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A. A. Salama - One of the best experts on this subject based on the ideXlab platform.
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Semi-Compact and Semi-Lindelӧf Spaces via Neutrosophic Crisp Set Theory
viXra, 2018Co-Authors: A. A. Salama, I. M. Hanafy, M. S. DabashAbstract:The aim of this paper is devoted to introduce and study the concepts of semi-compact (resp.semi-Lindelӧf, locally semi-compact) spaces in a neutrosophic Crisp topological space. Several properties, functions properties of neutrosophic Crisp semi-compact spaces are studied. In addition to these, we introduce and study the definition of neutrosophic Crisp semi-Lindelӧf spaces and neutrosophic Crisp locally semi-compact spaces. We show that neutrosophic Crisp semi-compact spaces is preserved under neutrosophic Crisp irresolute function and neutrosophic Crisp pre-semi-closed function with neutrosophic Crisp semi-compact point inverses.
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Retract Neutrosophic Crisp System for Gray Scale Image
viXra, 2018Co-Authors: A. A. Salama, Hewayda ElghawalbyAbstract:In this paper, we aim to develop a new type of neutrosophic Crisp Set called the retract neutrosophic Crisp Set and shows a grayscale image in a 2D Cartesian domain with neutrosophic Crisp components in the neutrosophic domain. The introduced Set is a retraction of any triple structured Crisp Set. Whereas, the retractSet deduced from any neutrosophic Crisp Set is coincide its corresponding star neutrosophic Crisp Set defined in by Salama et al. [1]. Hence we construct a new type of neutrosophic Crisp topological spaces, called the retract neutrosophic Crisp topological space as a retraction of the star neutrosophic topological space. Moreover, we investigate some of its properties.
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Topological Manifold Space via Neutrosophic Crisp Set Theory
Neutrosophic Sets and Systems, 2017Co-Authors: A. A. Salama, Hewayda Elghawalby, Shimaa Fathi AliAbstract:In this paper, we introduce and study a neutrosophic Crisp manifold as a new topological structure of manifold via neutrosophic Crisp Set. Therefore, we studysome new topological concepts and some metric distances on a neutrosophic Crisp manifold.
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Ultra Neutrosophic Crisp Sets and Relations
viXra, 2016Co-Authors: Hewayda Elghawalby, A. A. SalamaAbstract:In this paper we present a new neutrosophic Crisp family generated from the three components’ neutrosophic Crisp Sets presented by Salama [4]. The idea behind Salam’s neutrosophic Crisp Set was to classify the elements of a universe of discourse with respect to an event ”A” into three classes: one class contains those elements that are fully supportive to A, another class contains those elements that totally against A, and a third class for those elements that stand in a distance from being with or against A. Our aim here is to study the elements of the universe of discourse which their existence is beyond the three classes of the neutrosophic Crisp Set given by Salama. By adding more components we will get a four components’ neutrosophic Crisp Sets called the Ultra Neutrosophic Crisp Sets. Four types of Set’s operations is defined and the properties of the new ultra neutrosophic Crisp Sets are studied. Moreover, a definition of the relation between two ultra neutrosophic Crisp Sets is given.
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Neutrosophic Crisp Probability Theory & Decision Making Process
viXra, 2016Co-Authors: A. A. Salama, Florentin SmarandacheAbstract:Since the world is full of indeterminacy, the neutrosophics found their place into contemporary research. In neutrosophic Set, indeterminacy is quantified explicitly and truth-membership, indeterminacy-membership and falsity-membership are independent. For that purpose, it is natural to adopt the value from the selected Set with highest degree of truth-membership, indeterminacy membership and least degree of falsity-membership on the decision Set. These factors indicate that a decision making process takes place in neutrosophic environment. In this paper, we introduce and study the probability of neutrosophic Crisp Sets. After giving the fundamental definitions and operations, we obtain several properties and discuss the relationship between them. These notions can help researchers and make great use in the future in making algorithms to solve problems and manage between these notions to produce a new application or new algorithm of solving decision support problems. Possible applications to mathematical computer sciences are touched upon. Keyword Neutrosophic Set, Neutrosophic probability, Neutrosophic Crisp Set, Intuitionistic neutrosophic Set.
