There are several methods in the literature to find the fuzzy optimal solution of fully fuzzy linear programming (FFLP) problems. However, in all these methods, it is assumed that the product of two trapezoidal (triangular) fuzzy numbers will also be a trapezoidal (triangular) fuzzy number. Fan et al. (“Generalized fuzzy linear programming for decision making under uncertainty: Feasibility of fuzzy solutions and solving approach”, Information Sciences, Vol. 241, pp. 12–27, 2013) proposed a method for finding the fuzzy optimal solution of FFLP problems without considering this assumption. In this paper, it is shown that the method proposed by Fan et al. (2013) suffer from errors and to overcome these errors, a new method (named as Mehar method) is proposed for solving FFLP problems by modifying the method proposed by Fan et al. (2013) . To illustrate the proposed method, some numerical problems are solved.

This study was carried out at the Teaching and Research Farm of Landmark University, Omu-Aran. Treatments consisted of 3 levels of cocoa pod husk ash (0, 2 and 4 tonnes CPHA ha^-1), 3 levels of cocoa pod husk powder (0, 2 and 4 tonnes CPHP ha^-1), NPK and the control. The experiment was laid out in a Randomized Complete Block Design (RCBD) replicated four times. The following parameters were taken plant height, number of leaves (at 2, 3, and 4 weeks after sowing), total plant weight, root weight, leaf weight, roots girth and roots length. Data collected were subjected to Analysis of Variance (ANOVA) Using S.A.S, 2000. Treatment means were compared using Duncan Multiple Range Test (DMRT) at 0.05 level of probability. Results showed that chemical analysis of cocoa pod ash and powder contained plant nutrients as N, P, K, Ca, Mg and some other micronutrients in varying proportions. Application of CPHA 4 + CPHP 2 gave higher values for all the vegetative parameters. The implication of this study is that high level of cocoa pod husk powder in combination with high level of cocoa pod husk ash is detrimental to radish cultivation. In the same vein, the nutrition of radish was incomplete when NPK fertilizer was applied. It can therefore be recommended that the use of combined application of cocoa pod ash and cocoa pod powder at CPHA4 + CPHP2 was sufficient for the cultivation of radish (Raphanus sativus) in the study area as it compete favorably with application of NPK fertilizer.

Simple mathematical expressions are given for the betweenness centrality of nodes in trees, forests and cycles. As application, a centrality test is given for when a network might be a forest.

In this paper, electrically conductive composites comprised of silicone rubber and titanium diboride (TiB₂) were synthesized by conventional mixing methods. Fine particles of TiB₂ (in micron size) and 10 parts per hundred parts of rubber (phr) proportion of carbon black (XC-72) were used to make the composites with HTV silicone rubber. The composites were cured at appropriate temperature and pressure and the effect on the electrical properties was studied. The resistance of the silicone rubber is ~ 10¹⁵Ω which decreases to 1–2 kΩ in case of composites with negligible effect of heat ageing. The hardness increases by ~ 35% simultaneous to the decrease of ~ 47% in the tensile strength. Morphological characterization indicates the homogeneous dispersion of the fillers in the composite.