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As a powerful approach to data reasoning, rough set theory has proven to be invaluable in knowledge acquisition, decision analysis and forecasting, and knowledge discovery. With the ability to enhance the advantages of other soft technology theories, hybrid rough set theory is quickly emerging as a method of choice for decision making under uncerta
Book Synopsis Hybrid Rough Sets and Applications in Uncertain Decision-Making by : Lirong Jian
Download or read book Hybrid Rough Sets and Applications in Uncertain Decision-Making written by Lirong Jian and published by CRC Press. This book was released on 2010-09-07 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: As a powerful approach to data reasoning, rough set theory has proven to be invaluable in knowledge acquisition, decision analysis and forecasting, and knowledge discovery. With the ability to enhance the advantages of other soft technology theories, hybrid rough set theory is quickly emerging as a method of choice for decision making under uncerta
This book offers a timely overview of fuzzy and rough set theories and methods. Based on selected contributions presented at the International Symposium on Fuzzy and Rough Sets, ISFUROS 2017, held in Varadero, Cuba, on October 24-26, 2017, the book also covers related approaches, such as hybrid rough-fuzzy sets and hybrid fuzzy-rough sets and granular computing, as well as a number of applications, from big data analytics, to business intelligence, security, robotics, logistics, wireless sensor networks and many more. It is intended as a source of inspiration for PhD students and researchers in the field, fostering not only new ideas but also collaboration between young researchers and institutions and established ones.
Book Synopsis Uncertainty Management with Fuzzy and Rough Sets by : Rafael Bello
Download or read book Uncertainty Management with Fuzzy and Rough Sets written by Rafael Bello and published by Springer. This book was released on 2019-01-22 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a timely overview of fuzzy and rough set theories and methods. Based on selected contributions presented at the International Symposium on Fuzzy and Rough Sets, ISFUROS 2017, held in Varadero, Cuba, on October 24-26, 2017, the book also covers related approaches, such as hybrid rough-fuzzy sets and hybrid fuzzy-rough sets and granular computing, as well as a number of applications, from big data analytics, to business intelligence, security, robotics, logistics, wireless sensor networks and many more. It is intended as a source of inspiration for PhD students and researchers in the field, fostering not only new ideas but also collaboration between young researchers and institutions and established ones.
Book Synopsis Decision Making Under Uncertainty by :
Download or read book Decision Making Under Uncertainty written by and published by . This book was released on 2015 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt:
+e single-valued neutrosophic set (SVNS) can not only depict imperfect information in the real decision system but also handle undetermined and inconformity information flexibly and effectively. +ree-way decisions (3WDs) are often used as an effective method to deal with uncertainties, but the conditional probability is given by the decision maker subjectively, which makes the decision result too subjective. +is paper proposes a novel model based on 3WDs to settle the multiattribute decision-making (MADM) problems, where the attribute values are described by SVNS, and the attribute weights are entirely unknown. At first, we build a single-valued neutrosophic decision theory rough set (SVNDTRS) model based on Bayesian decision process. +en, we use the analytic hierarchy process (AHP) approach to calculate the subjective weight of each attribute, the information entropy to obtain the attribute’s objective weight, and the minimum total deviation approach to determine the combined weight of the attributes. After obtaining the standard weight, the grey relational analysis (GRA) method is utilized to calculate the grey correlation closeness with the ideal solution, and the conditional probability is estimated by it. In addition, we develop a decisionmaking method in view of the ideal solution of 3WDs with the SVNS. +is approach not only considers the lowest cost but also gives a corresponding semantic explanation for the decision result of each alternative, which can supplement the decision results of GRA. At last, we illustrate the feasibility and effectiveness of 3WDs through an example of supplier selection and compare it with other methods to verify the advantages of our approach.
