Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Granular Computing
Published in: Granular Computing 3/2021

24-03-2020 | Original Paper

Knowledge measure and entropy: a complementary concept in fuzzy theory

Authors: Vikas Arya, Satish Kumar

Published in: Granular Computing | Issue 3/2021

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

The knowledge measure can be considered as a dual measure of entropy for fuzzy sets. In the present work, a new entropy-based knowledge measure is proposed for FSs, which complies with the extended idea of De Luca and Termini axioms. Besides this, some of its major properties are also discussed. Comparison of the proposed measure with various existing fuzzy measures indicates that the proposed knowledge measure has a greater ability in discrimination of various FSs. Moreover, a fuzzy inaccuracy measure is introduced based on the proposed measure and investigated some properties. Considering the significance of integrated weights, a new multiple attribute decision-making (MADM) model is introduced under fuzzy set environment. The proposed knowledge measure is utilized to calculate the weights vector, when weights are partially known and other when weights are completely unknown. Finally, an example is employed to illustrate the effectiveness and consistency of the new MADM method.
previous article Intuitionistic fuzzy time series functions approach for time series forecasting
next article Complex Pythagorean Dombi fuzzy graphs for decision making

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
Literature
Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20(1):87–96MATH
Chen SJ, Chen SM (2001) A new method to measure the similarity between fuzzy numbers. IEEE Int Conf Fuzzy Syst 3:1123–1126
Chen SM, Chen SW (2014) Fuzzy forecasting based on two-factors second-order fuzzy-trend logical relationship groups and the probabilities of trends of fuzzy logical relationships. IEEE Trans Cybern 45(3):391–403
Chen TY, Li CH (2010) Determining objective weights with intuitionistic fuzzy entropy measures: a comparative analysis. Inf Sci 180(21):4207–4222
Chen SM, Manalu GM, Pan JS, Liu HC (2013) Fuzzy forecasting based on two-factors second-order fuzzy-trend logical relationship groups and particle swarm optimization techniques. IEEE Trans Cybern 43(3):1102–1117
Chen SM, Cheng SH, Lan TC (2016a) A novel similarity measure between intuitionistic fuzzy sets based on the centroid points of transformed fuzzy numbers with applications to pattern recognition. Inf Sci 343:15–40MathSciNetMATH
Chen SM, Cheng SH, Lan TC (2016b) Multicriteria decision making based on the TOPSIS method and similarity measures between intuitionistic fuzzy values. Inf Sci 367:279–295
De Luca A, Termini S (1972) A definition of a non-probabilistic entropy in the setting of fuzzy sets theory. Inf Control 20(4):301–312MATH
Fahmi A, Amin F, Ullah H (2019) Multiple attribute group decision making based on weighted aggregation operators of triangular neutrosophic cubic fuzzy numbers. Granul Comput 2019:1–3
Guo K (2016) Knowledge measure for Atanassov’s intuitionistic fuzzy sets. IEEE Trans Fuzzy Syst 24(5):1072–1078
Higashi M, Klir GJ (1982) On measures of fuzziness and fuzzy complements. Int J Gen Syst 8(3):169–180MathSciNetMATH
Hwang CL, Lin MJ (1987) Group decision making under multiple criteria: methods and applications. Springer, BerlinMATH
Hwang CH, Yang MS (2008) On entropy of fuzzy sets. Int J Uncertain Fuzzy Knowl-Based Syst 16:519–527MathSciNetMATH
Jamkhaneh EB, Garg H (2018) Some new operations over the generalized intuitionistic fuzzy sets and their application to decision making process. Granul Comput 3(2):111–122
Joshi R, Kumar S (2017) An \((R, S)\)-norm fuzzy information measure with its applications in multiple-attribute decision-making. Comput Appl Math 37(3):2943–2964MathSciNetMATH
Joshi R, Kumar S (2018) A novel fuzzy decision-making method using entropy weights-based correlation coefficients under intuitionistic fuzzy. Int J Fuzzy Syst 21(1):232–242MathSciNet
Li P, Liu B (2008) Entropy of credibility distributions for fuzzy variables. IEEE Trans Fuzzy Syst 16:123–129
Liu P, You X (2017) Probabilistic linguistic TODIM approach for multiple attribute decision-making. Granul Comput 2(4):333–342
