This paper extends the author’s earlier work on the Law of Large Numbers for fuzzy numbers [2] to the case where the fuzzy numbers are of type L-R. Namely, we shall define a class of Archimedean triangular norms in which the equality lim n→∞ Nes(mn − ≤ ηn ≤ mn + = 1, for any > 0, holds for all sequences of fuzzy numbers, ξi = (Mi, α, β)LR, i ∈ N, with twice differentiable and concave shape func...

Traditionally, the classes in thematic maps have been treated as crisp sets, using classical set theory. In this formulation, map classes are assumed to be mutually exclusive and exhaustive. This approach limits the ability of thematic maps to represent the continuum of variation found in most landscapes. Substitution of fuzzy sets allows more  exibility for treatment of map classes in the are...

We introduce the fuzzy supersphere as sequence of finite-dimensional, noncommu-tative Z 2-graded algebras tending in a suitable limit to a dense subalgebra of the Z 2-graded algebra of H ∞-functions on the (2|2)-dimensional supersphere. Noncom-mutative analogues of the body map (to the (fuzzy) sphere) and the super-deRham complex are introduced. In particular we reproduce the equality of the su...

We introduce the fuzzy supersphere as sequence of nite-dimensional, noncommu-tative Z 2-graded algebras tending in a suitable limit to a dense subalgebra of the Z 2-graded algebra of H 1-functions on the (2j2)-dimensional supersphere. Noncom-mutative analogues of the body map (to the (fuzzy) sphere) and the super-deRham complex are introduced. In particular we reproduce the equality of the supe...

Two principal semantics have been assigned to the division of fuzzy relations. In the first one, the weights of the divisor are seen as thresholds and in the other, they act as grades of importance. This paper discusses a third approach in which the weights play the role of ideal values. In this context, the notion of a graded inclusion between (fuzzy) sets moves to that of a graded equality. I...

We introduce the fuzzy supersphere as sequence of finite-dimensional, noncommutative Z2-graded algebras tending in a suitable limit to a dense subalgebra of the Z2-graded algebra of H∞-functions on the (2|2)-dimensional supersphere. Noncommutative analogues of the body map (to the (fuzzy) sphere) and the super-deRham complex are introduced. In particular we reproduce the equality of the superde...

-This paper presents a new and simple fuzzy neural network based on structured fuzzy logic processors. The modifications of the referential fuzzy logic processors provide the equality index. The major advantage of the proposed network is that the learning process is faster and it has the capability of self -determining the relative cardinality. The fast learning is due to incorporating the rece...

Strict lower sections, strict upper sections and open order intervals (strict order intervals) are classical 9 notions associated to crisp orderings (crisp total preorders). In this paper, we extend these notions to fuzzy orderings. We determine all the fuzzy orderings (they contain all the crisp orderings) which make it possible 11 to compare two fuzzy strict lower sections and two fuzzy stric...

Rough set theory has attracted much attention in modeling with imprecise and incomplete information. A generalized approximation space, called fuzzy probability approximation space has been proposed by introducing probability into fuzzy approximation space. The novel definition combines three types of uncertainty into a model. Information or knowledge is considered as a partition of the univers...

in this paper we continue development of formal theory of a special class offuzzy logics, called eq-logics. unlike fuzzy logics being extensions of themtl-logic in which the basic connective is implication, the basic connective ineq-logics is equivalence. therefore, a new algebra of truth values calledeq-algebra was developed. this is a lower semilattice with top element endowed with two binary...