Book Synopsis Three-Way Decisions with Single-Valued Neutrosophic Decision Theory Rough Sets Based on Grey Relational Analysis by : Peide Liu
Download or read book Three-Way Decisions with Single-Valued Neutrosophic Decision Theory Rough Sets Based on Grey Relational Analysis written by Peide Liu and published by Infinite Study. This book was released on with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt: +e single-valued neutrosophic set (SVNS) can not only depict imperfect information in the real decision system but also handle undetermined and inconformity information flexibly and effectively. +ree-way decisions (3WDs) are often used as an effective method to deal with uncertainties, but the conditional probability is given by the decision maker subjectively, which makes the decision result too subjective. +is paper proposes a novel model based on 3WDs to settle the multiattribute decision-making (MADM) problems, where the attribute values are described by SVNS, and the attribute weights are entirely unknown. At first, we build a single-valued neutrosophic decision theory rough set (SVNDTRS) model based on Bayesian decision process. +en, we use the analytic hierarchy process (AHP) approach to calculate the subjective weight of each attribute, the information entropy to obtain the attribute’s objective weight, and the minimum total deviation approach to determine the combined weight of the attributes. After obtaining the standard weight, the grey relational analysis (GRA) method is utilized to calculate the grey correlation closeness with the ideal solution, and the conditional probability is estimated by it. In addition, we develop a decisionmaking method in view of the ideal solution of 3WDs with the SVNS. +is approach not only considers the lowest cost but also gives a corresponding semantic explanation for the decision result of each alternative, which can supplement the decision results of GRA. At last, we illustrate the feasibility and effectiveness of 3WDs through an example of supplier selection and compare it with other methods to verify the advantages of our approach.
This volume is composed of selected papers from two conferences held in Warsaw, Poland on October 13-15, 2022: the BOS/SOR’2022 - National Conference on Operational and Systems Research, one of premiere conferences in the field of operational and systems research, and the Twentith International Workshop on Intuitionistic Fuzzy Sets and Generalized Nets, IWIFSGN-2022, one of premiere conferences on fuzzy logic, notably on extensions of the traditional fuzzy sets, also comprising a considerable part on the Generalized Nets (GNs). A joint publication of selected papers from the two conferences follows a long tradition of such a joint organization, and – from a substantial point of view – combines systems modeling, systems analysis, broadly perceived operational research, notably optimization, decision making and decision support, with various aspects of uncertain and imprecise information and their related tools and techniques.
Book Synopsis Uncertainty and Imprecision in Decision Making and Decision Support - New Advances, Challenges, and Perspectives by : Krassimir T. Atanassov
Download or read book Uncertainty and Imprecision in Decision Making and Decision Support - New Advances, Challenges, and Perspectives written by Krassimir T. Atanassov and published by Springer Nature. This book was released on 2023-10-20 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is composed of selected papers from two conferences held in Warsaw, Poland on October 13-15, 2022: the BOS/SOR’2022 - National Conference on Operational and Systems Research, one of premiere conferences in the field of operational and systems research, and the Twentith International Workshop on Intuitionistic Fuzzy Sets and Generalized Nets, IWIFSGN-2022, one of premiere conferences on fuzzy logic, notably on extensions of the traditional fuzzy sets, also comprising a considerable part on the Generalized Nets (GNs). A joint publication of selected papers from the two conferences follows a long tradition of such a joint organization, and – from a substantial point of view – combines systems modeling, systems analysis, broadly perceived operational research, notably optimization, decision making and decision support, with various aspects of uncertain and imprecise information and their related tools and techniques.
This book offers a timely overview of fuzzy and rough set theories and methods. Based on selected contributions presented at the International Symposium on Fuzzy and Rough Sets, ISFUROS 2017, held in Varadero, Cuba, on October 24-26, 2017, the book also covers related approaches, such as hybrid rough-fuzzy sets and hybrid fuzzy-rough sets and granular computing, as well as a number of applications, from big data analytics, to business intelligence, security, robotics, logistics, wireless sensor networks and many more. It is intended as a source of inspiration for PhD students and researchers in the field, fostering not only new ideas but also collaboration between young researchers and institutions and established ones.
Book Synopsis Uncertainty Management with Fuzzy and Rough Sets by : Rafael Bello
Download or read book Uncertainty Management with Fuzzy and Rough Sets written by Rafael Bello and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a timely overview of fuzzy and rough set theories and methods. Based on selected contributions presented at the International Symposium on Fuzzy and Rough Sets, ISFUROS 2017, held in Varadero, Cuba, on October 24-26, 2017, the book also covers related approaches, such as hybrid rough-fuzzy sets and hybrid fuzzy-rough sets and granular computing, as well as a number of applications, from big data analytics, to business intelligence, security, robotics, logistics, wireless sensor networks and many more. It is intended as a source of inspiration for PhD students and researchers in the field, fostering not only new ideas but also collaboration between young researchers and institutions and established ones.
