In this paper a Fuzzy Multi Objective LPP is first reduced to crisp Multi Objective LPP using ranking function. The crisp Multi Objective LPP is then solved by Zimmerman Technique using exponential membership functions. The results are compared with those obtained using trapezoidal and hyperbolic membership functions in Zimmerman Technique.

A mixed quadrature rule of precision nine for approximate evaluation of real definite integrals has been constructed by blending Clenshaw-Curtis five point rule modified by Richardson Extrapolation and Gauss-Legendre four point rule. An error analysis for this mixed rule is provided. The efficiency of this rule is highlighted through numerical evaluation of some definite integrals at the end.

<p style='text-indent:20px;'>A novel quadrature rule is formed combining Lobatto six point transformed rule and Gauss-Legendre five point transformed rule each having precision nine. The mixed rule so formed is of precision eleven. Through asymptotic error estimation the novelty of the quadrature rule is justified. Some test integrals have been evaluated using the mixed rule and its constituents both in non-adaptive and adaptive modes. The results are found to be quite encouraging for the mixed rule which is in conformation with the theoretical prediction.</p>

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This research described the development of a new mixed cubature rule for evaluation of surface integrals over rectangular domains. Taking the linear combination of Clenshaw-Curtis 5- point rule and Gauss-Legendre 3-point rule ( each rule is of same precision i.e. precision 5) in two dimensions the mixed cubature rule of higher precision was formed (i.e. precision 7). This method is iterative in nature and relies on the function values at uneven spaced points on the rectangle of integration. Also as supplement, an adaptive cubature algorithm is designed in order to reinforce our mixed cubature rule. With the illustration of numerical examples this mixed cubature rule is turned out to be more powerful when compared with the constituents standard cubature procedures both in adaptive and non-adaptive environment.