LR fuzzy numbers are quite common in real world applications involving the triangular fuzzy number, the Gaussian fuzzy number, and the Cauchy fuzzy number as special cases. In this paper, we first prove that a fuzzy number is an LR fuzzy number if and only if its credibility distribution is strictly increasing. After that, based on credibility measure, an operational law on independent LR fuzzy...

LI, PINGKE. Fuzzy Relational Equations: Resolution and Optimization. (Under the direction of Professor Shu-Cherng Fang). Fuzzy relational equations play an important role as a platform in various applications of fuzzy sets and systems. The resolution and optimization of fuzzy relational equations are of our particular interests from both of the theoretical and applicational viewpoints. In this ...

The aim of this paper is to study a comprehensive dynamics system called fractional fuzzy differential variational inequality, which composed nonlinear equation with Atangana-Baleanu derivative and time-dependent inequality. We explore an existence uniqueness theorem for the under consideration. Our proof based on F-KKM theorem, Banach fixed point principle, theory monotone operators.

We study the convergence of maximal monotone operators with the help of representations by convex functions. In particular, we prove the convergence of a sequence of sums of maximal monotone operators under a general qualification condition of the Attouch–Brezis type.

This paper studies sequence prediction based on the monotone Kolmogorov complexity Km=−logm, i.e. based on universal deterministic/one-part MDL. m is extremely close to Solomonoff’s prior M , the latter being an excellent predictor in deterministic as well as probabilistic environments, where performance is measured in terms of convergence of posteriors or losses. Despite this closeness to M , ...

We show that the sequence ? jIm(z n)j is never monotone when z is a non-real complex number, and ? jRe(z n)j is never monotone, unless z = re ii , where = k m for some odd m, and r is suuciently large or suuciently small. Similar results hold for the length of the projection of z n onto any line through the origin. The purpose of this note is to prove a simple, amusing and apparently new applic...

For any lacunary sequence $theta = (k_{r})$, we define the concepts of $S_{theta}-$limit point and $S_{theta}-$cluster point of a sequence of fuzzy numbers $X = (X_{k})$. We introduce the new sets  $Lambda^{F}_{S_{theta}}(X)$, $Gamma^{F}_{S_{theta}}(X)$ and prove some inclusion relaions between these and the sets $Lambda^{F}_{S}(X)$, $Gamma^{F}_{S}(X)$ introduced in ~cite{Ayt:Slpsfn} by Aytar [...

A sequence of positive integers a1 ≤ a2 ≤ . . . ≤ an is called an ascending monotone wave of length n, if ai+1−ai ≥ ai−ai−1 for i = 2, . . . , n−1. If ai+1−ai > ai−ai−1 for all i = 2, . . . , n−1 the sequence is called an ascending strong monotone wave of length n. Let Zk denote the cyclic group of order k. If k | n, then we define MW (n,Zk) as the least integer m such that for any coloring f :...