Skip to main content
SpringerLink
Log in

Strict intuitionistic fuzzy entropy and application in network vulnerability evaluation

  • Methodologies and Application
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

By analyzing existing construction methods of intuitionistic fuzzy entropy (IFE), the entropies of intuitionistic fuzzy numbers cannot be distinguished when membership function equals non-membership function. The generalization performance of traditional IFE is insufficient. To overcome the limitation of IFE definition, referencing classical mathematic strict comparison operation, an axiomatic definition of strict intuitionistic fuzzy entropy (SIFE) and four constraint requirements are proposed in this paper. Firstly, two SIFE construction methods are proposed and their constraint requirements are certified. Secondly, a general formula is extracted from the novel construction methods. Thirdly, combining vulnerability evaluation model and SIFE theory, IFE is applied in the network information security field. The proposed evaluation model is deployed in the common vulnerability scoring system to evaluate Apache Web Server chunked encoding remote overflow vulnerability. The experiment result shows that the proposed vulnerability evaluation method is a feasible multi-expert evaluation fusing model.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  • Apache Web Server chunk vulnerability (2002). http://httpd.apache.org/info/security_bulletin_20020617.txt

  • Atanassov K (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20(1):87–96

    Article  MATH  MathSciNet  Google Scholar 

  • Burillo P, Bustince H (1996) Entropy on intuitionistic fuzzy sets and interval valued fuzzy sets. Fuzzy Sets Syst 78:305–316

    Article  MATH  MathSciNet  Google Scholar 

  • Bustince H, Burillo P (1996) Vague sets are intuitionistic fuzzy sets. Fuzzy Sets Syst 79(3):403–405

    Article  MATH  MathSciNet  Google Scholar 

  • Chaira T (2012) Arank ordered filter for medical image edge enhancement and detection using intuitionistic fuzzy set. Appl Soft Comput J 12(4):1259–1266

    Article  Google Scholar 

  • Deepa J, Sanjay K (2014) Intuitionistic fuzzy entropy and distance measure based TOPSIS method for multi-criteria decision making. Egypt Inform J 15(2):97–104

    Article  Google Scholar 

  • Farhadinia B (2013) A theoretical development on the entropy of interval-valued fuzzy sets based on the intuitionistic distance and its relationship with similarity measure. Knowl Based Syst 39(2):79–84

    Article  MathSciNet  Google Scholar 

  • Hannes H, Khalida KA (2015) An expert-based investigation of the common vulnerability scoring system. Comput Secur 53(1):18–30

    Google Scholar 

  • Houmb SH, Franqueria VN (2009) Estimating ToE level using CVSS. In: Proceeding of the forth international conference on availability, reliability and security. IEEE Computer Society, Fukuoka, Japan, March 16–19, pp 718–725

  • Houmb SH, Franqueira VNL, Engum EA (2010) Quantifying security risk level from CVSS estimates of frequency and impact. J Syst Softw 83(9):1622–1634

    Article  Google Scholar 

  • Jaganathan P, Kuppuchamy R (2013) A threshold fuzzy entropy based feature selection for medical database classification. Comput Biol Med 43(12):2222–2229

    Article  Google Scholar 

  • Khaleie S, Fasanghari M (2012) An intuitionistic fuzzy group decision making method using entropy and association coefficient. SoftComputing 16(7):1197–1211

    Google Scholar 

  • Kucukvar M, Gumus S, Egilmez G et al (2014) Ranking the sustainability performance of pavements: an intuitionistic fuzzy decision making method. Autom Constr 40(15):33–43

    Article  Google Scholar 

  • Li J, Deng G, Li H, Zeng W (2012) The relationship between similarity measure and entropy of intuitionistic fuzzy sets. Inf Sci 188(1):314–321

    Article  MATH  MathSciNet  Google Scholar 

  • Liu Z, Pan Q, Dezert J et al (2017) Combination of classifiers with optimal weigh based on evidential reasoning. IEEE Trans Fuzzy Syst 99:1

    Google Scholar 

  • Liu Z, Pan Q, Dezert J et al (2018) Classifier fusion with contextual reliability evaluation. IEEE Trans Cybern 48(5):1605–1618

    Article  Google Scholar 

  • Mao JJ, Yao DB, Wang CC (2013) A novel cross-entropy and entropy measures of IFSs and their applications. Knowl Based Syst 48(8):37–45