Liu P, Chen SM, Liu J (2017) Multiple attribute group decision making based on intuitionistic fuzzy interaction partitioned Bonferroni mean operators. Inf Sci 411:98–121MathSciNetMATH
Lubbe JCA (1981) A generalized probabilistic theory of the measurement of certainty and information [Ph.D. thesis]. Department of Electrical Engineering, Delft University of Technology, Delft, The Netherlands
Mahmood T, Liu P, Ye J, Khan Q (2018) Several hybrid aggregation operators for triangular intuitionistic fuzzy set and their application in multicriteria decision making. Granul Comput 3(2):153–168
Nguyen H (2015) A new knowledge-based measure for intuitionistic fuzzy sets and its application in multiple attribute group decision making. Expert Syst Appl 42(22):8766–8774
Pal NR, Pal SR (1992) Higher order fuzzy entropy and hybrid entropy of a set. Inf Sci 61(3):211–231MathSciNetMATH
Rani P, Jain D, Hooda DS (2019) Extension of intuitionistic fuzzy TODIM technique for multi-criteria decision making method based on shapley weighted divergence measure. Granul Comput 4(3):407–420
Satty TL (1980) The analytical hierarchy process. Mc-Graw Hill, New-York
Singh S, Lalotra S, Sharma S (2019) Dual concepts in fuzzy theory:entropy and knowledge measure. Int J Intell Syst 34(5):1034–59
Szmidt E, Kacprzyk J, Bujnowski P (2014) How to measure amount of knowledge conveyed by Atanassov’s intuitionistic fuzzy sets. Inf Sci 257:276–285MathSciNetMATH
Szmidt E, Kacprzyk J (2007) Some problems with entropy measures for the Atanassov intuitionistic fuzzy sets. In: International workshop on fuzzy logic and applications, pp 291–297
Verma RK, Sharma BD (2011) A measure of Inaccuracy between two fuzzy sets. Cybern Inf Technol 11(2):13–23MathSciNet
Wang C, Fu X, Meng S, He Y (2017) Multi-attribute decision-making based on the SPIFGIA operators. Granul Comput 2(4):321–331
Wang HD, Pan XH, He SF (2019) A new interval type-2 fuzzy VIKOR method for multi-attribute decision making. Int J Fuzzy Syst 21(1):145–156  MathSciNet
 Wang G, Zhang J,  Song, Y,  Li Q (2018) An entropy-based knowledge measure for Atanassov’s intuitionistic fuzzy sets and its application to multiple attribute decision making. Entropy 20(12):981MathSciNet
Wei GW (2008) Maximizing deviation method for multiple attribute decision making in intuitionistic fuzzy setting. Know-Based Syst 21(8):833–836
Xia M, Xu Z (2012) Entropy /cross entropy-based group decision making under intuitionistic fuzzy environment. Inf Fusion 13(1):31–47
Xuecheng L (1992) Entropy, distance measure and similarity measure of fuzzy sets and their relations. Fuzzy Sets Syst 52(3):305–318MathSciNetMATH
Yager RR (1979) On the measure of fuzziness and negation. Part 1: Membership in the unit interval. Int J Gen Syst 5(4):221–229MATH
Zafar F, Akram M (2018) A novel decision-making method based on rough fuzzy information. Int J Fuzzy Syst 20(3):1000–1014MathSciNet
Zeng S, Chen SM, Kuo LW (2019) Multi-attribute decision making based on novel score function of intuitionistic fuzzy values and modified VIKOR method. Inf Sci 488:76–92
Zhang Z, Yuan S, Ma C, Xu J, Zhang J (2019) A parametric method for knowledge measure of intuitionistic fuzzy sets. In: Advances in computer communication and computational sciences, vol 924, pp 199–210
Metadata
Title
Knowledge measure and entropy: a complementary concept in fuzzy theory
Authors
Vikas Arya
Satish Kumar
Publication date
24-03-2020
Publisher
Springer International Publishing
Published in
Granular Computing / Issue 3/2021
Print ISSN: 2364-4966
Electronic ISSN: 2364-4974
DOI
https://doi.org/10.1007/s41066-020-00221-7

Other articles of this Issue 3/2021

Granular Computing 3/2021 Go to the issue

Original Paper

Unclear database search

Original Paper

A new approach to similarity measure for generalized trapezoidal fuzzy numbers and its application to fuzzy risk analysis

Original Paper

Decision-making approach based on Pythagorean Dombi fuzzy soft graphs

Original Paper

Complex Pythagorean Dombi fuzzy graphs for decision making

Original Paper

Hexagonal fuzzy number and its distinctive representation, ranking, defuzzification technique and application in production inventory management problem

Original Paper

Picture fuzzy Choquet integral-based VIKOR for multicriteria group decision-making problems

Premium Partner

    Image Credits