Frank Aggregation Operators in Decision Making
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Questions and Answers

Who is the author of the thesis?

Chitra R

What degree is being pursued by Chitra R?

  • Master of Science
  • Postgraduate Diploma
  • Doctor of Philosophy (correct)
  • Bachelor of Science

Who supervised Chitra R's research?

Dr. K. Prabakaran

Did Chitra R submit the thesis to multiple institutions?

<p>False (B)</p> Signup and view all the answers

Which department is Chitra R affiliated with?

<p>Department of Mathematics</p> Signup and view all the answers

What was the purpose of the thesis?

<p>To discuss the significance of Frank aggregation operators for multi-attribute decision making in the q-rung picture fuzzy context.</p> Signup and view all the answers

Chitra R has not published any research papers.

<p>False (B)</p> Signup and view all the answers

What type of check was certified regarding the thesis contents?

<p>Plagiarism check</p> Signup and view all the answers

What is a key property of the Frank t-norm?

<p>It is influenced by a parameter m. (D)</p> Signup and view all the answers

The union of two fuzzy sets J˘1 and J˘2 is represented by a t-norm function.

<p>False (B)</p> Signup and view all the answers

What is the output of the t-conorm function Uf when given inputs p and 0?

<p>p</p> Signup and view all the answers

The operation of the fuzzy intersection is represented by a __________.

<p>t-norm</p> Signup and view all the answers

Match the following properties with their corresponding fuzzy set operations:

<p>Boundary condition = Fuzzy intersection (t-norm) Idempotency = Frank t-conorm Monotonicity = Both t-norm and t-conorm Commutativity = Frank t-norm</p> Signup and view all the answers

Which of the following individuals provided expert guidance in technical tools for the research?

<p>Dr.D.Prakash (C)</p> Signup and view all the answers

Chitra R expressed gratitude only to the faculty and management at SRM Institute of Science and Technology.

<p>False (B)</p> Signup and view all the answers

What is the relationship of Mr.S.Rameshbabu to Chitra R?

<p>Father</p> Signup and view all the answers

Chitra R thanked _____ for providing necessary resources pertaining to her research work.

<p>Dr.P.Rajendran</p> Signup and view all the answers

Match the following individuals with their contributions:

<p>Dr.B.Neppolian = Dean Research, cooperative support Dr.A.Govindarajan = Support at the initial stage of research Dr.V.Subburayan = Humble regard during the research period Dr.Narasu Sivakumar = Caring support and advice</p> Signup and view all the answers

Flashcards

Frank aggregation operators

Mathematical tools for combining multiple pieces of information into a single value.

Multi-attribute decision making

A process for selecting the best option among several choices, considering multiple factors or attributes.

q-rung picture fuzzy context

A mathematical framework that allows for more nuanced and complex information than traditional fuzzy sets, representing a degree of truth, indeterminacy and falsity.

PhD thesis

A comprehensive research paper presenting original work and findings within a particular field, often the culmination of years of research leading up to a degree.

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Declaration by the scholar

A formal statement made by a candidate assuring that the work presented in a thesis is entirely their own and that they have properly cited any external sources.

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Research supervisor

A faculty member guiding a research scholar through their project, providing expertise and support.

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Plagiarism check

The process of evaluating written work for similarities with other sources to ensure originality.

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Ph.D. degree

Highest academic degree in philosophy, demonstrating advanced knowledge and research abilities.

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Copyright transfer

Action of relinquishing copyright to the institution where research is conducted.

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Research Plan Proposal Seminar

Organized presentation of a research project’s plan and its components to the academic community.

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Fuzzy Sets

Mathematical tools that model uncertainty and vagueness in information.

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t-norm

A mathematical operator used to combine degrees of truth in fuzzy logic.

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Aggregation Operations

Processes combining multiple pieces of information into a single value.

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Multi-Attribute Decision Making

Choosing the best option from several choices, considering many factors.

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Literature Review

Summary of existing research related to a topic.

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Fuzzy Intersection (t-norm)

A mathematical operation combining two fuzzy values, resulting in a fuzzy value representing their common characteristics. It follows specific axioms ensuring boundary conditions, monotonicity, commutativity, and associativity.