    Article  Google Scholar 

  • Mell P, Scarfone K, Romanosky S (2007) A complete guide to the common vulnerability scoring system version 2.0. http://www.first.org/cvss/cvss-guide.html

  • Meng FY, Chen XH (2016) Entropy and similarity measure of Atanassov’s intuitionistic fuzzy sets and their application to pattern recognition based on fuzzy measures. Pattern Anal Appl 19(1):11–20

    Article  MathSciNet  MATH  Google Scholar 

  • Nataliani Y, Hwang CM, Yang MS (2015) An exponential-type entropy measure on intuitionistic fuzzy sets. Lect Notes Comput Sci 9119(1):218–227

    Article  MATH  Google Scholar 

  • National Vulnerability Database Version 2 (2009). http://nvd.nist.gov

  • Pal NR, Bustice H, Pagola M et al (2013) Uncertainties with Atanassov’s intuitionistic fuzzy sets: fuzziness and lack of knowledge. Inf Sci 228(10):61–74

    Article  MATH  MathSciNet  Google Scholar 

  • Pedro MP, Pedro C, Humberto B et al (2013) Image segmentation using Atanassov’s intuitionistic fuzzy sets. Expert Syst Appl 4(1):15–26

    Google Scholar 

  • Qin JD, Liu XW (2013) Study on interval intuitionistic fuzzy multi-attribute group decision making method based on Choquet integral. Procedia Comput Sci 17(5):465–472

    Article  Google Scholar 

  • Song YF, Wang XD, Lei L et al (2015) A novel similarity measure on intuitionistic fuzzy sets with its application. Appl Intell 42(2):252–261

    Article  Google Scholar 

  • Song YF, Wang XD, Quan W, Huang W et al (2017) A new approach to construct similarity measure for intuitionistic fuzzy sets. Soft Comput 1:1–14

    Google Scholar 

  • Szmidt E, Kacprzyk J (2001) Entropy for intuitionistic fuzzy sets. Fuzzy Sets Syst 118(3):467–477

    Article  MATH  MathSciNet  Google Scholar 

  • Wang Y, Lei YJ (2007) A technique for constructing intuitionistic fuzzy entropy. Control Decis 22(12):1390–1394

    MATH  Google Scholar 

  • Wei CP, Wang P, Zhang YZ (2011) Entropy, similarity measure of interval-valued intuitionistic fuzzy sets and their applications. Inf Sci 181(19):4273–4286

    Article  MATH  MathSciNet  Google Scholar 

  • Ye J (2010) Two effective measures of intuitionistic fuzzy entropy. Computing 87(1/2):56–62

    MATH  MathSciNet  Google Scholar 

  • Zadeh LA (1965) Fuzzy set. Inf Control 8(3):338–356

    Article  MATH  Google Scholar 

  • Zeng WY, Li HX (2006) Relationship between similarity measure and entropy of interval-valued fuzzy sets. Fuzzy Sets Syst 157(11):1477–1484

    Article  MATH  MathSciNet  Google Scholar 

  • Zeng WY, Zhao YB, Gu YD (2016) Similarity measure for vague sets based on implication functions. Knowl Based Syst 94(2):124–131

    Article  Google Scholar 

  • Zhang QS, Jiang SY (2008) A note on information entropy measures for vague set and its application. Inf Sci 178(21):4184–4191

    Article  MATH  MathSciNet  Google Scholar 

  • Zhang HY, Zhang WX, Mei CL (2009) Entropy of interval-valued fuzzy sets based on distance and its relationship with similarity measure. Knowl Based Syst 22(6):449–454

    Article  Google Scholar 

  • Zhao F, Huang H, Jin H et al (2011) A hybrid ranking approach to estimate vulnerability for dynamic attacks. Comput Math Appl 62(12):4308–4321

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Joint Service College, National Defence University PLA, Beijing, 710036, People’s Republic of China

    Xiaoshi Fan

  2. Air and Missile Defense College, Air Force Engineering University, Xi’an, 710051, People’s Republic of China

    Chenghai Li & Yanan Wang

Authors
  1. Xiaoshi Fan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chenghai Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yanan Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xiaoshi Fan.

Ethics declarations

Conflict of interest

On behave of all co-authors, we declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work.

Additional information

Communicated by V. Loia.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fan, X., Li, C. & Wang, Y. Strict intuitionistic fuzzy entropy and application in network vulnerability evaluation. Soft Comput 23, 8741–8752 (2019). https://doi.org/10.1007/s00500-018-3474-5

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-018-3474-5

Keywords

Search

Navigation