International Journal of Advanced Computer Research (IJACR) ISSN (P): 2249-7277 ISSN (O): 2277-7970 Vol - 6, Issue - 22, January 2016
  1. 1
    Google Scholar
  2. 4
    Impact Factor
Robustness of triple I algorithms based on Schweizer-Sklar operators in fuzzy reasoning

Minxia Luo and Yaping Wang

Abstract

In this paper, the perturbation of fuzzy connectives and the robustness of fuzzy reasoning are investigated. This perturbation of Schweizer-Sklar parameterized t-norms and its residuated implication operators are given. We show that full implication triple I algorithms based on Schweizer-sklar operators are robust for normalized Minkowski distance.

Keyword

Schweizer-Sklar operators, Triple I algorithms, Fuzzy reasoning, Robustness.

Cite this article

Refference

[1][1]Cai KY. Robustness of fuzzy reasoning and δ-equalities of fuzzy sets. IEEE Transactions on Fuzzy Systems. 2001;9(5):738-50.

[2][2]Dai S, Pei D, Wang SM. Perturbation of fuzzy sets and fuzzy reasoning based on normalized Minkowski distances. Fuzzy Sets and Systems. 2012;189(1):63-73.

[3][3]Dai S, Pei D, Guo D. Robustness analysis of full implication inference method. International Journal of Approximate Reasoning. 2013;54(5):653-66.

[4][4]Hardy GH, Littlewood JE, Pólya G. Inequalities. Cambridge University Press;1952.

[5][5]He H,Wang H, Liu Y, Wang Y, Du Y. Principle of universal logics. Science Press, Beijing; 2001.

[6][6]Hung WL, Yang MS. Similarity measures of intuitionistic fuzzy sets based on Lp metric. International Journal of Approximate Reasoning. 2007;46(1):120-36.

[7][7]Klement EP, Mesiar R, Pap E. Triangular norms. Position paper II: general constructions and parameterized families. Fuzzy Sets and Systems. 2004;145(3):411-38.

[8][8]Luo M, Yao N. Triple I algorithms based on Schweizer–Sklar operators in fuzzy reasoning. International Journal of Approximate Reasoning. 2013;54(5):640-52.

[9][9]Li Y, Qin K, He X. Robustness of fuzzy connectives and fuzzy reasoning. Fuzzy Sets and Systems. 2013;225:93-105.

[10][10]Pei D. Unified full implication algorithms of fuzzy reasoning. Information Sciences. 2008;178(2):520-30.

[11][11]Pei D. Formalization of implication based fuzzy reasoning method. International Journal of Approximate Reasoning. 2012;53(5):837-46.

[12][12]Wang GJ. The full implication triple I method of fuzzy reasoning. Science in China (Series E).1999;29(1):43-53. (in Chinese).

[13][13]Wang GJ. On the logic foundation of fuzzy reasoning. Information Sciences. 1999;117(1):47-88.

[14][14]Whalen T. Parameterized R-implications. Fuzzy Sets and Systems. 2003;134(2):231-81.

[15][15]Wang GJ, Fu L. Unified forms of triple I method. Computers & Mathematics with Applications. 2005;49(5):923-32.

[16][16]Wang GJ. Non-classical mathematical logic and approximate reasoning. Science Press, Beijing;2008. (in Chinese).

[17][17]Xu WH, Xie ZK, Yang JY, Ye YP. Continuity and approximation properties of two classes of algorithms for fuzzy inference. Journal of Software. 2004;15(10):1485-92. (in Chinese).

[18][18]Zadeh LA. Fuzzy sets. Information and Control. 1965;8(3):338-53.

[19][19]Zadeh LA. The concept of a linguistic variable and its application to approximate reasoning—I. Information Sciences. 1975;8(3):199-249.

[20][20]Zadeh LA. The concept of a linguistic variable and its application to approximate reasoning—II. Information Sciences. 1975;8(4):301-57.

[21][21]Zadeh LA. The concept of a linguistic variable and its application to approximate reasoning-III. Information Sciences. 1975;9(1):43-80.

[22][22]Zadeh LA. Toward a generalized theory of uncertainty (GTU)–an outline. Information Sciences. 2005;172(1):1-40.