Arithmetic operations for LR mixed fuzzy random variables via mean chance measure with applications

This paper introduces arithmetic operations for LR mixed fuzzy random variables commonly used in practice for modeling fuzzy stochastic phenomena. The operations are proposed based on mean chance measure, which as a natural extension of both the probability of a random event and the credibility of a fuzzy event, measures the mean or expected (in the sense of probability) credibility that the fuzzy random event occurs. Following from the proposed operational laws, the mean chance distributions of LR mixed fuzzy random variables can be deduced explicitly rather than obtained by simulation, which will provide greater convenience for the decision making or optimization in mixed fuzzy and random environments. Furthermore, some important conclusions on the expected value operator defined via the mean chance measure as well as applications of the proposed arithmetic operations in system reliability analysis are also presented.

[1]  Hua Ke,et al.  Solving project scheduling problem with the philosophy of fuzzy random programming , 2012, Fuzzy Optim. Decis. Mak..

[2]  Tao Tang,et al.  FUZZY TRAIN ENERGY CONSUMPTION MINIMIZATION MODEL AND ALGORITHM , 2011 .

[3]  Lotfi A. Zadeh,et al.  A Theory of Approximate Reasoning , 1979 .

[4]  Didier Dubois,et al.  Fuzzy sets and systems ' . Theory and applications , 2007 .

[5]  Baoding Liu,et al.  Fuzzy random chance-constrained programming , 2001, IEEE Trans. Fuzzy Syst..

[6]  M. Puri,et al.  Fuzzy Random Variables , 1986 .

[7]  Jun Li,et al.  A class of multiobjective linear programming model with fuzzy random coefficients , 2006, Math. Comput. Model..

[8]  Wansheng Tang,et al.  A fuzzy supply chain contract problem with pricing and warranty , 2014, J. Intell. Fuzzy Syst..

[9]  Yian-Kui Liu,et al.  Fuzzy random programming with equilibrium chance constraints , 2005, Inf. Sci..

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

[11]  Xiang Li,et al.  Chance measure for hybrid events with fuzziness and randomness , 2009, Soft Comput..

[12]  Yian-Kui Liu,et al.  Fuzzy Random Variables: A Scalar Expected Value Operator , 2003, Fuzzy Optim. Decis. Mak..

[13]  Tao Huang,et al.  Risk model with fuzzy random individual claim amount , 2009, Eur. J. Oper. Res..

[14]  Zhenzhou Lu,et al.  Reliability Analysis in Presence of Random Variables and Fuzzy Variables , 2015, J. Appl. Math..

[15]  Yian-Kui Liu,et al.  A Bank Hedging Decision Problem , and formulated it as a stochastic possibilistic bank hedging decision model , 2004 .

[16]  Dan A. Ralescu,et al.  Overview on the development of fuzzy random variables , 2006, Fuzzy Sets Syst..

[17]  R. Kruse,et al.  Statistics with vague data , 1987 .

[18]  Baoding Liu,et al.  A survey of credibility theory , 2006, Fuzzy Optim. Decis. Mak..

[19]  Junzo Watada,et al.  Reliability optimization of a series-parallel system with fuzzy random lifetimes , 2009 .

[20]  Lu Zhenzhou,et al.  Reliability Analysis in Presence of Random Variables and Fuzzy Variables , 2015 .

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

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

[23]  Yuhan Liu,et al.  Uncertain random programming with applications , 2013, Fuzzy Optim. Decis. Mak..

[24]  D. Dubois,et al.  Operations on fuzzy numbers , 1978 .

[25]  Yian-Kui Liu,et al.  The convergent results about approximating fuzzy random minimum risk problems , 2008, Appl. Math. Comput..

[26]  Robert LIN,et al.  NOTE ON FUZZY SETS , 2014 .

[27]  Binod Chandra Tripathy,et al.  γ-Open sets and γ-continuous mappings in fuzzy bitopological spaces , 2013, J. Intell. Fuzzy Syst..

[28]  Baoding Liu.  Why is There a Need for Uncertainty Theory , 2012 .

[29]  Dan A. Ralescu,et al.  CREDIBILISTIC PARAMETER ESTIMATION AND ITS APPLICATION IN FUZZY PORTFOLIO SELECTION , 2011 .

[30]  Xinyu Shao,et al.  Sequential optimisation and reliability assessment for multidisciplinary design optimisation under hybrid uncertainty of randomness and fuzziness , 2013 .

[31]  Wansheng Tang,et al.  Reliability and Mean Time to Failure of Unrepairable Systems With Fuzzy Random Lifetimes , 2007, IEEE Transactions on Fuzzy Systems.

[32]  Wansheng Tang,et al.  Minimum risk criterion for uncertain production planning problems , 2011, Comput. Ind. Eng..

[33]  Binod Chandra Tripathy,et al.  On mixed fuzzy topological spaces and countability , 2012, Soft Comput..

[34]  Anupam Ojha,et al.  A transportation problem with fuzzy-stochastic cost , 2014 .

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

[36]  Binod Chandra Tripathy,et al.  A new class of fuzzy sequences related to the ℓp space defined by Orlicz function , 2014, J. Intell. Fuzzy Syst..

[37]  Fan Yang,et al.  Fuzzy α-minimum spanning tree problem: definition and solutions , 2016, Int. J. Gen. Syst..

[38]  Fan Yang,et al.  Fuzzy arithmetic on LR fuzzy numbers with applications to fuzzy programming , 2015, J. Intell. Fuzzy Syst..