Distance and distance induced intuitionistic entropy of generalized intuitionistic fuzzy soft sets

Ganeshsree Selvachandran, P. K. Maji, Raghad Qasim Faisal, Abdul Razak Salleh

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

This paper examines the generalized intuitionistic fuzzy soft set (GIFSS) model which is an intuitively straightforward extension of the intuitionistic fuzzy soft set (IFSS) model. This concept which arises from IFSSs, is generalized by including a moderator’s opinion regarding the validity of the information at hand, thus making it highly suitable for use in decision-making problems that involve uncertain, vague and/or unreliable data. In this paper, we introduce the tools that measure the distance, similarity and the degree of fuzziness of GIFSSs. The axiomatic definitions of the distance measure is introduced and subsequently used to define the similarity measure and intuitionistic entropy induced by this distance measure. Some of the algebraic properties of these measures are also verified. The well-known Hamming, normalized Hamming, Euclidean and normalized Euclidean distances are generalized to make them compatible with the concept of GIFSSs. Subsequently, some relations among these information measures are proposed and verified. These results indicate how these measures are related and how they can be deduced from one another. Finally, we demonstrate the application of the information measure between GIFSSs by applying it to a case study related to the moderation of school-based assessment components of students in externally accredited academic programs.

Original languageEnglish
Pages (from-to)1-16
Number of pages16
JournalApplied Intelligence
DOIs
Publication statusAccepted/In press - 18 Feb 2017

Fingerprint

Entropy
Moderators
Decision making
Students

Keywords

  • Distance
  • Entropy
  • Generalized intuitionistic fuzzy soft set
  • Intuitionistic entropy induced by distance measure
  • Similarity measure

ASJC Scopus subject areas

  • Artificial Intelligence

Cite this

Distance and distance induced intuitionistic entropy of generalized intuitionistic fuzzy soft sets. / Selvachandran, Ganeshsree; Maji, P. K.; Faisal, Raghad Qasim; Salleh, Abdul Razak.

In: Applied Intelligence, 18.02.2017, p. 1-16.

Research output: Contribution to journalArticle

@article{34e0354e8b4f4e0a913d842ca6948848,
title = "Distance and distance induced intuitionistic entropy of generalized intuitionistic fuzzy soft sets",
abstract = "This paper examines the generalized intuitionistic fuzzy soft set (GIFSS) model which is an intuitively straightforward extension of the intuitionistic fuzzy soft set (IFSS) model. This concept which arises from IFSSs, is generalized by including a moderator’s opinion regarding the validity of the information at hand, thus making it highly suitable for use in decision-making problems that involve uncertain, vague and/or unreliable data. In this paper, we introduce the tools that measure the distance, similarity and the degree of fuzziness of GIFSSs. The axiomatic definitions of the distance measure is introduced and subsequently used to define the similarity measure and intuitionistic entropy induced by this distance measure. Some of the algebraic properties of these measures are also verified. The well-known Hamming, normalized Hamming, Euclidean and normalized Euclidean distances are generalized to make them compatible with the concept of GIFSSs. Subsequently, some relations among these information measures are proposed and verified. These results indicate how these measures are related and how they can be deduced from one another. Finally, we demonstrate the application of the information measure between GIFSSs by applying it to a case study related to the moderation of school-based assessment components of students in externally accredited academic programs.",
keywords = "Distance, Entropy, Generalized intuitionistic fuzzy soft set, Intuitionistic entropy induced by distance measure, Similarity measure",
author = "Ganeshsree Selvachandran and Maji, {P. K.} and Faisal, {Raghad Qasim} and Salleh, {Abdul Razak}",
year = "2017",
month = "2",
day = "18",
doi = "10.1007/s10489-016-0884-x",
language = "English",
pages = "1--16",
journal = "Applied Intelligence",
issn = "0924-669X",
publisher = "Springer Netherlands",

}

TY - JOUR

T1 - Distance and distance induced intuitionistic entropy of generalized intuitionistic fuzzy soft sets

AU - Selvachandran, Ganeshsree

AU - Maji, P. K.

AU - Faisal, Raghad Qasim

AU - Salleh, Abdul Razak

PY - 2017/2/18

Y1 - 2017/2/18

N2 - This paper examines the generalized intuitionistic fuzzy soft set (GIFSS) model which is an intuitively straightforward extension of the intuitionistic fuzzy soft set (IFSS) model. This concept which arises from IFSSs, is generalized by including a moderator’s opinion regarding the validity of the information at hand, thus making it highly suitable for use in decision-making problems that involve uncertain, vague and/or unreliable data. In this paper, we introduce the tools that measure the distance, similarity and the degree of fuzziness of GIFSSs. The axiomatic definitions of the distance measure is introduced and subsequently used to define the similarity measure and intuitionistic entropy induced by this distance measure. Some of the algebraic properties of these measures are also verified. The well-known Hamming, normalized Hamming, Euclidean and normalized Euclidean distances are generalized to make them compatible with the concept of GIFSSs. Subsequently, some relations among these information measures are proposed and verified. These results indicate how these measures are related and how they can be deduced from one another. Finally, we demonstrate the application of the information measure between GIFSSs by applying it to a case study related to the moderation of school-based assessment components of students in externally accredited academic programs.

AB - This paper examines the generalized intuitionistic fuzzy soft set (GIFSS) model which is an intuitively straightforward extension of the intuitionistic fuzzy soft set (IFSS) model. This concept which arises from IFSSs, is generalized by including a moderator’s opinion regarding the validity of the information at hand, thus making it highly suitable for use in decision-making problems that involve uncertain, vague and/or unreliable data. In this paper, we introduce the tools that measure the distance, similarity and the degree of fuzziness of GIFSSs. The axiomatic definitions of the distance measure is introduced and subsequently used to define the similarity measure and intuitionistic entropy induced by this distance measure. Some of the algebraic properties of these measures are also verified. The well-known Hamming, normalized Hamming, Euclidean and normalized Euclidean distances are generalized to make them compatible with the concept of GIFSSs. Subsequently, some relations among these information measures are proposed and verified. These results indicate how these measures are related and how they can be deduced from one another. Finally, we demonstrate the application of the information measure between GIFSSs by applying it to a case study related to the moderation of school-based assessment components of students in externally accredited academic programs.

KW - Distance

KW - Entropy

KW - Generalized intuitionistic fuzzy soft set

KW - Intuitionistic entropy induced by distance measure

KW - Similarity measure

UR - http://www.scopus.com/inward/record.url?scp=85013076563&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85013076563&partnerID=8YFLogxK

U2 - 10.1007/s10489-016-0884-x

DO - 10.1007/s10489-016-0884-x

M3 - Article

SP - 1

EP - 16

JO - Applied Intelligence

JF - Applied Intelligence

SN - 0924-669X

ER -