Florentin Smarandache - One of the best experts on this subject based on the ideXlab platform.
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Entropy Measures for Plithogenic Sets and Applications in Multi-Attribute Decision Making
Mathematics, 2020Co-Authors: Shio Gai Quek, Florentin Smarandache, Ganeshsree Selvachandran, J. Vimala, Quang-thinh Bui, Vassilis C. GerogiannisAbstract:Plithogenic Set is an extension of the Crisp Set, fuzzy Set, intuitionistic fuzzy Set, and neutrosophic Sets, whose elements are characterized by one or more attributes, and each attribute can assume many values. Each attribute has a corresponding degree of appurtenance of the element to the Set with respect to the given criteria. In order to obtain a better accuracy and for a more exact exclusion (partial order), a contradiction or dissimilarity degree is defined between each attribute value and the dominant attribute value. In this paper, entropy measures for plithogenic Sets have been introduced. The requirements for any function to be an entropy measure of plithogenic Sets are outlined in the axiomatic definition of the plithogenic entropy using the axiomatic requirements of neutrosophic entropy. Several new formulae for the entropy measure of plithogenic Sets are also introduced. The newly introduced entropy measures are then applied to a multi-attribute decision making problem related to the selection of locations.
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Neutrosophic Crisp Probability Theory & Decision Making Process
viXra, 2016Co-Authors: A. A. Salama, Florentin SmarandacheAbstract:Since the world is full of indeterminacy, the neutrosophics found their place into contemporary research. In neutrosophic Set, indeterminacy is quantified explicitly and truth-membership, indeterminacy-membership and falsity-membership are independent. For that purpose, it is natural to adopt the value from the selected Set with highest degree of truth-membership, indeterminacy membership and least degree of falsity-membership on the decision Set. These factors indicate that a decision making process takes place in neutrosophic environment. In this paper, we introduce and study the probability of neutrosophic Crisp Sets. After giving the fundamental definitions and operations, we obtain several properties and discuss the relationship between them. These notions can help researchers and make great use in the future in making algorithms to solve problems and manage between these notions to produce a new application or new algorithm of solving decision support problems. Possible applications to mathematical computer sciences are touched upon. Keyword Neutrosophic Set, Neutrosophic probability, Neutrosophic Crisp Set, Intuitionistic neutrosophic Set.
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Neutrosophic Crisp Set Theory
viXra, 2015Co-Authors: A. A. Salama, Florentin SmarandacheAbstract:The purpose of this paper is to introduce new types of neutrosophic Crisp Sets with three types 1, 2, 3. After given the fundamental definitions and operations, we obtain several properties, and discussed the relation- ship between neutrosophic Crisp Sets and others. Also, we introduce and study the neutrosophic Crisp point and neu- trosophic Crisp relations. Possible applications to data- base are touched upon.
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Neutrosophic Crisp Set Theory
viXra, 2015Co-Authors: A. A. Salama, Florentin SmarandacheAbstract:In this book the authors introduce and study the following notions: Neutrosophic Crisp Points, Neutrosophic Crisp Relations, Neutrosophic Crisp Sets, Neutrosophic Set Generated by (Characteristic Function), α-cut Level for Neutrosophic Sets, Neutrosophic Crisp Continuous Function, Neutrosophic Crisp Compact Spaces, Neutrosophic Crisp Nearly Open Sets, Neutrosophic Crisp Ideals, Neutrosophic Crisp Filter, Neutrosophic Crisp Local Functions, Neutrosophic Crisp Sets via Neutrosophic Crisp Ideals, Neutrosophic Crisp L-Openness and Neutrosophic Crisp L-Continuity, Neutrosophic Topological Region, Neutrosophic Closed Set and Neutrosophic Continuous Function, etc. They compute the distances between neutrosophic Sets and extend it to Neutrosophic Hesitancy Degree. The authors also generalize the Crisp Topological Space and Intuitionistic Topological Space to the notion of Neutrosophic Crisp Topological Space. At the end, they present applications to Neutrosophic Database, and show a security scheme based on Public Key Infrastructure (PKI) using Neutrosophic Logic Manipulation. The authors utilize neutrosophic Sets in order to analyze social networks data conducted through learning activities, and for the Geographical Information Systems (GIS) they employ fundamental concepts and properties of a Neutrosophic Spatial Region.
