AIRCC's International Journal of Computer Science and Information Technology

Open Access Open Access  Restricted Access Subscription Access

A New Approach for Ranking Shadowed Fuzzy Numbers and its Application


Affiliations
1 Department of Management Information Systems, Modern Academy for Computer Science and Management Technology, Cairo, Egypt
 

In many decision situations, decision-makers face a kind of complex problems. In these decision-making problems, different types of fuzzy numbers are defined and, have multiple types of membership functions. So, we need a standard form to formulate uncertain numbers in the problem. Shadowed fuzzy numbers are considered granule numbers which approximate different types and different forms of fuzzy numbers. In this paper, a new ranking approach for shadowed fuzzy numbers is developed using value, ambiguity and fuzziness for shadowed fuzzy numbers. The new ranking method has been compared with other existing approaches through numerical examples. Also, the new method is applied to a hybrid multi-attribute decision making problem in which the evaluations of alternatives are expressed with different types of uncertain numbers. The comparative study for the results of different examples illustrates the reliability of the new method.

Keywords

Fuzzy Numbers, Intuitionistic Fuzzy Numbers, Shadowed Sets, Shadowed Fuzzy Numbers, Ranking, Fuzziness Measure.
User
Notifications
Font Size

  • Krassimir T. Atanassov, (1986) "Intuitionistic fuzzy sets", Fuzzy Sets and Systems Vol. 20, Issue (1), pp.87 -96.

  • Witold Pedrycz,(1998) "Shadowed Sets: Representing and Processing Fuzzy Sets", IEEE Transactions on systems, man, and cybernetics-part B: Cybernetics, Vol. 28, No. I.

  • Mohamed A. H. EI_Hawy, Hesham A. Hassan, Hesham A. Hefny, Khaled T. Wassif , (2015) " An Improved Fuzzy Number Approximation using Shadowed Sets" , International Journal of Computer Applications (0975 - 8887), Vol. 118 , No.25, pp. 9-15.

  • Mohamed A. H. EI_Hawy, Hesham A. Hassan, Hesham A. Hefny, Khaled T. Wassif ,(2015)"A Proposed Shadowed Intuitionistic Fuzzy Numbers ",Computer Engineering & Systems (ICCES), 10th, IEEE.

  • Shyi-Ming Chen, Kata Sanguansat, (2011) ”Analyzing fuzzy risk based on a new fuzzy ranking method between generalized fuzzy numbers”, Expert Systems with Applications, Vol. 38, Issue 3, pp. 2163-2171.

  • A.S.A. Bakar,D.Mohamad and N.H. Sulaiman, (2010) “Ranking fuzzy numbers using similarity measure with centroid”, IEEE International Conference on Science and Social Research, pp.58–63.

  • Chen, S., Chen, S.,(2007), “Fuzzy risk analysis based on the ranking of generalized trapezoidal fuzzy numbers.”, Applied Intelligence Vol. 26, Issue 1.

  • S.M. Chen and K. Sanguansat,(2011) “Analyzing fuzzy risk based on a new fuzzy ranking method between generalized fuzzy numbers”, Expert System with Applications, Vol. 38, Issue 3, pp. 2163–2171.

  • Shi-jay chen & shyi-mingchen ,(2003) “a new method for handling multicriteria fuzzy decision-making problems using fn-iowa operators”, Cybernetics and Systems, Vol. 34, Issue 2.

  • L.H. Chen and H.W. Lu, (2002) “The preference order of fuzzy numbers”, Computers & Mathematics with Applications, Vol. 44, Issues 10–11, pp. 1455-1465.

  • A.S.A. Bakar, D. Mohamad and N.H. Sulaiman, (2012) “Distance –based ranking fuzzy numbers”, Advances in Computational Mathematics and Its Applications, Vol. 1, No. 3, pp.146–150.

  • Shyi-Ming Chen, Jim-Ho Chen, (2009) “Fuzzy risk analysis based on ranking generalized fuzzy numbers with different heights and different spreads”, Expert Systems with Applications, Vol.36, Issue 3, Part 2, pp. 6833-6842.

  • Ahmad Syafadhli Abu Bakar , Alexander Gegov, (2014) “Ranking of Fuzzy Numbers Based on Centroid Point and Spread”, Journal of Intelligent & Fuzzy Systems, vol. 27, no. 3, pp. 1179-1186.

  • RituparnaChutia, BijitChutia, (2017) ”A new method of ranking parametric form of fuzzy numbers using value and ambiguity”, Applied Soft Computing,Vol. 52, pp. 1154-1168.

  • Deng-Feng Li,(2010) ”A ratio ranking method of triangular intuitionistic fuzzy numbers and its application to MADM problems”, Computers & Mathematics with Applications ,Vol. 60, Issue 6, pp. 1557-1570.

