, a method to calculate the correlation coefficient of neutrosophic sets is proposed. But the method is not suitable for the measurement of the strength of relationship between the sets and the whether the two sets are positively or negatively related.
Abstract: In this paper, we propose another method to calculate the correlation coefficient of neutrosophic sets. The value which obtained fro m this method tells us the strength of relationship between the neutrosophic sets and the whether the neutrosophic sets are positively or negatively related. Finally we g ive some proposition and examples.
54 citations
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TL;DR: The classical probability is generalized to the notion of neutrosophic probability, necessary because it provides a better representation than classical probability to uncertain events.
Abstract: In this paper we introduce a new type of classical set called the neutrosophic classical set. After given the fundamental definitions of neutrosophic classical set operations, we obtain several properties, and discussed the relationship between neutrosophic classical sets and others. Finally, we generalize the classical probability to the notion of neutrosophic probability. This kind of probability is necessary because it provides a better representation than classical probability to uncertain events. Possible applications to computer sciences are touched upon.
37 citations
TL;DR: This paper introduces and study the concept of fuzzy completely continuous functions between intuitionistic fuzzy topological spaces.
Abstract: In this paper, after giving the basic results related to the product of functions and the graph of functions in intuitionistic fuzzy topological spaces, we introduce and study the concept of fuzzy completely continuous functions between intuitionistic fuzzy topological spaces.
36 citations
TL;DR: The value obtained from the "centroid" method tell us the strength of relationship between the generalized intuitionistic fuzzy sets and the whether the generalized intuitional fuzzy sets are positively or negatively related.
Abstract: In this paper, we propose a method to calculate the correlation coefficient of generalized intuitionistic fuzzy sets by means of \"centroid\". The value which obtained from this method tell us the strength of relationship between the generalized intuitionistic fuzzy sets [11] and the whether the generalized intuitionistic fuzzy sets are positively or negatively related. This method looks better than previous methods which only evaluated the strength of relation. Furthermore, we extended the \"centroid\" method to interval-valued generalized intuitionistic fuzzy sets. The value of the correlation coefficient between interval-valued generalized intuitionistic fuzzy sets lies in the interval [-1, 1], as computed from our formula.
13 citations
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TL;DR: The originality and value of IFT are here demonstrated, which show that the results obtained by various authors on intuitionistic fuzzy topological spaces (IFTSs), are not redundant with others for the ordinary fuzzy sense.
Abstract: Purpose – In 2000, Wang and He published an important result on the theory of intuitionistic fuzzy sets (IFSs) Indeed, they showed that every IFS may be regarded as an L‐fuzzy set for some appropriate lattice L This paper aims to show that, nevertheless, the results obtained by various authors on intuitionistic fuzzy topological spaces (IFTSs), are not redundant with others for the ordinary fuzzy senseDesign/methodology/approach – The most important definitions and results on intuitionistic fuzzy topology (IFT) one compared with the result obtained by Wang and HeFindings – That these results are not redundantResearch limitations/implications – Clearly, this paper is devoted to IFTSsPractical implications – The main applications are in the mathematical fieldOriginality/value – The originality and value of IFT are here demonstrated
161 citations
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TL;DR: In this article, the concept of correlation coefficients of interval valued neutrosophic set (INS) was introduced for the first time, and the first numerical examples are presented in the paper.
Abstract: In this paper we introduce for the first time the concept of correlation coefficients of interval valued neutrosophic set (INS for short). Respective numerical examples are presented.
156 citations
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TL;DR: The dominancy of complex neutrosophic set to all current methods through the graph is showed, and the drawbacks and failure of the current methods are shown.
Abstract: Complex fuzzy sets and complex intuitionistic fuzzy sets cannot handle imprecise, indeterminate, inconsistent, and incomplete information of periodic nature. To overcome this difficulty, we introduce complex neutrosophic set.
154 citations
TL;DR: An overview on neutrosophic set is presented with the aim of offering a clear perspective on the different concepts, tools and trends related to their extensions and indicates that some developing economics (such as China, India, Turkey) are quite active in neutrosophile set research.
Abstract: Neutrosophic set, initiated by Smarandache, is a novel tool to deal with vagueness considering the truth-membership T, indeterminacy-membership I and falsity-membership F satisfying the condition $$0\le T+I+F\le 3$$. It can be used to characterize the uncertain information more sufficiently and accurately than intuitionistic fuzzy set. Neutrosophic set has attracted great attention of many scholars that have been extended to new types and these extensions have been used in many areas such as aggregation operators, decision making, image processing, information measures, graph and algebraic structures. Because of such a growth, we present an overview on neutrosophic set with the aim of offering a clear perspective on the different concepts, tools and trends related to their extensions. A total of 137 neutrosophic set publication records from Web of Science are analyzed. Many interesting results with regard to the annual trends, the top players in terms of country level as well as institutional level, the publishing journals, the highly cited papers, and the research landscape are yielded and explained in-depth. The results indicate that some developing economics (such as China, India, Turkey) are quite active in neutrosophic set research. Moreover, the co-authorship analysis of the country and institution, the co-citation analysis of the journal, reference and author, and the co-occurrence analysis of the keywords are presented by VOSviewer software.
150 citations
TL;DR: In this paper, the concept of correlation coefficients of interval valued neutrosophic set (INS) was introduced for the first time, and the first numerical examples are presented in the paper.
Abstract: In this paper we introduce for the first time the concept of correlation coefficients of interval valued neutrosophic set (INS for short). Respective numerical examples are presented.
141 citations