A new lexicographical approach for ranking fuzzy numbers

In the literature many ranking methods have been proposed for comparing the fuzzy numbers, most of them suffer from plenty of shortcomings such as complex calculations, inconsistency with human intuition. To overcome such shortcomings, a new ranking method is proposed for L-R flat fuzzy numbers which is based on the lexicographical ordering approach. It is shown that proposed ranking method satisfies all the reasonable properties of the ordering fuzzy quantities proposed by Wang & Kerre (Fuzzy Sets and Systems 118(2001) 375-385). Finally a comprehensive comparison is done between the existing ranking methods with the proposed one to demonstrate the effectiveness of the proposed ranking method. Keywords: Ranking method, L-R flat fuzzy number

Some Remarks on Ricci Solitons

We obtain an intrinsic formula of a Ricci soliton vector field and a differential condition for the non-steady case to be gradient. Next we provide a condition for a Ricci soliton on a Kaehler manifold to be a Kaehler–Ricci soliton. Finally we give an example supporting the first result

Carbon Sequestration Potential of Pasture-Based Systems Along an Altitudinal Gradient in the North-Western Himalayas

The present investigation was carried out in the Chamba district of Himachal Pradesh (India) to identify the pasture-based land use systems being practiced by farmers and to find out their carbon sequestration potential along different altitudes. For carrying out the study, the area was divided into four altitudinal ranges viz., zone-I (\u3c1000 m amsl), zone-II (1000-1500 m amsl), zone-III (1500- 2500 m amsl) and zone-IV (\u3e 2500 m amsl), according to agro-ecological zones in the state. Results revealed that the pasture-based systems practiced by the farmers in the altitudinal zone-I and zone-II were silvo-pasture and pastoral-silviculture, while, at altitudinal zone-III and zone-IV, the pasture-based systems being practiced were pastoral-silviculture and horti-pastoral depending upon the composition of the components. The aboveground biomass was found ranging between 27.78- 38.18 Mg ha-1 among different pasture-based land use systems with maximum aboveground biomass under silvo-pasture system and minimum under pastoral-silviculture. Along altitudinal gradient, aboveground biomass was found to have been increased with values varying between 29.09- 34.12 Mg ha-1 . Belowground biomass ranged between 6.93- 9.80 Mg ha-1 in different systems under consideration and generally showed increasing trend with increasing altitude. Overall biological productivity was found to be highest under silvo-pasture system followed by horti-pastoral and pastoral-silviculture system. Being biologically most productive, silvopasture system stored maximum carbon stock and ultimately sequestered more carbon as compared to the other systems. The estimated vegetation carbon sequestration potential of the pasture-based systems was 63.71- 88.06 Mg ha-1 , while, along altitude the carbon sequestration potential varied from 67.14- 78.62 Mg ha-1 showing increasing trend with altitude

Impact of cropping systems on physico-chemical characteristics of surface water during different seasons in Shimla region of Himachal Pradesh

The present investigations were carried out in the year 2014 with an objective to find out the impact of different cropping systems on nearby surface water resources in Shimla region of Himachal Pradesh. The aim of the study was to monitor the surface water bodies for pollution caused by nearby cropping systems in the Shimla area. In this study fruit, fruit + vegetable, vegetable and cereal based cropping systems were selected along with control (uncultivated land) and sampling was done during winter, summer and rainy seasons. The estimated water quality parameters revealed very less organic pollution and pH values were within the BIS prescribed limits of 6.5-8.5. Under vegetable based cropping system EC (500.23 µS cm?1), TDS (329.17 mg/l), BOD (1.48 mg/l), COD (31.09 mg/l), Cl- (25.66 mg/l), Ca (75.59 mg/l) and Mg (11.14 mg/l) were in high concentration, whereas No3- content were high under fruit + vegetable based cropping system. DO were maximum (8.61mg/l) under uncultivated land. Calcium and COD were high in some samples, which could be from anthropogenic sources, rest of the parameters were within the desirable limits prescribed by Bureau of Indian Standards (BIS). The experimental data were statistically analysed through Analysis of variance (two way classification of data) indicated positive correlation among most of the physical and chemical parameters. Study reveals that cropping systems as well as seasonal changes has affected the water quality. The study carried out for water quality parameters, revealed the correlation of each parameter with one another under different cropping systems