  • P. K. De and D. Das, (2012) "Ranking of trapezoidal intuitionistic fuzzy numbers", 12th International Conference on Intelligent Systems Design and Applications (ISDA), Kochi, pp.184-188.

  • Zhong-Xing Wang, Jian Li, (2009) “The Method for Ranking Fuzzy Numbers Based on the Approximate Degree and the Fuzziness”, Sixth International Conference on Fuzzy Systems and Knowledge Discovery, IEEE.

  • L. A. Zadeh, (1965) "Fuzzy sets." Information and Control, 8(3), pp.338-353.

  • A. Kaufmann, M.M. Gupta,( 1985) “Introduction to Fuzzy Arithmetic Theory and Applications”, Van Nostrand Reinhold, New York.

  • George. J. Klir, Bo. Yuan, (1995) "Fuzzy Sets and Fuzzy Logic Theory and Applications", Prentice Hall press.

  • Krassimir T. Atanassov,(1999) "Intuitionistic Fuzzy Sets. Theory and Applications", Physica-Verlag, Heidelberg New York.

  • P.Grzegorzewski, (2003) ” Distances and orderings in a family of intuitionistic fuzzy numbers”,.In: EUSFLAT Conf., pp. 223–227.

  • M. Kumar and S.P. Yadav, (2012) “Analyzing Fuzzy System Reliability Using Arithmetic Operations on Different Types of Intuitionistic Fuzzy Numbers” K. Deep et al. (Eds.): Proceedings of the International Conference on SocProS 2011, AISC 130, pp. 725–736. Springer India.

  • Witold Pedrycz, (2009) "From Fuzzy Sets to Shadowed Sets: Interpretation and Computing", international journal of intelligent systems, Vol. 24, pp. 48-61.

  • Yiyu Yao, Shu Wang, XiaofeiDeng,(2017) “Constructing shadowed sets and three-way approximations of fuzzy sets “, Information Sciences, Vol. 412–413, pp. 132-153.

  • OlgierdHryniewicz,(2006) "An Evaluation of the Reliability of Complex Systems Using Shadowed Sets and Fuzzy Lifetime Data", International Journal of Automation and Computing, Vol. 2 ,pp. 145-150.

  • George J. Klir, Mark l. Wierman,(1999) "Uncertainty –Based Information Elements of Generalized Information Theory" Springer-Verlag Berlin Heidelberg GmbH.

  • HoomanTahayori, Alireza Sadeghian, Witold Pedrycz, (2013) "lnduction of Shadowed Sets Based on the Gradual Grade of Fuzziness", Fuzzy Systems, IEEE Transactions on , vo1.21, no.5, pp.937-949.

  • M. Delgado, M.A. Vila, W. Voxman, (1998)”On a canonical representation of fuzzy numbers”, Fuzzy Sets and Systems, Vol. 93, Issue 1, pp. 125-135.

  • Iraj Mahdavi, Nezam Mahdavi-Amiri, Armaghan Heidarzade, Rahele Nourifar,(2008 )“Designing a model of fuzzy TOPSIS in multiple criteria decision making”, Applied Mathematics and Computation,Vol. 206, Issue 2, pp. 607-617.

  • Deng Feng Li, Jiang Xia Nan & Mao Jun Zhang ,(2010)” A Ranking Method of Triangular Intuitionistic Fuzzy Numbers and Application to Decision Making”, International Journal of Computational Intelligence Systems, Vol. 3,Issue 5, pp. 522-530.


Abstract Views: 218

PDF Views: 93




  • A New Approach for Ranking Shadowed Fuzzy Numbers and its Application

Abstract Views: 218  |  PDF Views: 93

Authors

Mohamed A. H. El-Hawy
Department of Management Information Systems, Modern Academy for Computer Science and Management Technology, Cairo, Egypt

Abstract


In many decision situations, decision-makers face a kind of complex problems. In these decision-making problems, different types of fuzzy numbers are defined and, have multiple types of membership functions. So, we need a standard form to formulate uncertain numbers in the problem. Shadowed fuzzy numbers are considered granule numbers which approximate different types and different forms of fuzzy numbers. In this paper, a new ranking approach for shadowed fuzzy numbers is developed using value, ambiguity and fuzziness for shadowed fuzzy numbers. The new ranking method has been compared with other existing approaches through numerical examples. Also, the new method is applied to a hybrid multi-attribute decision making problem in which the evaluations of alternatives are expressed with different types of uncertain numbers. The comparative study for the results of different examples illustrates the reliability of the new method.

Keywords


Fuzzy Numbers, Intuitionistic Fuzzy Numbers, Shadowed Sets, Shadowed Fuzzy Numbers, Ranking, Fuzziness Measure.

References