Analytical structure for a fuzzy PID controller is introduced by employing two fuzzy sets for each of the three input variables and four fuzzy sets for the output variable. This structure is derived via left and right trapezoidal membership functions for inputs, trapezoidal membership functions for output, algebraic product triangular norm, bounded sum triangular co-norm, Mamdani minimum infere...

in the present paper, we rst modify the concepts of weakly fuzzy boundedness, strongly fuzzy boundedness, fuzzy continuity, strongly fuzzy continuity and weakly fuzzy continuity. then, we try to nd some relations by making a comparative study of the fuzzy norms of linear operators.

Fuzzy best simultaneous approximation of a finite number of functions is considered. For this purpose, a fuzzy norm on $Cleft (X, Y right )$ and its fuzzy dual space and also the  set of subgradients of a fuzzy norm are introduced. Necessary case of a proved theorem about characterization of simultaneous approximation will be extended to the fuzzy case.

This paper reveals the analytical structure of a fuzzy twoterm (PI/PD) controller which employs N1 (≥3) number of symmetric fuzzy sets for the input variable ‘displacement’, N2 (≥3) number of symmetric fuzzy sets for the input variable ‘velocity’ and N1+N2-1 number of symmetric fuzzy sets for the output variable ‘controller output’. The analytical structures are derived via triangular membershi...

In the present paper, we investigate a connection between two fuzzy inner product one of which arises from Felbin's fuzzy norm and the other is based on Bag and Samanta's fuzzy norm. Also we show that, considering a fuzzy inner product space, how one can construct another kind of fuzzy inner product on this space.

in a fuzzy metric space (x;m; *), where * is a continuous t-norm,a locally fuzzy contraction mapping is de ned. it is proved that any locally fuzzy contraction mapping is a global fuzzy contractive. also, if f satis es the locally fuzzy contractivity condition then it satis es the global fuzzy contrac-tivity condition.

in this paper, we introduce the notion of an action $y_x$as a generalization of the notion of a module,and the notion of a norm $vt: y_xto f$, where $f$ is a field and $vartriangle(xy)vartriangle(y') =$ $ vartriangle(y)vartriangle(xy')$ as well as the notion of fuzzy norm, where $vt: y_xto [0, 1]subseteq {bf r}$, with $bf r$  the set of all real numbers. a great many standard mappings on algebr...

As a generalization of fuzzy sets , Atanassov [14] introduced and studied the concept of intuitionistic fuzzy sets park[11] using the idea of intuitionistic fuzzy sets defined the notion of intuionistic fuzzy metric spaces with the help of continuous t-norm and continuous t co-norm as a generalization of fuzzy metric space due to George & veeramani [6] had showed that every metric induces an in...