A non-polynomial spline (NPS) is an approximation method that relies on the triangular and polynomial parts, so the method has infinite derivatives of the triangular part of the NPS to compensate for the loss of smoothness inherited by the polynomial. In this paper, we propose polynomial-free linear and quadratic spline types to solve fuzzy Volterra integral equations (FVIE) of the 2nd kind with the weakly singular kernel (FVIEWSK) and Abel's type kernel. The linear type algorithm gives four parameters to form a linear spline. In comparison, the quadratic type algorithm gives five parameters to create a quadratic spline, which is more of a credit for the exact solution. These algorithms process kernel singularities with a simple techniqu

    The attribute quality control charts are one of the main useful tools to use in control of quality product in companies. In this paper utilizing the statistical procedures to find the attribute quality control charts for through fuzzified the real data which we got it from Baghdad Soft Drink Company in Iraq, by using triangular membership function to obtain the fuzzy numbers then employing the proposed ranking function to transform to traditional sample. Then, compare between crisp and fuzzy attribute quality control.

In this research two algorithms are applied, the first is Fuzzy C Means (FCM) algorithm and the second is hard K means (HKM) algorithm to know which of them is better than the others these two algorithms are applied on a set of data collected  from the Ministry of Planning on the water turbidity of five areas in Baghdad to know which of these areas are less turbid in clear water to see which months during the year are less turbid in clear water in the specified area.

In this paper the concept of (m, n)- fully stable Banach Algebra-module relative to ideal (F − (m, n) − S − B − A-module relative to ideal) is introducing, we study some properties of F − (m, n) − S − B − A-module relative to ideal and another characterization is given

Abstract

The traffic jams taking place in the cities of the Republic of Iraq in general and the province of Diwaniyah especially, causes return to the large numbers of the modern vehicles that have been imported in the last ten years and the lack of omission for old vehicles in the province, resulting in the accumulation of a large number of vehicles that exceed the capacity of the city's streets, all these reasons combined led to traffic congestion clear at the time of the beginning of work in the morning, So researchers chose local area network of the main roads of the province of Diwaniyah, which is considered the most important in terms of traffic congestion, it was identified  fuzzy numbers for

In this paper, we introduce the concept of almost Quasi-Frobcnius fuzzy ring as a " " of Quasi-Frobenius ring. We give some properties about this concept with qoutient fuzzy ring. Also, we study the fuzzy external direct sum of fuzzy rings.

     In this paper, we study a new concept of fuzzy sub-module, called  fuzzy socle semi-prime sub-module that is a generalization the concept of semi-prime fuzzy sub-module and fuzzy of approximately semi-prime sub-module in the ordinary sense.  This leads us to introduce level property which studies the relation between the ordinary and fuzzy sense of approximately semi-prime sub-module. Also, some of its characteristics and notions such as the intersection, image and external direct sum of fuzzy socle semi-prime sub-modules are introduced. Furthermore, the relation between the fuzzy socle semi-prime sub-module and other types of fuzzy sub-module presented.

 In this paper, we introduce three robust fuzzy estimators of a location parameter based on Buckley’s approach, in the presence of outliers. These estimates were compared using the variance of fuzzy numbers criterion, all these estimates were best of Buckley’s estimate. of these, the fuzzy median was the best in the case of small and medium sample size, and in large sample size, the fuzzy trimmed mean was the best.