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Neutrosophic Crisp Open Set and Neutrosophic Crisp Continuity via Neutrosophic Crisp Ideals
viXra, 2014Co-Authors: A. A. Salama, Said Broumi, Florentin SmarandacheAbstract:The focus of this paper is to propose a new notion of neutrosophic Crisp Sets via neutrosophic Crisp ideals and to study some basic operations and results in neutrosophic Crisp topological spaces. Also, neutrosophic Crisp L-openness and neutrosophic Crisp Lcontinuity are considered as a generalizations for a Crisp and fuzzy concepts. Relationships between the above new neutrosophic Crisp notions and the other relevant classes are investigated. Finally, we define and study two different types of neutrosophic Crisp functions. Index Terms—Neutrosophic Crisp Set; Neutrosophic Crisp Ideals; Neutrosophic Crisp L-open Sets; Neutrosophic Crisp L- Continuity; Neutrosophic Sets. I. INTRODUCTION The fuzzy Set was introduced by Zadeh [20] in 1965, where each element had a degree of membership. In 1983 the intuitionstic fuzzy Set was introduced by K. Atanassov [1, 2, 3] as a generalization of fuzzy Set, where besides the degree of membership and the degree of non- membership of each element. Salama et al [11] defined intuitionistic fuzzy ideal and neutrosophic ideal for a Set and generalized the concept of fuzzy ideal concepts, first initiated by Sarker [19]. Smarandache [16, 17, 18] defined the notion of neutrosophic Sets, which is a generalization of Zadeh's fuzzy Set and Atanassov's intuitionistic fuzzy Set. Neutrosophic Sets have been investigated by Salama et al. [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]. In this paper is to introduce and study some new neutrosophic Crisp notions via neutrosophic Crisp ideals. Also, neutrosophic Crisp L-openness and neutrosophic Crisp L- continuity are considered. Relationships between the above new neutrosophic Crisp notions and the other relevant classes are investigated. Recently, we define and study two different types of neutrosophic Crisp functions. The paper unfolds as follows. The next section briefly introduces some definitions related to neutrosophic Set theory and some terminologies of neutrosophic Crisp Set and neutrosophic Crisp ideal. Section 3 presents neutrosophic Crisp L- open and neutrosophic Crisp Lclosed Sets. Section 4 presents neutrosophic Crisp L– continuous functions. Conclusions appear in the last section.
Hewayda Elghawalby - One of the best experts on this subject based on the ideXlab platform.
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Retract Neutrosophic Crisp System for Gray Scale Image
viXra, 2018Co-Authors: A. A. Salama, Hewayda ElghawalbyAbstract:In this paper, we aim to develop a new type of neutrosophic Crisp Set called the retract neutrosophic Crisp Set and shows a grayscale image in a 2D Cartesian domain with neutrosophic Crisp components in the neutrosophic domain. The introduced Set is a retraction of any triple structured Crisp Set. Whereas, the retractSet deduced from any neutrosophic Crisp Set is coincide its corresponding star neutrosophic Crisp Set defined in by Salama et al. [1]. Hence we construct a new type of neutrosophic Crisp topological spaces, called the retract neutrosophic Crisp topological space as a retraction of the star neutrosophic topological space. Moreover, we investigate some of its properties.
