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Generalized Rough Sets

Hybrid Structure and Applications

  • Book
  • © 2015

Overview

Authors:
  1. Anjan Mukherjee

    1. Department of Mathematics, Tripura University, Agartala, India

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  • Introduces the concept of "generalized interval valued intuitionistic fuzzy soft sets"
  • Details concept of interval valued intuitionistic fuzzy sets of type 2
  • Discusses all hybrid structures of fuzzy set, rough set and soft set
  • Includes supplementary material: sn.pub/extras

Part of the book series: Studies in Fuzziness and Soft Computing (STUDFUZZ, volume 324)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xiii
    Download chapter PDF

  2. Introduction to Fuzzy Sets, Rough Sets, and Soft Sets

    • Anjan Mukherjee
    Pages 1-22

  3. On Generalised Interval-Valued Intuitionistic Fuzzy Soft Sets

    • Anjan Mukherjee
    Pages 23-30

  4. Soft Rough Intuitionistic Fuzzy Sets

    • Anjan Mukherjee
    Pages 31-36

  5. Interval-Valued Intuitionistic Fuzzy Soft Rough Sets

    • Anjan Mukherjee
    Pages 37-48

  6. Interval-Valued Intuitionistic Fuzzy Soft Topological Spaces

    • Anjan Mukherjee
    Pages 49-65

  7. Interval-Valued Intuitionistic Fuzzy Soft Multi-Sets and Their Relations

    • Anjan Mukherjee
    Pages 67-87

  8. Interval-Valued Neutrosophic Soft Sets

    • Anjan Mukherjee
    Pages 89-109

  9. Topological Structure Formed by Soft Multi-Sets and Soft Multi-Compact Spaces

    • Anjan Mukherjee
    Pages 111-129

  10. Soft Interval-Valued Intuitionistic Fuzzy Rough Sets

    • Anjan Mukherjee
    Pages 131-149

  11. IF Parameterised Intuitionistic Fuzzy Soft Set Theories on Decisions-Making

    • Anjan Mukherjee
    Pages 151-157

  12. Back Matter

    Pages 159-160
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Keywords

About this book

The book introduces the concept of “generalized interval valued intuitionistic fuzzy soft sets”. It presents the basic properties of these sets and also, investigates an application of generalized interval valued intuitionistic fuzzy soft sets in decision making with respect to interval of degree of preference. The concept of “interval valued intuitionistic fuzzy soft rough sets” is discussed and interval valued intuitionistic fuzzy soft rough set based multi criteria group decision making scheme is presented, which refines the primary evaluation of the whole expert group and enables us to select the optimal object in a most reliable manner. The book also details concept of interval valued intuitionistic fuzzy sets of type 2. It presents the basic properties of these sets. The book also introduces the concept of “interval valued intuitionistic fuzzy soft topological space (IVIFS topological space)” together with intuitionistic fuzzy soft open sets (IVIFS open sets) and intuitionistic fuzzy soft closed sets (IVIFS closed sets).

Reviews

“This book is designed for researchers and students working in the field of fuzzy sets, rough sets, soft sets, and their hybrid models. It introduces the concept and basic properties of generalized interval-valued intuitionistic fuzzy soft sets.” (Bijan Davvaz, Mathematical Reviews, January, 2016)

Authors and Affiliations

  • Department of Mathematics, Tripura University, Agartala, India

    Anjan Mukherjee

About the author

Prof. Anjan Mukherjee is Pro Vice-Chancellor of Tripura University. He has completed his B.Sc. and M.Sc. in Mathematics from University of Calcutta and obtained his Ph.D. from Tripura University. Dr. Mukherjee has 26 years of vast experience in research and teaching. He has published more than 150 research papers in different national and international journals and conference proceedings and has delivered several invited talks. Dr. Mukherjee is in the Editorial Board of Universal Journal of Computational Mathematics and also associated with Fuzzy and Rough Sets Association. He has presented his work at University of Texas (USA), City College of New York (USA), Malaysia (AMC 5th Asian Mathematical Conference), Bangladesh, Turkey and many other universities.

Bibliographic Information

  • Book Title: Generalized Rough Sets

  • Book Subtitle: Hybrid Structure and Applications

  • Authors: Anjan Mukherjee

  • Series Title: Studies in Fuzziness and Soft Computing

  • DOI: https://doi.org/10.1007/978-81-322-2458-7

  • Publisher: Springer New Delhi

  • eBook Packages: Engineering, Engineering (R0)

  • Copyright Information: Springer India 2015

  • Hardcover ISBN: 978-81-322-2457-0Published: 10 June 2015

  • Softcover ISBN: 978-81-322-3441-8Published: 23 October 2016

  • eBook ISBN: 978-81-322-2458-7Published: 28 May 2015

  • Series ISSN: 1434-9922

  • Series E-ISSN: 1860-0808

  • Edition Number: 1

  • Number of Pages: XIII, 160

  • Number of Illustrations: 1 b/w illustrations

  • Topics: Computational Intelligence, Complexity, Mathematics of Algorithmic Complexity

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