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  In this paper, we obtain the closed form expressions for covariance of different types of fuzzy numbers including triangular, trapezoidal, parabolic and Gaussian. An estimate of the fuzzy parameter is obtained by minimizing the possibilistic mean square error and the method is applied to fuzzy volatility estimation problem. We also study the recursive estimation for some fuzzy volatility models with asymmetric innovations using possibility theory. Keywords: Fuzzy volatility models, Possibilistic mean square error, Recursive estimates, Triangular fuzzy number, Trapezoidal fuzzy number.

  It is an attempt to draw a clear picture of development disparities among the districts of Assam in agriculture with the help of composite index. Eighty-three indicators are considered here which are directly related to the agriculture. On the basis of these indicators Nagaon, Borpeta, Dhubri and Kamrup are developed districts but Karbi Anglong, Hailakandi, Dhemaji and N.C. Hills are low developed districts. The developed districts cover 18.31 percent areas and 30.47 percent population of the state whereas low developed area covers 25.35 percent areas and 7.94 percent population of the state. The entire agriculture sector is divided into seven sub sectors namely Production of miscellaneous crops, Production of pulse, cereals and oil seeds, Fertilizer used, and Percentage of livestock population, Rice production, Fish production and Infrastructure facilities. In each sector developed and low developed districts have been identified. In crop production Kokrajar, Dhubri and Sonitpur are high- developed, Jorhat, N.C. Hills and Nagaon are low developed. In production of pulse, cereal and oilseeds Goalpara, Sonitpur, Bongaigaon and Karbi Anglong are developed districts and Nagaon, Tinsukia, Karimganj, Jorhat and Morigaon are low developed districts. In case of livestock population Jorhat is the developed district and Dhemaji, Hailakandi and N.C. Hills are low developed district. In fish production Nagaon, Borpeta, Cachar and Karimganj are developed districts and Karbi Anglong and N.C. Hills are low developed districts. In case of rice production Golaghat, Karimganj, Hailakandi, Sibsagar, Dibrugarh and Cachar are high developed and Bongaigaon, Borpeta, Nalbari, Dhemaji and Lakhimpur are low developed. In case of infrastructure facilities e.g. irrigation, use of electricity in agriculture etc. are availed by the districts Nagaon, Nalbari, Borpeta and Kamrup are high developed and Hailakandi, Dhemaji, N.C. Hills are low developed. From the study it also reveals that the districts, which are low developed in overall agriculture sector they are also low developed in using infrastructure facilities essential for agriculture except Karbi Anglong. For bringing the uniform development in the state, model districts and potential target for low developed districts have been identified. eywords: Composite Index, Potential targets, Development disparities, Model districts.

  The Composite Indices (C.I.) of development in respect of 17 developmental indicators for 32 WSHGs doing aquaculture activities in Keonjhar and Koraput districts of Odisha have been estimated in three dimensions - Economic, Social and Empowerment along with Overall development for the year 2008-09. More than 63% WSHGs have developed to both the stages of High middle (HM) and Low middle (LM) level. The members of the WSHGs were empowered to a higher level (C.I. = 0.38) compared to Economic development (C.I. = 0.57), Social development (C.I. = 0.65) and Overall development (C.I. = 0.66). Overall development was found to be highly associated with Social development (r = 0.88) followed by Economic development (r = 0.66) and Empowerment (r = 0.56) (significant at 1% l.s.). There was a significant poor correlation between Economic Development and Social Development (r = 0.41 (at 5% level of significance)). The Composite Indices (C.I.) of development in respect of 17 developmental indicators for 32 WSHGs doing aquaculture activities in Keonjhar and Koraput districts of Odisha have been estimated in three dimensions - Economic, Social and Empowerment along with Overall development for the year 2008-09. More than 63% WSHGs have developed to both the stages of High middle (HM) and Low middle (LM) level. The members of the WSHGs were empowered to a higher level (C.I. = 0.38) compared to Economic development (C.I. = 0.57), Social development (C.I. = 0.65) and Overall development (C.I. = 0.66). Overall development was found to be highly associated with Social development (r = 0.88) followed by Economic development (r = 0.66) and Empowerment (r = 0.56) (significant at 1% l.s.). There was a significant poor correlation between Economic Development and Social Development (r = 0.41 (at 5% level of significance)). Keywords: WSHG, Aquaculture, Development, Statistical evaluation.

