in this paper‎, ‎we study some properties of analytic extension of a $n$th roots of $m$-hyponormal operator‎. ‎we show that every analytic extension of a $n$th roots of $m$-hyponormal operator is subscalar of order $2k+2n$‎. ‎as a consequence‎, ‎we get that if the spectrum of such operator $t$ has a nonempty interior in $mathbb{c}$‎, ‎then $t$ has a nontrivial invariant subspace‎. ‎finally‎, ‎w...

A sum of real numbers equals the mutual entropy of a fuzzy set and its complement set. A " fuzzy " or multivalued set is a point in a unit hypercube. Fuzzy mutual (Kullback) entropy arises from the logarithm of a unique measure of fuzziness. The proof uses the logistic map, a diffeomorphism that maps extended real space onto the fuzzy cube embedded in it. The logistic map equates the sum of a v...

Fuzzy numbers in number theory are a foundation of fuzzy sets and fuzzy mathematics that extend the domain of numbers from those of real numbers to fuzzy numbers. Fuzzy arithmetic is a system of fuzzy operations on fuzzy numbers. A theory of fuzzy arithmetic is presented towards a fuzzy mathematical structure for fuzzy inference and cognitive computation. The mathematical models of fuzzy number...

Some manipulations with vague quantities consist in an aggregation of vague amounts where the resulting aggregated quantity (in our case a sum of vague summands) is expected to be (almost) crisp. The aim of this contribution is to analyze and briefly discuss various approaches to this problem which can be supported by the elementary theory of fuzzy quantities. The analysis is focused on the pos...

Several approaches are followed in project scheduling under multiple resources. Typically, priorities for each activity are obtained using qualitative data. In this paper, both quantitative and qualitative data are considered in a fuzzy environment. A Fuzzy Analytical Hierarchy process is developed to obtain weightages for each activity that needs multiple resources. Fuzzy AHP efficiently handl...

When restricted to cost arrays possessing the sum Monge property, many combinatorial optimization problems with sum objective functions become signi cantly easier to solve. The more general algebraic assignment and transportation problems are similarly easier to solve given cost arrays possessing the corresponding algebraic Monge property. We show that Monge-array results for two sum-of-edge-co...

The principle of a complex interval-valued Pythagorean fuzzy set (CIVPFS) is valuable procedure to manage inconsistent and awkward information genuine life troubles. CIVPFS mixture the two separated theories such as which covers truth grade (TG) falsity (FG) in form number whose real unreal parts are sub-interval unit interval. superiority that sum square upper part (also for an part) duplet re...

  In order to have better insight of project characteristics, different kinds of fuzzy analysis for project networks have been recently proposed, most of which consider activities duration as the main and only source of imprecision and vagueness, but as it is usually experienced in real projects, the structure of the network is also subject to changes. In this paper we consider three types of i...

When restricted to cost arrays possessing the sum Monge property, many combinatorial optimization problems with sum objective functions become significantly easier to solve. The more general algebraic assignment and transportation problems are similarly easier to solve given cost arrays possessing the corresponding algebraic Monge property. We show that Monge-array results for two sum-of-edge-c...

—Let f be an interval-valued fuzzy subset of a nite set U of size n. This yields n closed intervals inside the unit interval. Picking a point in each interval and dividing by the sum of the points gives rise to a probability density on the set of intervals. For a given measure of dispersion, such as entropy, the problem is to pick points that maximize (or minimize) this dispersion. The particul...