In this paper, we propose a new definition of intuitionistic fuzzy quasi-metric and pseudo-metric spaces based on intuitionistic fuzzy points. We prove some properties of intuitionist fuzzy quasi- metric and pseudo-metric spaces, and show that every intuitionist fuzzy pseudo-metric space is intuitionist fuzzy regular and intuitionistic fuzzy completely normal and hence intuitionistic fuzzy normal. These are the intuitionistic fuzzy generalization of the corresponding properties of fuzzy quasi-metric and pseudo- metric spaces.

For a class of fuzzy metric spaces (in the sense of George and Veeramani) with an H-type t-norm, we present a method to construct a metric on a fuzzy metric space. The induced metric space shares many important properties with the given fuzzy metric space. Specifically, they generate the same topology, and have the same completeness. Our results can give the constructive proofs to some problems for fuzzy metric spaces in the literature, which are shown by examples in this paper.

Irregular development of agricultural areas, crops planting with high water need in the Urmia Lake Basin and also low irrigation efficiency have caused a significant reduction in the lake surface in recent years, so estimating water consumption in agriculture can be efficient in both accurate agriculture management and water resources management. In this context, by using METRIC algorithm and Landsat 8 and MODIS satellite images, the actual evapotranspiration have been estimated for a part of the Urmia Lake basin - Hasanlu dam downstream - in the year 2015 and 2016. Therefore, by considering the percipitation at Naghadeh station as the representative of percipitation in the study area, the valoum of irrigation water used in the agricultural area downstream of Hasanlu Dam was estimated. Then, the valoum of water allocated to this dam and estimation water volume was compared to the WaPOR product. The estimated values for Landsat 8 are 468 and 315 mm and for MODIS, 240 and 208 mm for 2015 and 2016, respectively. The estimated usage of the METRIC algorithm is significantly different from the allocated values and the WaPOR system. The estimated values are far higher than the ground statistics and the WaPOR system for nearly all months of the two years. The difference between METRIC and ground statistics and WaPOR product in the study area is calculated equal 23 and 26.6 million cubic meters, respectively.

In this paper, we introduce the concept of the rectangular M-metric spaces, along with its topology and we prove some fixed-point theorems under different contraction principles with various techniques. The obtained results generalize some classical fixed-point results such as the Banach’ s contraction principle, the Kannan’ s fixed-point theorem and the Chatterjea’ s fixed-point theorem. Also we give an application to the fixed-circle problem.

In this paper, an applicable control-relevant nonlinearity assessment method is proposed for nonlinear dynamic systems. In this method, nonlinear system is decomposed to a bank of linear systems using gap metric, a smart tool for measuring the distance between two linear systems. Then, the ability of each local linear model is investigated to stabilize all linear models. A criterion is proposed to measure the nonlinearity of nonlinear system based on gap metric and maximum stability margin values which bounded between 0 and 1. Unlike most of the current nonlinearity measurement, the proposed method could be used for both integrating and unstable nonlinear systems. Besides, the presented method supplies to distinguish that a single linear controller is adequate to control the nonlinear system or it is necessary to employ the multi-model based controllers design methods. Therefore, the redundancy problem could be avoided by employing the proposed method. A nonlinear Continues Stirred Reactor Tank (CSTR) process is studied that the results confirm the capability of presented nonlinearity assessment method..

The aim of the present paper is to study the Lagrange spaces due to changed (α,β)-metric with Z. Shen square- Randers metric L ̅= 〖(α+β)〗^2/α+ β and obtained fundamental tensor fields for these space. Further, we studied about the variational problem with fixed endpoints for the Lagrange spaces due to above change.