  Ahsan et al. (2005) introduced the idea of ?Mixed Allocation? in stratified sampling. In the present paper the authors worked out the ?Compromise Mixed Allocation? for multivariate stratified sampling in which p (> 1) characteristics are defined on each population unit. It is assumed that the properties of the strata on which the grouping scheme of Ahsan et al. (2005) is based are prevalent in the multivariate case also. A numerical example is also presented to illustrate the computational details. Keywords: Stratified sampling, Optimum allocation, Mixed allocation, Multivariate stratified sampling, Compromise allocation, Compromise mixed allocation, Relative loss in efficiency.

  The optimal controlled nearest proportional to size sampling scheme suggested by Tiwari et al. (2007) uses only one objective function based programming approach for solving the controlled selection problems. In this article we apply the concept of multiple objective functions on optimal controlled nearest proportional to size sampling scheme to minimize the sampling variance of the Yates-Grundy form of the Horvitz-Thompson estimator. The proposed procedure minimizes the true sampling variance of the Horvitz-Thompson estimator while assigning zero probabilities to non-preferred samples. Empirical illustrations have been used to show that the true sample variance of the proposed procedure compares favorably with that of the existing optimal controlled and uncontrolled high entropy selection procedures. Keywords: Controlled selection, Non-preferred samples, Quadratic programming, Variance estimation, High entropy variance, Multiple objective problem.

  The purpose of this article is to propose unified methods of construction of resolvable incomplete block designs for factorial experiments. These designs have orthogonal factorial structure, have balance, estimate all main effects with full efficiency and have control over the interaction efficiencies. These designs have applications in crop-sequence experiments. A catalogue of designs is prepared for number of levels of any factor at most 12. Keywords: Orthogonal factorial structure, Balance, Efficiency, Structure K, Replacement technique.

  Expressions for probability of misclassification (PMC) for multiple groups sample linear discriminant function (MSLDF) are obtained and some approximations are suggested in case of three groups. The PMC for MSLDF has also been obtained by leave-one-out method using simulated samples from three multivariate normal populations to examine the performance of proposed approximations. The numerical results based on simulated data revealed that the PMC for MSLDF are closer to those provided by the approximations suggested. The modified Johnson approximation is suggested for practical applications to obtain PMC in case of three groups sample linear discriminant function. Keywords: Multiple groups population linear discriminant function, Multiple groups sample linear discriminant function, Probability of misclassification.

  Data generated from the designed experiments is analyzed under the assumptions that the error distribution of observations is normal and homogeneous and data do not contain any outlier. If any of these assumptions is violated, the conclusion drawn from this analysis may be false. In the present paper various M-estimation procedures are applied to designed experiments. Efficiencies of these procedures are measured in terms of average variance. An example is given to illustrate the fact that application of robust method changed the conclusions drawn with analysis of original data. For computation of M-estimation, SAS codes are written in IML and given as Appendix.

  Ranked Set Sampling (RSS) is a useful technique for improving the estimates of mean and variance when the sampling units in a study can be more easily ranked than actually measured. Under equal allocation, RSS is found to be more precise than simple random sampling (SRS). Further gain in precision of the estimate may be obtained with appropriate use of unequal allocation. For skewed distributions, the optimum gain in precision is obtained through unequal allocation based on Neyman?s approach, in which the sample size corresponding to each rank order is proportional to its standard deviation. However, the unavailability of the standard deviations of the rank orders makes the Neyman?s approach impractical. The two models, viz., ?t-model? and ?(s, t)-model? suggested by Kaur et al. (1997) are also impractical due to their dependence on population parameters of rank orders and complexities in finding the optimum values of ?t? and ?(s, t)?. In this article, we propose a simple and systematic approach for unequal allocation for RSS with skew distributions. The proposed approach performs better than SRS and RSS with equal allocation. It also appears to perform better than the RSS with unequal allocation using ?t-model? and quite close to the ?(s, t)-model? in most of the situations we have considered. The performance of the proposed procedure relative to existing models has been numerically evaluated for some skewed distributions. Keywords : Ranked set sampling, Relative precision, Neyman?s allocation, Positively skewed distributions, Order statistics.