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Fuzzy Union (t-conorm)

A mathematical operation merging two fuzzy values into a single fuzzy value, representing their combined characteristics. Also follows axioms like t-norms.

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Frank t-norm/t-conorm

Specific types of fuzzy intersection (t-norm) and union (t-conorm) operations. They use a parameter 'm' to control the shape of the operation.

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Axiom 1 (Boundary Condition)

A rule for fuzzy intersection/union requiring that when one input is at its maximum (1 or 0), the output mirrors the other input.

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Monotonicity (Axiom 2)

If one input fuzzy value increases, the output of fuzzy intersection/union cannot decrease.

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Study Notes

Thesis Title and Details

  • Significance of Frank Aggregation Operators for Multi Attribute Decision Making in the q-Rung Picture Fuzzy Context
  • A thesis submitted by Chitra R
  • In partial fulfillment of the requirements for the degree of Doctor of Philosophy
  • Submitted to SRM Institute of Science and Technology, Kattankulathur, September 2024

Chapters

  • Chapter 1: Introduction

    • Background and Motivation
    • Exploring fuzzy sets and their extensions
    • Navigating essentials of t-norm, t-conorm, and aggregation operations
    • Frank Norm
    • Aggregation Operations
    • Multi Attribute Decision Making
    • Literature Review
    • Overview of the Thesis

  • Chapter 2: Employing q-rung Picture Fuzzy Frank Aggregation Operators for Decision-Making

    • Introduction
    • Key Concepts
    • Results and Discussion
      • MADM Method in the q-rung Picture Fuzzy Framework
      • Practical Instance
      • Examining the Influence of Parameters m and q on Decision Outcomes
      • Comparative Analysis
    • Conclusion

  • Chapter 3: Ordering q-rung Picture Fuzzy Numbers by Possible Grading Technique and its Utilization in Decision-Making Problem

    • Introduction
    • Key Concepts
    • Possible Grading Technique
    • Results and Discussion
      • Mathematical approach to solve MADM using Possible Grading Technique
      • Practical Instance
      • Examining the influence of parameters ğ and m on decision outcomes
      • Comparative Analysis
    • Conclusion

  • Chapter 4: Exploring Group Decision-Making with q-rung Picture Fuzzy Frank Bonferroni Operators

    • Introduction
    • Key Concepts
    • Results and Discussion
      • Framework for Group Decision-Making using Proposed Operator
      • Practical Instance
      • Parameters impact on the Decision-Making Outcomes
      • Comparison of Proposed and Current Operators
    • Conclusion

  • Chapter 5: Incorporating q-rung Picture Fuzzy Frank Prioritized Weighted Aggregators with Multimoora Strategy for Decision Making

    • Introduction
    • Key Concepts
    • Results and Discussions
      • Mathematical Formulation of Integrated MULTIMOORA approach based on Proposed Aggregators
      • Practical Instance
      • Impact of the Parameters m and ğ on MULTIMOORA q-RPFS
      • Comparative examination
    • Conclusion

  • Chapter 6: Handling Decision-Making Issue Based on Hesitant Frank Aggregators in the Linguistic q-rung Picture Fuzzy Context

    • Introduction
    • Key Concepts
    • Set Operations of Hğ-RPFS
    • Frank Operations of hesitant q-rung Picture Fuzzy Numbers
    • Results and Discussion
      • MCGDM approach with Hesitant q-rung picture fuzzy data
      • Practical Instance
    • Conclusion

  • Chapter 7: Summary and Future Work

    • Summary of the Thesis
    • Future Work

List of Tables and Figures

  • Includes tables and figures related to the different chapters

List of Symbols

  • Contains mathematical symbols and their definitions

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Related Documents

Significance of Frank Aggregation Operators for Multi-Attribute Decision Making in the q-Rung Picture Fuzzy Context PDF

Description

Explore the significance of Frank aggregation operators for multi-attribute decision-making in the context of q-rung picture fuzzy sets. This quiz covers the foundations of fuzzy sets, decision-making methods, and the key concepts discussed in the thesis. Test your understanding of these advanced topics and their practical applications.

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