Dual simplex method for solving fuzzy number linear programming problems in addition, a new method for solving linear programming with symmetric trapezoidal fuzzy numbers (flp) has been proposed by ganesan and veeramani (2006. Triangular fuzzy number and generalized trapezoidal fuzzy number here material density of the bar, be obtained by solving its corresponding dual maximization problem because the dual constraints are linear, and yang et al  discussd about the basic and its applications of fuzzy geometric programming ojha et al used binary. Transportation problem have uncertainties, this paper develops a generalized fuzzy transportation problem with fuzzy supply, demand and cost for simplicity, these parameters are assumed to be fuzzy trapezoidal numbers.
9 xiaolu zhang, zeshui xu, manfeng liu, hesitant trapezoidal fuzzy qualiflex method and its application in the evaluation of green supply chain initiatives, sustainability, 2016, 8, 10, 952crossref 10 chuan-yang ruan , jian-hui yang , li-na han , jing duan , ruo-bing liu , international conference on oriental thinking and fuzzy logic, 2016. Programming problems and its applications programming problems involving symmetric trapezoidal fuzzy numbers without converting them to the crisp linear programming problems ebrahimnejad et al  by a nat- deﬁnition 21 a fuzzy number u is completely deter-mined by any pair u ¼ðuuþ of functions uðaþuðaþ . M barkhordari ahmadi , n a kiani , n mikaeilvand, laplace transform formula on fuzzy nth-order derivative and its application in fuzzy ordinary differential equations, soft computing - a fusion of foundations, methodologies and applications, v18 n12, p2461-2469, december 2014. Keywords fuzzy, system of linear equations, m-matrix, h-matrix, strictly diagonally the proposed methods are based on analytical decomposition of a fuzzy linear system into its equivalent crisp form they also proposed a new method based on linear for fuzzy number is the trapezoidal representation ˜u = (x 0,y 0,α,β) with defuzziﬁer.
Production and use of large number of vehicles accounts high percentage of air pollution in india in this paper, we analyze the health hazards of human beings and environmental damage due to emissions from vehicles using induced fuzzy associative memories. International journal of computer applications generalized trapezoidal fuzzy number if its membership function is given by , a x b w, w(x a) (b a) b x c, c x d 0, otherwi d e c s) ° dd ° ° dd ® ° dd ¯ ° ° % % : dual variable corresponding to 27 remark a generalized trapezoidal fuzzy number a a,b, c,d w can be explained as. Two existing methods for solving a class of fuzzy linear programming (flp) problems involving symmetric trapezoidal fuzzy numbers without converting them to crisp linear programming problems are the fuzzy primal simplex method proposed by ganesan and veeramani  and the fuzzy dual simplex method proposed by ebrahimnejad and nasseri [2. Ii) fuzzy posynomial gp classiﬁcation and its corresponding class properties  iii) possibility gp  a large number of applications have been discovered for fuzzy gp in a wide variety.
So far fuzzy numbers like triangular fuzzy number, trapezoidal fuzzy numbers, pentagonal, hexagonal, octagonal pyramid and diamond fuzzy numbers have been introduced with its membership functions these numbers have got many applications like non-linear equations, risk analysis and reliability. Trapezoidal fuzzy numbers without converting them bounded dual simplex method for bounded fuzzy number linear programming problems in which some or all the variables are restricted to remain 24 interval-valued fully fuzzy linear programming problem. Fuzzy set theo~y-a~~ its applications, third edition ga 248 ~2s$ 19q6' c fuzzy set theoryand its applications third edition h-j zimmermann kluwer academic publishers boston/dordrecht/london.
Finally, on the basis of the interval-valued dual hesitant fuzzy set correlation coefficient and optimal model, ranking intuitionistic trapezoidal fuzzy number and its[j]. Recently ganesan and veeramani introduced a new approach for solving a kind of linear programming problems involving symmetric trapezoidal fuzzy numbers without converting them to the crisp linear programming problems but their approach is not efficient for situations in which some or all variables are restricted to lie within fuzzy lower and fuzzy upper bounds. The fuzzy primal simplex method proposed by mahdavi-amiri et al and the fuzzy dual simplex method proposed by sh nasseri and a ebrahimnejad are two current procedures for solving linear programming problems with fuzzy cost coefficients known as reduced fuzzy numbers linear. Conflict measure model for large group decision based on interval intuitionistic trapezoidal fuzzy number and its some similarity measures for triangular fuzzy. Key words： interval-valued intuitionistic trapezoidal fuzzy number score function ordered weighted averaging operator hybrid aggregation operator.
Abstract the aim of this work is to construct quantified trapezoidal fuzzy numbers as an extension of trapezoidal fuzzy numbers, by using modal intervals and accepting the possibility that the α-cuts of a trapezoidal fuzzy number may also be improper intervals. Fuzzy applications in research is defined multi-criteria decision making (mcdm) methods have evolved to accommodate as evidenced by the large number of citations found, fuzzy set theory is an established and growing research variable differs from numerical variable in that its values are not numbers but words or sentences in a. The alpha cuts associated with a trapezoidal fuzzy number can be modal intervals, also allowing when we observe a fuzzy number from the point of view of its a we can ﬁnd applications of.
Type-2 fuzzy sets and intuitionistic fuzzy sets have a wide range of practical applicationstype-2 fuzzy sets enhance the ability of the system for dealing with uncertainties. New approach for ranking of trapezoidal fuzzy numbers for an arbitrary trapezoidal fuzzy number u = ( x 0 , y 0 , σ , β ) , with parametric form u = ( u ¯ ( r ) , u ¯ ( r ) ) , we define the magnitude of the trapezoidal fuzzy number u as. A fuzzy number is a normal and convex fuzzy subset of the real line in this paper, based on membership function, we redefine the concepts of mean and variance for fuzzy numbers.