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Topological Manifold Space via Neutrosophic Crisp Set Theory
Neutrosophic Sets and Systems, 2017Co-Authors: A. A. Salama, Hewayda Elghawalby, Shimaa Fathi AliAbstract:In this paper, we introduce and study a neutrosophic Crisp manifold as a new topological structure of manifold via neutrosophic Crisp Set. Therefore, we studysome new topological concepts and some metric distances on a neutrosophic Crisp manifold.
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Ultra Neutrosophic Crisp Sets and Relations
viXra, 2016Co-Authors: Hewayda Elghawalby, A. A. SalamaAbstract:In this paper we present a new neutrosophic Crisp family generated from the three components’ neutrosophic Crisp Sets presented by Salama [4]. The idea behind Salam’s neutrosophic Crisp Set was to classify the elements of a universe of discourse with respect to an event ”A” into three classes: one class contains those elements that are fully supportive to A, another class contains those elements that totally against A, and a third class for those elements that stand in a distance from being with or against A. Our aim here is to study the elements of the universe of discourse which their existence is beyond the three classes of the neutrosophic Crisp Set given by Salama. By adding more components we will get a four components’ neutrosophic Crisp Sets called the Ultra Neutrosophic Crisp Sets. Four types of Set’s operations is defined and the properties of the new ultra neutrosophic Crisp Sets are studied. Moreover, a definition of the relation between two ultra neutrosophic Crisp Sets is given.
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neutrosophic Crisp Set neutrosophic Crisp relations
Neutrosophic Sets and Systems, 2014Co-Authors: A. A. Salama, Hewayda ElghawalbyAbstract:Since the world is full of indeterminacy, the neutro- sophics found their place into contemporary research. The pur- pose of this paper is to introduce a new type of neutrosophic Crisp Set as the *- neutrosophic Crisp Sets as a generalization to star intuitionistic Set due to Indira et al.(4 ), and study some of its properties. Finally we introduce and study the notion of *- neutrosophic relation and some of its properties. .
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*- Neutrosophic Crisp Set & relations
Neutrosophic Sets and Systems, 2014Co-Authors: A. A. Salama, Hewayda ElghawalbyAbstract:In a world full of indeterminacy, traditional Crisp Set with its boundaries of truth and false has not infused it- self with the ability of reflecting the reality. Therefore, neutrosophic found its place into contemporary research as an alternative representation of the real world. In this pa- per, we aim to develop a new type of neutrosophic Crisp Sets called the *-Neutrosophic Crisp Sets as a generaliza- tion of the star intuitionistic Set introduced by Indira et al.(4) , and hence studying some of its properties . To this end we will investigate the notion of *-Neutrosophic rela- tion and some of its properties. .
Axel Marx - One of the best experts on this subject based on the ideXlab platform.
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Crisp-Set Qualitative Comparative Analysis in Organizational Studies
Research in the Sociology of Organizations, 2013Co-Authors: Axel Marx, Bart Cambré, Benoît RihouxAbstract:Qualitative Comparative Analysis (QCA), initiated by Charles C. Ragin, is a research strategy with distinctive added value for organization studies. QCA constitutes in essence two configurational approaches, each grounded in Set theory. One approach uses Crisp-Sets (dichotomous variables) to analyze cases. The other approach uses fuzzy-Sets. While the use of fuzzy-Sets has been increasing over the last few years, the Crisp-Set (csQCA) approach is still used in a majority of empirical applications. This chapter discusses in-depth the application of csQCA in organization studies. This chapter starts with a stylized presentation of two dominant research strategies, case-based research and variable-based research, and how csQCA relates to them. Subsequently, csQCA is further introduced and the different applications in organization studies are discussed. This section ends with a brief step-wise “how to” presentation. The chapter then turns to a presentation of the main distinctive strengths of the approach. In the final part, the chapter discusses extensively the main criticisms which have been raised with regard to (cs)QCA and draws out some of the main implications of this discussion.
