This paper introduces the concept of fuzzy σ-ring as a generalization of fuzzy σ-algebra and basic properties; examples of this concept have been given. As the first result, it has been proved that every σ-algebra over a fuzzy set x* is a fuzzy σ-ring-over a fuzzy set x* and construct their converse by example. Furthermore, the fuzzy ring concept has been studied to generalize fuzzy algebra and its relation. Investigating that the concept of fuzzy σ-Ring is a stronger form of a fuzzy ring that is every fuzzy σ-Ring over a fuzzy set x* is a fuzzy ring over a fuzzy set x* and construct their converse by example. In addition, the idea of the smallest, as an important property in the study of real analysis, is studied as well. Finally, the main goal of this paper is to study these concepts and give basic properties, examples, characterizations and relationships between them.
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.
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.
To investigate the research objectives, the researchers put the following hypothesis:
There was no statistically significant difference at the level of (0.05) between the average score of the students of the experimental group who studied the language of rhetoric according to model of learning method, and the average score of the students of the control group who studied the same article in the traditional way acquiring rhetorical concept. The researchers relied on the experimental design with the partial setting of the post-test, which depends on the experimental group that is taught using the model of the learning method, and the control group taught using the traditional method.
... Show MoreFinancial compensation contracts related to Hajj
The analysis of the orientations of Iraqi art commodification contributed to the discovery of deliberation, which was founded in the deliberative discourse in the trends towards commodification in the Iraqi art, since the important transformations in social structures and relations produced a dictionary with new vocabulary and tools that replaced the traditions and norms that have been in circulation for a century. Deliberation and commodification have become more prevalent in the mechanics and trends of the art where the pace of change is becoming increasingly frantic towards the market. The general market for art constitutes one of the most effective phenomena within contemporary art, that there has been a proliferation of sales auctio
... Show MoreIn this research, we prepared a hybrid composite material of polymeric matrix hand cast method, composite material has been attended from epoxy resin EP as matrix materials reinforced woven roving fiber jute is constant volume fraction (13%), PVC fibers and woven glass fiber with different fraction on the properties of prepared composite materials to PVC fiber and glass fiber, some of mechanical tests were done at room temperature (impact test and banding test). Result shows that the values of (modulus bending elastic and fracture toughness) increase fraction of fiber with the increase of PVC, E-glass, there include (thermal conductivity and dielectric constant). Also experimental result indicated that the (thermal conductivity and diele
... Show MoreBy condensation of benzaldehyde with thiourea in absolute ethanol in the presence of glacial acetic acid as a catalyst, the Schiff base(1-benzylidenethiourea)[I] was synthesized by synthesis of 4-(3-benzylidenethioureido)-4-thioxobut-2-enoic acid compound[II] by reaction of maleic anhydride with schiff base [I] in DMF. When treating compound [II] with ammonium persulfate (NH4)2S2O8 (APS) as an ethanol initiator to obtain polymer [III], compound [III] reacted to polymer [IV] with SOCl2 in benzene. Sulfamethizole, celecoxib, salbutamol, 4-aminoantipyrine to yield polymers [V-VIII], compound [IV] reaction with different drugs. Spectral evidence established the structure of synthesized co
This research included the preparation of 2-mercaptobenzoxazole (N1) by the reaction of ortho-aminophenol with carbon disulfide in an alcoholic potassium hydroxide solution. The 2-mercapto benzoxazole (N1) was then treated with hydrazine to obtain the 2-hydrazino benzoxazole (N2). A number of hydrazones (N3-N5) were prepared through the reaction of N2 with different benzaldehydes. The compound (N6) was also prepared whereby the ring closing of hydrazone (N3) using chloroacetylchloride, while the compound (N7) was prepared by treating 2-hydrazino benzoxazole with acetylacetone. When the compound (N1) was treated with formaldehyde, it afforded the compound (N8). Also, the N9 was obtained from the reaction of N1 with chloroacetic acid in th
... Show MoreInvestigation of mesomorphic properties of new 1,3,4-thiadiazolines (which are synthesised via many steps in Scheme 1) was carried out in this study. These compounds are designed to have a heterocyclic unit, a carboxylate linkage group and a polar ether chain at the end of the molecule adjacent to the benzene ring, which enhance the dipolar interactions forces (varied from one to eight carbons) to investigate the association properties of their phases. The structure of the target compounds and the intermediates were confirmed by 1H NMR, 13C NMR, mass and FTIR spectral techniques. Polarised microscopic studies revealed that all the compounds in the series exhibited enantiotropic liquid crystalline properties. This was further confirmed using
... Show MoreCompounds [II - [51 namely 2,5-(N,N'-diphenyldiamino) -1,3,4- oxadiazole [I], 2,5-(N,N'- diphenyl diamino) -1.3,4- thiadia:zole (2] ,4-
phenyl ·3-(N-phenyl amino)-5-hydroxy-1,2,4- triazolc [31 ,3,5-(N,N'Â
diphenyl diamino)-1 ,2,4- triazolc r4) and 4-phenyl -5-(N-phenyl arnino)-
3- th io l -1 ,2.4· triazole [5) are prepared and studied. Their electronic
spectra in different pH media and in dilferent solvents were studied. The lR spectrum of compounds [3) and [5] showed that these compounds are present in keto
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