In this paper, the definition of fuzzy anti-inner product in a linear space is introduced. Some results of fuzzy anti-inner product spaces are given, such as the relation between fuzzy inner product space and fuzzy anti-inner product. The notion of minimizing vector is introduced in fuzzy anti-inner product settings.

        In this paper, an estimate has been made for parameters and the reliability function for Transmuted power function (TPF) distribution through using some estimation methods as proposed new technique for white, percentile, least square, weighted least square and modification moment methods. A simulation was used to generate random data that follow the (TPF) distribution on three experiments (E₁ , E₂ , E₃)  of the real values of the parameters, and with sample size (n=10,25,50 and 100) and iteration samples (N=1000), and taking reliability times (0< t < 0) . Comparisons have been made between the obtained results from the estimators using mean square error (MSE). The results showed the

In this paper, a new seven-parameter Mittag-Leffler function of a single com-plex variable is proposed as a generalization of the standard Mittag-Leffler function, certain generalizations of Mittag-Leffler function, hypergeometric function and confluent hypergeometric function. Certain essential analytic properties are mainly discussed, such as radius of convergence, order, type, differentiation, Mellin-Barnes integral representation and Euler transform in the complex plane. Its relation to Fox-Wright function and H-function is also developed.

     We introduce and discuss the modern type of fibrewise topological spaces, namely fibrewise fuzzy topological spaces. Also, we introduce the concepts of fibrewise closed fuzzy topological spaces, fibrewise open fuzzy topological spaces, fibrewise locally sliceable fuzzy topological spaces and fibrewise locally sectionable fuzzy topological spaces. Furthermore, we state and prove several theorems concerning these concepts.

Fuzzy measures are considered important tools to solve many environmental problems. Water pollution is one of the environmental problems, which has negatively effect on the health of consumers. In this paper, a mathematical model is proposed to evaluate water quality in the distribution networks of Baghdad city. Fuzzy logic and fuzzy measures have been applied to evaluate water quality with respect to chemical and microbiological contaminants. Our results are evaluate water pollution of some chemical and microbiological contaminants, which are difficult to evaluation through traditional methods.

The fuzzy sets theory has been applied in many fields, such as operations research, control theory and management sciences, etc. In particular, an application of this theory in decision making problem is linear programming problems with fuzzy technological coefficients numbers, as well as studying the parametric linear programming problems in the case of changes in the objective function. In this paper presenting a new procedure which connects and makes link between fuzzy linear programming problem with fuzzy technological coefficients numbers and parametric linear programming problem with change in coefficients of the objective function, then develop a numerical example illustrates the steps of solution to this kind of problems.

An adaptive fuzzy weighted linear regression model in which the output is based
on the position and entropy of quadruple fuzzy numbers had dealt with. The solution
of the adaptive models is established in terms of the iterative fuzzy least squares by
introducing a new suitable metric which takes into account the types of the influence
of different imprecisions. Furthermore, the applicability of the model is made by
attempting to estimate the fuzzy infant mortality rate in Iraq using a selective set of
inputs.

     In the complex field, special functions are closely related to geometric holomorphic functions. Koebe function is a notable contribution to the study of the geometric function theory (GFT), which is a univalent function. This sequel introduces a new class that includes a more general Koebe function which is holomorphic in a complex domain. The purpose of this work is to present a new operator correlated with GFT. A new generalized Koebe operator is proposed in terms of the convolution principle. This Koebe operator refers to the generality of a prominent differential operator, namely the Ruscheweyh operator. Theoretical investigations in this effort lead to a number of implementations in the subordination function theory. The ti

In this paper, we study the effect of group homomorphism on the chain of level subgroups of fuzzy groups. We prove a necessary and sufficient conditions under which the chains of level subgroups of homomorphic images of an a arbitrary fuzzy group can be obtained from that of the fuzzy groups . Also, we find the chains of level subgroups of homomorphic images and pre-images of arbitrary fuzzy groups

      The objective of this research is employ the special cases of  function  trapezoid in the composition of fuzzy sets to make decision within the framework of the theory of games traditional to determine the best strategy for the mobile phone networks in the province of  Baghdad and Basra, has been the adoption of different periods of the  functions belonging to see the change happening in the matrix matches and the impact  that the strategies  and decision-making  available to each player and the impact on  societ