It is well known that the fuzzy sets theory can be successfully used in quantum models ([5, 26]). In this paper we give first a review of recent development in the probability theory on tribes and their generalizations – multivalued (MV)-algebras. Secondly we show some applications of the described method to develop probability theory on IF-events.
In this paper we examine discrete functions that depend on their variables in a particular way, namely the H-functions. The results obtained in this work make the “construction” of these functions possible. H-functions are generalized, as well as their matrix representation by Latin hypercubes.
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...
We give some structures without quantifier elimination but in which the closure, and hence the interior and the boundary, of a quantifier free definable set is also a quantifier free definable set.
This paper is devoted to characterize monotonicity, conditionality and transitivity of some rational relations defined in a probabilized Boolean Algebra.
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.
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.
Let R be a real closed field, and denote by the ring of germs, at the origin of Rⁿ, of functions in a neighborhood of 0 ∈ Rⁿ. For each n ∈ ℕ, we construct a quasianalytic subring with some natural properties. We prove that, for each n ∈ ℕ, is a noetherian ring and if R = ℝ (the field of real numbers), then , where ₙ is the ring of germs, at the origin of ℝⁿ, of real analytic functions. Finally, we prove the Real Nullstellensatz and solve Hilbert’s 17th Problem for the ring .
We present a negative answer to problem 3.7(b) posed on page 193 of [2], where, in fact, A. Rosłanowski asked: Does every set of Lebesgue measure zero belong to some Mycielski ideal?
A language grounding problem is considered for nonuniform sets of modal conjunctions consisting of conjunctions extended with more than one modal operator of knowledge, belief or possibility. The grounding is considered in the context of semiotic triangles built from language symbols, communicative cognitive agents and external objects. The communicative cognitive agents are assumed to be able to observe external worlds and store the results of observations in internal knowledge bases. It is assumed...
We introduce new properties of Hamel bases. We show that it is consistent with ZFC that such Hamel bases exist. Under the assumption that there exists a Hamel basis with one of these properties we construct a discontinuous and additive function that is Marczewski measurable. Moreover, we show that such a function can additionally have the intermediate value property (and even be an extendable function). Finally, we examine sums and limits of such functions.