On homomorphisms of fuzzy groups.
On injective -modules.
On Krull's intersection theorem of fuzzy ideals.
On -fuzzy ideals in semirings. I
In this paper we extend the concept of an -fuzzy (characteristic) left (resp. right) ideal of a ring to a semiring , and we show that each level left (resp. right) ideal of an -fuzzy left (resp. right) ideal of is characteristic iff is -fuzzy characteristic.
On -fuzzy ideals in semirings. II
We study some properties of -fuzzy left (right) ideals of a semiring related to level left (right) ideals.
On mean value in -quantum spaces
The paper deals with a new mathematical model for quantum mechanics based on the fuzzy set theory [1]. The indefinite integral of observables is defined and some basic properties of the integral are examined.
On Michálek's fuzzy topological spaces
The aim of this paper is to study some properties of Michálek’s fuzzy topology which are quite different of the classic properties of the Chang’s topology.
On practical problems with the explanation of the difference between possibility and probability
On properties of fuzzy left -ideals in hemirings with -norms.
On reverses of some binary operators
The notion of reverse of any binary operation on the unit interval is introduced. The properties of reverses of some binary operations are studied and some applications of reverses are indicated.
On sensible fuzzy ideals of BCK-algebras with respect to a t-conorm.
On some geometric transformation of t-norms.
Given a triangular norm T, its t-reverse T*, introduced by C. Kimberling (Publ. Math. Debrecen 20, 21-39, 1973) under the name invert, is studied. The question under which conditions we have T** = T is completely solved. The t-reverses of ordinal sums of t-norms are investigated and a complete description of continuous, self-reverse t-norms is given, leading to a new characterization of the continuous t-norms T such that the function G(x,y) = x + y - T(x,y) is a t-conorm, a problem originally studied...
On some isomorphisms of De Morgan algebras of fuzzy sets.
In this paper the classes of De Morgan algebras (P(X),∩,U,n) are studied. With respect to isomorphisms of such algebras, being P(X) the fuzzy sets on a universe X taking values in [0,1], U and ∩ the usual union and intersection given by max and min operations and n a proper complement.
On some kinds of fuzzy connected spaces
In this paper we introduce new results in fuzzy connected spaces. Among the results obtained we can mention the good extension of local connectedness. Also we prove that in a -fuzzy compact space the notions c-zero dimensional, strong c-zero dimensional and totally -disconnected are equivalent.
On some properties of -planes of type-2 fuzzy sets
Some basic properties of -planes of type-2 fuzzy sets are investigated and discussed in connection with the similar properties of -cuts of type-1 fuzzy sets. It is known, that standard intersection and standard union of type-1 fuzzy sets (it means intersection and union under minimum t-norm and maximum t-conorm, respectively) are the only cutworthy operations for type-1 fuzzy sets. Recently, a similar property was declared to be true also for -planes of type-2 fuzzy sets in a few papers. Thus,...
On somewhat fuzzy semicontinuous functions
In this paper the concept of somewhat fuzzy semicontinuous functions, somewhat fuzzy semiopen functions are introduced and studied. Besides giving characterizations of these functions, several interesting properties of these functions are also given. More examples are given to illustrate the concepts introduced in this paper.
On the additivity of the cardinalities of fuzzy sets of type II.
In this short note we show that for fuzzy sets of type II the additive rule for cardinalities holds true. The proof of this result requires an application of approximate reasoning as means of inference by use of the entailment principle.
On the central limit theorem on IFS-events.
A probability theory on IFS-events has been constructed in [3], and axiomatically characterized in [4]. Here using a general system of axioms it is shown that any probability on IFS-events can be decomposed onto two probabilities on a Lukasiewicz tribe, hence some known results from [5], [6] can be used also for IFS-sets. As an application of the approach a variant of Central limit theorem is presented.
On the construction of t-norms (t-conorms) by using interior (closure) operator on bounded lattices
Recently, the topic of construction methods for triangular norms (triangular conorms), uninorms, nullnorms, etc. has been studied widely. In this paper, we propose construction methods for triangular norms (t-norms) and triangular conorms (t-conorms) on bounded lattices by using interior and closure operators, respectively. Thus, we obtain some proposed methods given by Ertuğrul, Karaçal, Mesiar [15] and Çaylı [8] as results. Also, we give some illustrative examples. Finally, we conclude that the...
On the constructions of t-norms and t-conorms on some special classes of bounded lattices
Recently, the topic related to the construction of triangular norms and triangular conorms on bounded lattices using ordinal sums has been extensively studied. In this paper, we introduce a new ordinal sum construction of triangular norms and triangular conorms on an appropriate bounded lattice. Also, we give some illustrative examples for clarity. Then, we show that a new construction method can be generalized by induction to a modified ordinal sum for triangular norms and triangular conorms on...