Plenty of researches have been carried out, focusing on the measures of distance, similarity, and correlation between intuitionistic fuzzy sets (IFSs).However, most of them are single-valued measures and lack of potential for efficiency validation.In this paper, a new vector valued similarity measure for IFSs is proposed based on OWA operators.The vector is defined as a two-tuple consisting of ...

The concept of pseudo valuations on hoop-algebras is introduced, and then the relationship between pseudo-valuations filers investigated. Some conditions for a real-valued function to be valuation are provided. Finally, we prove fact that binary operations uniformly continuous based notion valuation.

The j-function acts as a parametrization of the classical modular curve. Its values at complex multiplication (CM) points are called singular moduli and are algebraic integers. A Shimura curve is a generalization of the modular curve and, if the Shimura curve has genus 0, a rational parameterizing function exists and when evaluated at a CM point is again algebraic over Q. This paper shows that ...

The Fefferman-Stein vector-valued maximal function inequality is proved for spaces of homogeneous type. The approach taken here is based on the theory of vector-valued Calderón-Zygmund singular integral theory in this context, which is appropriately developed.

We’re not interested in a function here or a function there. We’re interested in the collection of all functions to R or to C. Why are we interested in these? Functions describe lots of things. For example, a function on a “physical body” could be used to describe the temperature at every point on the body. Functions to R or C are scalar-valued: they have their image in a field. We are often in...

1. Topological Vector Spaces 1 1.1. The Krein-Milman theorem 7 2. Banach Algebras 11 2.1. Commutative Banach algebras 14 2.2. ∗–Algebras (over complexes) 17 2.3. Exercises 20 3. The Spectral Theorem 21 3.1. Problems on the Spectral Theorem (Multiplication Operator Form) 26 3.2. Integration with respect to a Projection Valued Measure 27 3.3. The Functional Calculus 34 4. Unbounded Operators 37 4...

Recent work has shown that in some cases the phase information of synaptic signal is important in the learning and representation capabilities of networks. Modelling such information with complex valued activation signals is possible, and indeed complex back-propagation algorithms have been derived 3]. Cliiord algebras give a way to generalise complex numbers to many dimensions. This paper pres...

Based on the Buşneag’s model ([2, 3, 4]), the notion of pseudovaluations (valuations) on a BE-algebra is introduced, and a pseudometric is induced by a pseudo-valuation on BE-algebras. Related properties are investigated, and conditions for a real-valued function on a BE-algebra to be a pseudo-valuation are discussed. Using the notion of (pseudo) valuation, we show that the binary operation in ...