The primary objective of any supervised learning technique is to learn an unknown function (or at least a good approximation of it) from a set of observed input-output patterns. Pattern classification is a special case of function approximation, where each pattern is assigned to a particular class, i.e., the output in classification problem is one of the discrete values corresponding to class rather than real-valued function in regression. Precisely, in a classification problem output belongs to one of the discrete classes, while in a regression problem output belongs to a set of real number R. This book discuss various fuzzy-rough approach to pattern classification, and develops some hybrid measures and algorithms for attribute (or feature) selection and induction of fuzzy decision trees. Hybrid fuzzy-rough algorithms derive best benefits of both the worlds; fuzzy systems and rough sets theory. Fuzzy systems are well known for their ability to handle vagueness in the data. On the other hand, rough sets are pure data driven knowledge discovery tools capable of handling ambiguity very well by various approximations. In general, vagueness is related to the difficulty in making sharp classification boundaries. Ambiguity is associated with one-to-many mapping. This book develops feature selection and pattern classification models which take care of these two inherent problems associated with knowledge discovery from data. Many interesting properties of the developed fuzzy-rough measures are derived and their importance from pattern classification view point is shown. Later it is shown that how neural type of learning algorithms can be integrated in fuzzy decision tree induction technique to improve their learning accuracy. Neural learning is introduced by two ways; first by transforming fuzzy decision tree structure in the equivalent Gaussian radial basis function (RBF) structure and second by directly applying back-propagation gradient descent learning algorithm on the structure of fuzzy decision trees. Former technique provide a novel solution for initialization of structure and parameters of Gaussian RBF network and later technique build novel neuro-fuzzy models known as Neuro-Fuzzy Decision Trees. It is shown that how fuzzy decision trees are functionally equivalent to Gaussian RBF networks and this equivalence is used to establish a mapping from one fuzzy decision trees to Gaussian RBF networks and vice versa. Such mappings allow applying various gradient descent type of learning algorithms to the mapped Gaussian RBF network structure and improve classification accuracy of the model. It is shown that how fuzzy decision trees' classification accuracy is improved after mapping to Gaussian RBF network and how the structure of fuzzy decision trees are changing after mapping back from Gaussian RBF network structure. This leads to an interesting discussion about destructive and non-destructive type of learning algorithms. Later it is shown that how Neuro-fuzzy decision trees are keeping the structure of fuzzy decision trees intact and still improve their learning accuracy. All the proposed algorithms have been stated explicitly in the formal notation and in pseudo code format. Extensive computational experiments have been reported and the proposed algorithms have been experimentally compared with well-known algorithms from the literature using real-world standard datasets. Readers will also find literature review of rough sets and fuzzy decision trees very useful, especially classification of fuzzy decision tree literature in six different categories, rough sets fundamentals and applications of fuzzy decision trees and rough sets theory in many domains.
Book Synopsis Fuzzy-Rough Approaches for Pattern Classification by : Rajen Bhatt
Download or read book Fuzzy-Rough Approaches for Pattern Classification written by Rajen Bhatt and published by . This book was released on 2017-08-29 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: The primary objective of any supervised learning technique is to learn an unknown function (or at least a good approximation of it) from a set of observed input-output patterns. Pattern classification is a special case of function approximation, where each pattern is assigned to a particular class, i.e., the output in classification problem is one of the discrete values corresponding to class rather than real-valued function in regression. Precisely, in a classification problem output belongs to one of the discrete classes, while in a regression problem output belongs to a set of real number R. This book discuss various fuzzy-rough approach to pattern classification, and develops some hybrid measures and algorithms for attribute (or feature) selection and induction of fuzzy decision trees. Hybrid fuzzy-rough algorithms derive best benefits of both the worlds; fuzzy systems and rough sets theory. Fuzzy systems are well known for their ability to handle vagueness in the data. On the other hand, rough sets are pure data driven knowledge discovery tools capable of handling ambiguity very well by various approximations. In general, vagueness is related to the difficulty in making sharp classification boundaries. Ambiguity is associated with one-to-many mapping. This book develops feature selection and pattern classification models which take care of these two inherent problems associated with knowledge discovery from data. Many interesting properties of the