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.

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.

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..

Introduction Payment system nowadays are encouraged to more toward electronic pay Payments, with low cost and high convenience for making Payments. Beside the Promoting of Policy towards e-payment, cash denomination should be considered and restructured cash denomination to be compatible with the real demand especially when there are various changes in circumstances such as e-payment usage, price level, and social performances. This paper examines optimal currency denomination structure from the cost and cash payment efficiency perspective, focusing on banknotes in Iran. The study proposes conceptual methodology together with empirical study and numerical analysis for Iran. Theoretical framework One of the tasks of central banks is to issue sufficient stock of banknotes and coins to respond the market demand. This also entails modernizing from time to time the banknotes’ security features. It seems that in the situation of absence of changes in the currency denomination structure in Iran. There is a need to analyses its denomination structure in terms of its correspondence with the prevailing economic conditions. Central banks worldwide not only perform a periodical review of banknotes’ security features in the face of ongoing advances in counterfeiting techniques: the central banks’ practice also involves the review of parameters determining the currency denomination structure, such as values of the lowest denomination coins and the highest denomination banknotes, the boundary between banknotes and coins and the number of denominations. All of them are analyzed in detail in this paper. An additional parameter should also be distinguished, namely the so-called spacing of denominations, which is analyzed, among others, by Wynne (1997), Van Hove (2001) and Tschoegl (2001). This parameter changed, for example, in Netherlands as a result of the launch of the euro in 2002: the 1– 2. 5– 5 system used in the case of the Dutch guilder was replaced with the 1– 2– 5 euro system. Iran currency already follows the 1– 2– 5 system and there is no need to deal with this problem. he decision about the modification of the denomination structure by the introduction new notes almost coincided with the debate about the rationality of keeping the highest denominations in circulation. To exemplify the emotions surrounding these debates, let us quote Charles Goodhart, who called the European Central Bank and the Swiss National Bank “ shameless” for issuing “ vastly high denomination notes” , namely the EUR 500 and CHF 1, 000, “ which are there to finance the drug deals. ” 2 Another example comes from The Washington Post, where Summers (2016), writing and citing a working paper by Sands (2016), extended the indictment to the USD 100 bill: “ it too is used by criminals, so let’ s get rid of it. ” Less emotional and more matter-of-fact analyses of the issue can also be found. One of these is certainly the latest report of Europol (2015) entitled unambiguously Why is cash still king? Van Hove, Vuchelen (1996b) and Van Hove (2007) suggested that the ECB should place the upper limit of its banknote series at EUR 50 instead of EUR 500. Among opposite opinions were those voiced, among others, by Antti Heinonen, former head of the ECB’ s Directorate, Banknotes, who said: “ Clearly cash is used by criminals because it is an anonymous instrument. But to say that it would be more difficult to commit a crime if we didn’ t have high denomination notes would be to confuse cause and effect. If we didn’ t have the higher denominations, criminals would use the lower denominations – or other global currencies, such as the US dollar or Swiss franc. ” (Atkins 2006). A reasonable stance in this matter was taken by, among others, Rogoff (2015), who besides the above-mentioned benefits of withdrawing cash, presented a set of arguments for its preservation: 3Even though cashless payment instruments are proliferating and there is talk of the expected demise of cash, the latter is still widely used, The sharp rise in cash in circulation, especially over the last few years, makes it interesting to take a closer look at its most important characteristic – the denomination structure. In this study we analyses this structure with the use of the D-METRIC model in the context of NBP’ s recent decision to introduce the new banknote. A comparative analysis is also performed of the structure of the domestic currency with the structures observed in other countries. We show that the denomination structure of the Iran currency has been almost UN suitable to the prevailing economic conditions. The decision about the introduction of the new higher denomination note seems to be an element of adjusting the denomination structure to the conditions in Iran. Result and discussion In this study we analyses denomination structure in Iran by using the D-METRIC model to introduce the new bank note. A comparative analysis is also performed of the structure of the domestic currency with the structures observed in other countries. We show that the denomination structure of IRAN isn't suitable and also the current denomination structure in Iran is not optimal. It’ s necessary to say, one the most important factor that impact on the denominate structure in Iran is inflation. In fact because high inflation denomination continually is changing and the central bank can't have the same speed to coordinate the changes. The result also show that minimum 4 low denomination have been deleted from deal and IRAN need enter new denominations as bank note. 5- Conclusion and suggestion This paper examines optimal currency denomination structure from the cost and cash payment efficiency perspective, focusing on banknotes. The study proposes conceptual methodology together with empirical study and numerical analysis for Iran. At the following some of the most important suggestion have been presented. Introducing a 20000 rial new banknote, because between denomination 10000 rial and 500000 rail is empty space and this issue will be resulted to impress on the 10000 rial domination and a side effect more cost for central bank. The 10000 rial banknote should be change from banknote to coin And a 10000 rial new coin and after that 20000 rial must be introduced. 3-the average time for introducing new denomination in IRAN is 10 year and this time should be shorter. The speed of this process depend on inflation rate.