The sufficient and necessary condition for chance distribution of bifuzzy variable

Fuzzy sets and fuzzy variables have undergone several different extensions overtime. One of them involved including a “bifuzzy variable” as a fuzzy element for describing the more complete systems. The properties of bifuzzy variable were obtained by introducing the concept of “chance distribution”. In this paper, we will present a sufficient and necessary condition for chance distribution of bifuzzy variable. Here we present a constructive proof base on credibility theory for the sufficient part.

[1]  Didier Dubois,et al.  Possibility Theory - An Approach to Computerized Processing of Uncertainty , 1988 .

[2]  Xiang Li,et al.  A Sufficient and Necessary Condition for Credibility Measures , 2006, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[3]  M. W. Warner,et al.  Higher separation axioms in bifuzzy topological spaces , 1996, Fuzzy Sets Syst..

[4]  Baoding Liu.  Uncertainty Theory: An Introduction to its Axiomatic Foundations , 2004 .

[5]  L. Zadeh.  Fuzzy sets as a basis for a theory of possibility , 1999 .

[6]  Huibert Kwakernaak,et al.  Fuzzy random variables - I. definitions and theorems , 1978, Inf. Sci..

[7]  Lotfi A. Zadeh,et al.  Quantitative fuzzy semantics , 1971, Inf. Sci..

[8]  Yuanguo Zhu,et al.  A Sufficient and Necessary Condition for Chance Distributions of Random Fuzzy Variables , 2007, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[9]  Yian-Kui Liu,et al.  Type-2 fuzzy variables and their arithmetic , 2010, Soft Comput..

[10]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[11]  Baoding Liu,et al.  Theory and Practice of Uncertain Programming , 2003, Studies in Fuzziness and Soft Computing.

[12]  Baoding Liu,et al.  Toward Fuzzy Optimization without Mathematical Ambiguity , 2002, Fuzzy Optim. Decis. Mak..

[13]  Ronald R. Yager.  A Foundation for a Theory of Possibility , 1980, Cybern. Syst..

[14]  Lixing Yang,et al.  On Inequalities And Critical Values Of Fuzzy Random Variables , 2005, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[15]  A. Kaufman,et al.  Introduction to the Theory of Fuzzy Subsets. , 1977 .

[16]  Krassimir T. Atanassov,et al.  Intuitionistic fuzzy sets , 1986 .

[17]  Keping Li,et al.  $${\fancyscript{B}}$$ -Valued fuzzy variable , 2008, Soft Comput..

[18]  Jian Zhou,et al.  Analysis And Algorithms Of Bifuzzy Systems , 2004, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[19]  Rekha Srivastava,et al.  On compactness in bifuzzy topological spaces , 2001, Fuzzy Sets Syst..

[20]  Ziyou Gao,et al.  Train Timetable Problem on a Single-Line Railway With Fuzzy Passenger Demand , 2009, IEEE Transactions on Fuzzy Systems.

[21]  Yian-Kui Liu,et al.  Expected value of fuzzy variable and fuzzy expected value models , 2002, IEEE Trans. Fuzzy Syst..