developed fuzzy-rough measures are derived and their importance from pattern classification view point is shown. Later it is shown that how neural type of learning algorithms can be integrated in fuzzy decision tree induction technique to improve their learning accuracy. Neural learning is introduced by two ways; first by transforming fuzzy decision tree structure in the equivalent Gaussian radial basis function (RBF) structure and second by directly applying back-propagation gradient descent learning algorithm on the structure of fuzzy decision trees. Former technique provide a novel solution for initialization of structure and parameters of Gaussian RBF network and later technique build novel neuro-fuzzy models known as Neuro-Fuzzy Decision Trees. It is shown that how fuzzy decision trees are functionally equivalent to Gaussian RBF networks and this equivalence is used to establish a mapping from one fuzzy decision trees to Gaussian RBF networks and vice versa. Such mappings allow applying various gradient descent type of learning algorithms to the mapped Gaussian RBF network structure and improve classification accuracy of the model. It is shown that how fuzzy decision trees' classification accuracy is improved after mapping to Gaussian RBF network and how the structure of fuzzy decision trees are changing after mapping back from Gaussian RBF network structure. This leads to an interesting discussion about destructive and non-destructive type of learning algorithms. Later it is shown that how Neuro-fuzzy decision trees are keeping the structure of fuzzy decision trees intact and still improve their learning accuracy. All the proposed algorithms have been stated explicitly in the formal notation and in pseudo code format. Extensive computational experiments have been reported and the proposed algorithms have been experimentally compared with well-known algorithms from the literature using real-world standard datasets. Readers will also find literature review of rough sets and fuzzy decision trees very useful, especially classification of fuzzy decision tree literature in six different categories, rough sets fundamentals and applications of fuzzy decision trees and rough sets theory in many domains.
Multi-attribute decision-making (MADM) is a part of management decision-making and an important branch of the modern decision theory and method. MADM focuses on the decision problem of discrete and finite decision schemes. Uncertain MADM is an extension and development of classical multi-attribute decision making theory. When the attribute value of MADM is shown by neutrosophic number, that is, the attribute value is complex data and needs three values to express, it is called the MADM problem in which the attribute values are neutrosophic numbers. However, in practical MADM problems, to minimize errors in individual decision making, we need to consider the ideas of many people and synthesize their opinions.
Book Synopsis Non-Dual Multi-Granulation Neutrosophic Rough Set with Applications by : Chunxin Bo
Download or read book Non-Dual Multi-Granulation Neutrosophic Rough Set with Applications written by Chunxin Bo and published by Infinite Study. This book was released on with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multi-attribute decision-making (MADM) is a part of management decision-making and an important branch of the modern decision theory and method. MADM focuses on the decision problem of discrete and finite decision schemes. Uncertain MADM is an extension and development of classical multi-attribute decision making theory. When the attribute value of MADM is shown by neutrosophic number, that is, the attribute value is complex data and needs three values to express, it is called the MADM problem in which the attribute values are neutrosophic numbers. However, in practical MADM problems, to minimize errors in individual decision making, we need to consider the ideas of many people and synthesize their opinions.
In this paper, to combine single valued neutrosophic sets (SVNSs) with covering-based rough sets, we propose two types of single valued neutrosophic (SVN) covering rough set models. Furthermore, a corresponding application to the problem of decision making is presented.
Book Synopsis Two Types of Single Valued Neutrosophic Covering Rough Sets and an Application to Decision Making by : Jingqian Wang
Download or read book Two Types of Single Valued Neutrosophic Covering Rough Sets and an Application to Decision Making written by Jingqian Wang and published by Infinite Study. This book was released on with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, to combine single valued neutrosophic sets (SVNSs) with covering-based rough sets, we propose two types of single valued neutrosophic (SVN) covering rough set models. Furthermore, a corresponding application to the problem of decision making is presented.
Rough set theory and neutrosophic set theory are mathematical models to deal with incomplete and vague information.
Book Synopsis Decision-Making Approach Based on Neutrosophic Rough Information by : Muhammad Akram
Download or read book Decision-Making Approach Based on Neutrosophic Rough Information written by Muhammad Akram and published by Infinite Study. This book was released on with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rough set theory and neutrosophic set theory are mathematical models to deal with incomplete and vague information.