  Ranked Set Sampling (RSS) is a useful technique for improving the estimates of mean and variance when the sampling units in a study can be more easily ranked than actually measured. Under equal allocation, RSS is found to be more precise than simple random sampling (SRS). Further gain in precision of the estimate may be obtained with appropriate use of unequal allocation. For skewed distributions, the optimum gain in precision is obtained through unequal allocation based on Neyman?s approach, in which the sample size corresponding to each rank order is proportional to its standard deviation. However, the unavailability of the standard deviations of the rank orders makes the Neyman?s approach impractical. The two models, viz., ?t-model? and ?(s, t)-model? suggested by Kaur et al. (1997) are also impractical due to their dependence on population parameters of rank orders and complexities in finding the optimum values of ?t? and ?(s, t)?. In this article, we propose a simple and systematic approach for unequal allocation for RSS with skew distributions. The proposed approach performs better than SRS and RSS with equal allocation. It also appears to perform better than the RSS with unequal allocation using ?t-model? and quite close to the ?(s, t)-model? in most of the situations we have considered. The performance of the proposed procedure relative to existing models has been numerically evaluated for some skewed distributions. Keywords : Ranked set sampling, Relative precision, Neyman?s allocation, Positively skewed distributions, Order statistics.

  Unbiased direct estimators for small area quantities are usually considered too variable to be of any practical use. This paper describes a class of model-based direct estimators for small area quantities that appears to overcome this objection, in the sense that these estimators are comparable in efficiency to the indirect model-based small area estimators such as empirical best linear unbiased predictor (EBLUP) or Pseudo-EBLUP that are now widely used. There are many practical advantages associated with such model-based direct estimation (MBDE), arising from the fact that they are computed as weighted linear combinations of the actual sample data from the small areas of interest. Note that in this case the weights ?borrow strength? via a model that explicitly allows for small area effects. Empirical results show that the MBDE estimator represents a real alternative to the EBLUP and Pseudo-EBLUP, with the simple MSE estimator associated with the MBDE estimator providing good coverage performance. The results further indicate that the MBDE estimator may be more robust than the EBLUP and Pseudo-EBLUP when the small area model is incorrectly specified. Keywords: Small area estimation, Model-based direct estimation, Linear mixed model, EBLUP, Pseudo-EBLUP.

  The paper describes the development of a new fuzzy-logic approach for designing the web based Intelligent Information Systems. The new approach named as rule-promotion approach is suggested for the intelligent systems. The new approach is found to enable the drawing of inferences with enhanced intelligence. It improved the conventional inference process for inferencing. It significantly strengthened the inference drawing power of the rule-based expert system. Rule-promotion approach for web based Intelligent Information Systems is used for diagnosis of diseases in crops. The new approach has been tested and verified for the intelligent diagnosis of diseases of Oilseed-crops. The paper describes evaluation of rule promotion novel approach. It includes the studies on the comparison of the diagnostic results obtained by running the intelligent system without applying rule-promotion approach in conventional way and by applying the rule-promotion approach. The results obtained by applying the rule-promotion approach were found to be more acceptable and lead to more successful diagnosis. The application of Intelligent Information System for Disease Diagnosis in Crops (IISDDC) is made to three Oilseed crops viz. Soybean, Groundnut and Rapeseed Mustard. Keywords: Disease diagnosis, Fuzzy-logic, Inference-drawing, Intelligent information system, Knowledge base, Rule-promotion.

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