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Crisp-Set Qualitative Comparative Analysis (csQCA), Contradictions and Consistency Benchmarks for Model Specification:
Methodological Innovations Online, 2011Co-Authors: Axel Marx, Adrian DuşaAbstract:The purpose of this paper is to address and test two assumptions on which csQCA is based, namely that csQCA will generate contradictions and low consistency scores if models are ill-specified. The first part of the paper introduces csQCA in general and as a stepwise approach. In a second part a real-life example is introduced with the purpose of illustrating how csQCA operates and as an input for a simulation in the subsequent part. The third part introduces contradictions, consistency, their interrelatedness and the assumptions which are made with regard to contradictions and consistency. Subsequently the assumptions are tested via a simulation on the basis of a csQCA analysis of over 5 million random dataSets. The paper argues that researchers cannot always assume that csQCA will generate contradictions or low consistency scores when models are ill-specified. Such an assumption is only justified when csQCA applications take limitations with regard to model specification (the number of conditions and the number of cases) into account. Benchmark tables for model specification purposes are developed. Since these tables are based on a probability value of 0.5 the paper also tests the results for contradictions and consistency for the probabilities which were present in a real-life example. This test shows that the 0.5 probability generates an appropriate measure for the occurrence of contradictions and consistency indicating that the benchmark tables can be used for different applications with different distributions of 0's and 1's in the conditions and outcomes. The paper ends with a conclusion.
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Crisp-Set Qualitative Comparative Analysis (csQCA) and Model Specification: Benchmarks for Future csQCA Applications
International Journal of Multiple Research Approaches, 2010Co-Authors: Axel MarxAbstract:Crisp-Set qualitative comparative analysis (csQCA), a research approach developed by Charles Ragin in the 1980s, aims to combine qualitative and quantitative research strategies. Applications of the method have appeared in numerous journals. Recently, csQCA has been criticized concerning the validity of the models it generates as a result of the fact that it is unable to distinguish real from random data. It is argued that csQCA always identifies an explanatory model, even on the basis of random data. The paper addresses this hypothesis via a simulation. It uses randomly created datamatrices to show that csQCA can make a distinction between real and random data when model specification parameters are taken into account. First of all, the proportion of explanatory conditions on cases should be below a certain threshold, which differs as a function of the combination of conditions on cases. Secondly, there is an upper-limit to the number of explanatory conditions which can be used in a csQCA-analysis. The importance of the design parameters are the result of the problem of uniqueness which is a consequence of the use of Boolean algebra. Five implications for comparative case research-design and csQCA are discussed.
Benoît Rihoux - One of the best experts on this subject based on the ideXlab platform.
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Crisp-Set Qualitative Comparative Analysis in Organizational Studies
Research in the Sociology of Organizations, 2013Co-Authors: Axel Marx, Bart Cambré, Benoît RihouxAbstract:Qualitative Comparative Analysis (QCA), initiated by Charles C. Ragin, is a research strategy with distinctive added value for organization studies. QCA constitutes in essence two configurational approaches, each grounded in Set theory. One approach uses Crisp-Sets (dichotomous variables) to analyze cases. The other approach uses fuzzy-Sets. While the use of fuzzy-Sets has been increasing over the last few years, the Crisp-Set (csQCA) approach is still used in a majority of empirical applications. This chapter discusses in-depth the application of csQCA in organization studies. This chapter starts with a stylized presentation of two dominant research strategies, case-based research and variable-based research, and how csQCA relates to them. Subsequently, csQCA is further introduced and the different applications in organization studies are discussed. This section ends with a brief step-wise “how to” presentation. The chapter then turns to a presentation of the main distinctive strengths of the approach. In the final part, the chapter discusses extensively the main criticisms which have been raised with regard to (cs)QCA and draws out some of the main implications of this discussion.
