A New Operation on Triangular Fuzzy Number for Solving Fuzzy Linear Programming Problem

The fuzzy set theory has been applied in many fields such as operation research, control theory and management sciences etc. The fuzzy numbers and fuzzy values are widely used in engineering applications because of their suitability for representing uncertain information. In standard fuzzy arithmetic operations we have some problem in subtraction and division operations. In this paper, a new operation on Triangular Fuzzy Numbers is defined, where the method of subtraction and division has been modified. These modified operators yield the exact inverse of the addition and multiplication operators.

[1]  Ramon E. Moore Methods and applications of interval analysis , 1979, SIAM studies in applied mathematics.

[2]  Caroline M. Eastman,et al.  Review: Introduction to fuzzy arithmetic: Theory and applications : Arnold Kaufmann and Madan M. Gupta, Van Nostrand Reinhold, New York, 1985 , 1987, Int. J. Approx. Reason..

[3]  Madan M. Gupta,et al.  Introduction to Fuzzy Arithmetic , 1991 .

[4]  Matrix Inversion with the Square Root Method , 1964 .

[5]  Masaharu Mizumoto,et al.  Some Properties of Fuzzy Sets of Type 2 , 1976, Inf. Control..

[6]  E. Hansen Interval Arithmetic in Matrix Computations, Part I , 1965 .

[7]  Luc Jaulin,et al.  Applied Interval Analysis , 2001, Springer London.

[8]  Eldon Hansen,et al.  Global optimization using interval analysis , 1992, Pure and applied mathematics.

[9]  A. Bonaert Introduction to the theory of Fuzzy subsets , 1977, Proceedings of the IEEE.

[10]  Lotfi A. Zadeh,et al.  Please Scroll down for Article International Journal of General Systems Fuzzy Sets and Systems* Fuzzy Sets and Systems* , 2022 .

[11]  Weldon A. Lodwick,et al.  Interval Methods and Fuzzy Optimization , 1997, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[12]  E. Hansen,et al.  Interval Arithmetic in Matrix Computations, Part II , 1965 .

[13]  A. Neumaier Interval methods for systems of equations , 1990 .

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

[15]  Shyi-Ming Chen,et al.  OPERATIONS ON FUZZY NUMBERS WITH FUNCTION PRINCIPAL , 1985 .

[16]  H. Carter Fuzzy Sets and Systems — Theory and Applications , 1982 .

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

[18]  Lotfi A. Zadeh,et al.  The concept of a linguistic variable and its application to approximate reasoning-III , 1975, Inf. Sci..

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

[20]  G. Alefeld,et al.  Introduction to Interval Computation , 1983 .

[21]  Hung T. Nguyen,et al.  A note on the extension principle for fuzzy sets , 1978 .

[22]  E. Hansen On the solution of linear algebraic equations with interval coefficients , 1969 .

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