In this work, we consider the Dirichlet boundary value problem for nonlinear Tihmonic equation. Due to the reduction of the problem to operator equation for the pair of tr: right hand function and the unknown second normal derivative of the function to be we design iterative method at both continuous and discrete levels for numerical solution problem. Some examples demonstrate that the numerical method is of fourth order convergeze. “hen the hand side function does not depend on the unknown function and its deritatives- numerical method gives more accurate results in comparison with the results obtained by the firefly: method Gudi and Neilan.

This paper is to present a novel model of estimating trustworthiness 6 a truster on a trustee based on experience trust and reputation trust from some community xvii: 131- context of user‘s topic interests. Firstly, we construct a measure of experience topic-21mm:-which isdefined as a function of degrees of interaction from a truster to some trustee and a ties-interests in topics. Secondly, we construct a measure of reliability degree of conic-.137: on some trustee by means of a function which is computed via degrees of reliability of truster members of the community and similarity of these members with the trustee. Thirdly. we propose a (imposition function for estimating an overal topic-aware trust based on experience topic—aware trust and the reputation topic-aware trust. Our experimental results show that the degree of experience topic- aware trust depends on interaction degree among truster and trustee more than on trustee‘s interest degree. They also indicate that the overall topic-aware trust estimation depends on reputation from community more than user’s own experience evaluation.

Instead of handling fuzzy sets associated with linguistic (L-) laltmis asset the devel—opers’ intuition immediately, the study follows the hedge algebras (HA-) approach to Lie- time seriesforecasting problems, in which the linguistic time series forecasting model was. for the first time.proposed and examined in 2020. It can handle the declared forecasting L—variabie word-set directly and, hence, the terminology linguistic time-series (LTS) is used instead of the fuzzy time-series (FTS). Instead of utilizing a limited number of fuzzy sets, this study views the L-variable under considera - tion as to the numeric forecasting variable’s human linguistic counterpart. Hence. its word—domain becomes potentially infinite to positively utilize the HA-approach formalism for increasing the LTS forecasting result exactness. Because the forecasting model proposed in this study can directly handle L—words. the LTS, constructed from the numeric time series and its L-relationship groups. Considered human knowledges of the given time—series variation helpful for the human-machine interface. The study shows that the proposed formalism can more easily handle the LTS forecasting models and increase their performance compared to the FTS forecasting models when the words‘ munher grows.

Many networks possess a community structure, such that nodes form densely 3; unified groups are more sparsely linked to other groups. In many cases, these groups overlap. with some nodes rat; between two or more communities. Overlapping node plays a role of interface between cormm. , and it is really interesting to study the community establishment of these it reflect the. dynamic behavior of participants. Nowadays, community identification a mining are the main directions in social network analysis. 111 this paper, we present an algorithm to find overlapping communities in “erg: Large social networks. The algorithm is based on the label propagation technique, and we find the overlapping communities in the network by improving the clustering coefficient. Tests on a set of popular- standard social networks and certain real networks have shown the high speed and high efficiency in finding overlapping cormnunities.

Pythagorean picture fuzzy set (PPFS) is a combination of Picture Fuzzy 5+1 and theYagcr‘s l"ythagorcan Fuzzy Set [12—14]. In the first part of the paper [17] we introduced some basic notions namely the set operators on PPFS. The missing part in our previous wort: is Fefining the extension of such the operators on the Spherical Fuzzy Sets toward applications of :ztitiaz'zribute group decision making problems. In this second part, we will tackle this issue and preset. some main operators on PPFS such as the picture negation operator, picture t—norm. picture picture implication operators on PPFS. Lastly, the compositional rule of inference in PPFS is presented accompanied with a numerical example.