In this paper the chain length of a space of fuzzy orderings is defined, and various properties of this invariant are proved. The structure theorem for spaces of finite chain length is proved. Spaces of Fuzzy Orderings Throughout X = (X,A) denoted a space of fuzzy orderings. That is, A is a fuzzy subgroup of abelian group G of exponent 2. (see [1] (i.e. x 2 = 1,  x  G), and X is a (non empty) fuzzy subset of the character group ï£ (A) = Hom(A,{1,–1}) satisfying: 1. X is a fuzzy closed subset of ï£ (A). 2.  an element e  A such that ï³(e) = – 1  ï³ ïƒŽ X. 3. Xïž :={a  A\ ï³(a) = 1  ï³ ïƒŽ X} = 1. 4. If f and g are forms over A and if x  D( f  g) then  y  D( f ) and z  D(g) such that x  D<y, z >. Observe, by 3, that the element e  A whose existence is asserted by 2 is unique. Also, e  1 (since ï³(1) = 1  ï³ ïƒŽ X). Notice that for a  A, the set X(a):= {ï³ ïƒŽ Xï³(a) = 1} is clopen (i.e. both closed and open) in X. Moreover, ï³(a) = – 1  ï³(– a) = 1 holds for any ï³ ïƒŽ X (by 2).
The primary purpose of this paper is to introduce the, 2- coprobabilistic normed space, coprobabilistic dual space of 2- coprobabilistic normed space and give some facts that are related of them
The aims of the paper are to present a modified symmetric fuzzy approach to find the best workable compromise solution for quadratic fractional programming problems (QFPP) with fuzzy crisp in both the objective functions and the constraints. We introduced a modified symmetric fuzzy by proposing a procedure, that starts first by converting the quadratic fractional programming problems that exist in the objective functions to crisp numbers and then converts the linear function that exists in the constraints to crisp numbers. After that, we applied the fuzzy approach to determine the optimal solution for our quadratic fractional programming problem which is supported theoretically and practically. The computer application for the algo
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This work is concerned with designing two types of controllers, a PID and a Fuzzy PID, to be used
for flying and stabilizing a quadcopter. The designed controllers have been tuned, tested, and
compared using two performance indices which are the Integral Square Error (ISE) and the Integral
Absolute Error (IAE), and also some response characteristics like the rise time, overshoot, settling
time, and the steady state error. To try and test the controllers, a quadcopter mathematical model has
been developed. The model concentrated on the rotational dynamics of the quadcopter, i.e. the roll,
pitch, and yaw variables. The work has been simulated with “MATLAB”. To make testing the
simulated model and the controllers m
It is the dynamic tension between the relatively fixed built environment and the constantly changing in social life that determines the nature of urban spaces belonging to different historical periods, and considered as a tool for diagnosing transformations in urban spaces, that’s why, the characteristics of urban space became unclear between positive spaces and negative spaces, so emerged the need to study contemporary urban space belonging to the current period of time and show the most important transformations that have occurred in contemporary urban space to reach urban spaces that meet the current life requirements. Therefore, the research dealt with a study of the characteristics of contemporary urban space and the most pr
... Show MoreLet R be a commutative ring with identity. A proper ideal I of R is called semimaximal if I is a finite intersection of maximal ideals of R. In this paper we fuzzify this concept to fuzzy ideals of R, where a fuzzy ideal A of R is called semimaximal if A is a finite intersection of fuzzy maximal ideals. Various basic properties are given. Moreover some examples are given to illustrate this concept.
Let R be a commutative ring with unity. In this paper we introduce the notion of chained fuzzy modules as a generalization of chained modules. We investigate several characterizations and properties of this concept
Let R be a commutative ring with unity and an R-submodule N is called semimaximal if and only if
the sufficient conditions of F-submodules to be semimaximal .Also the concepts of (simple , semisimple) F- submodules and quotient F- modules are introduced and given some properties .
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In this paper we introduce the notion of semiprime fuzzy module as a generalization of semiprime module. We investigate several characterizations and properties of this concept.
Let R be a commutative ring with unity. In this paper we introduce and study fuzzy distributive modules and fuzzy arithmetical rings as generalizations of (ordinary) distributive modules and arithmetical ring. We give some basic properties about these concepts.
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