New Mathematics and Natural Computation

This paper presents a simple, hybrid two phase global optimization algorithm called DE-PSO for solving global optimization problems. DE-PSO consists of alternating phases of Differential Evolution (DE) and Particle Swarm Optimization (PSO). The algorithm is designed so as to preserve the strengths of both the algorithms. Empirical results show that the proposed DE-PSO is quite competent for solving the considered test functions as well as real life problems.

There are much more publications in open literature on the topic of linguistic variables as compared with Computing With Words (CWW). This paper intends to change that situation by demonstrating the feasibility of a working system. In order to accomplish this goal, a very focused example of an insurance evaluation system, no matter how rudimentary, is presented. Lotfi A. Zadeh has persistently stressed the importance of CWW for a contemporary society and he is absolutely right on target. We have proceeded our project, taking the advantage of the previously established works of Chen, Hsieh and Wang, such as linguistic logic, uncertainty numbers modeling, fuzzifications and defuzzifications schemes, etc. Basically, the Linguistic Evaluating System (LES), consists of Linguistic Descriptions Evaluating Algorithm (LDEA), Linguistic Descriptions Base (LDB), and Fuzzy Knowledge Base (FKB). The previously published works on linguistic methodology and linguistic logic make it possible to develop our LDEA. This main algorithm intends to appraise the linguistic descriptions based upon the newly proposed preferred evaluation rules. In addition, the measuring evaluations of the linguistic descriptions, which have been based on the innovative combination of different IF-THEN fuzzy rules, which in term has been based upon the use of the linguistic distance measurements, reflected the preference of a humane expert. If then, only then, the desired user friendly applications of the essential thrust of risk assessment required for insurance industry has been finally realized.

In this paper, we propose a wet lab algorithm for classification of SODAR data by DNA computing. The concept of DNA computing is essentially exploited to generate the classifier algorithm in the wet lab. The classifier is based on a new concept of similarity-based fuzzy reasoning suitable for wet lab implementation. This new concept of similarity-based fuzzy reasoning is different from conventional approach to fuzzy reasoning based on similarity measure and also replaces the logical aspect of classical fuzzy reasoning by DNA chemistry. Thus, we add a new dimension to the existing forms of fuzzy reasoning by bringing it down to nanoscale. We exploit the concept of massive parallelism of DNA computing by designing this new classifier in the wet lab. This newly designed classifier is very much generalized in nature and apart from SODAR data, this methodology can be applied to other types of data also. To achieve our goal we first fuzzify the given SODAR data in a form of synthetic DNA sequence which is called fuzzy DNA and which handles the vague concept of human reasoning. In the present approach, we can avoid the tedious choice of a suitable implication operator (for a particular operation) necessary for the classical approach to fuzzy reasoning based on fuzzy logic. We adopt the basic notion of DNA computing based on standard DNA operations. We consider double stranded DNA sequences, whereas, most of the existing models of DNA computation are based on single stranded DNA sequences. In the present model, we consider double stranded DNA sequences with a specific aim of measuring similarity between two DNA sequences. Such similarity measure is essential for designing the classifier in the wet lab. Note that, we have developed a completely new measure of similarity based on base pair difference which is absolutely different from the existing measure of similarity and which is very much suitable for expert system approach to classifier design, using DNA computing. In the present model of DNA computing, the end result of the wet lab algorithm produces multi valued status which can be linguistically interpreted to match the perception of an expert.

This paper deals with the validity in fuzzy logic of some classical schemes of reasoning, namely, with those of disjunctive reasoning, resolution, reductio ad absurdum, and the so-called constructive dilemma.

Using the idea of changing the basis-lattice, we investigate in this article the impact of change-of-basis to the notion of stratified lattice-valued generalized convergence group by the so-called functorial mechanism. We discuss here some of the subcategories of the category of stratified lattice-valued generalized convergence groups, such as, stratified lattice-valued Kent convergence groups, stratified lattice-valued limit groups, and look into the possible link between these objects with stratified lattice-valued neighborhood groups and stratified lattice-valued neighborhood topological groups when bases are changed. Moreover, with the help of the notion of stratified lattice-valued filter attributed to U. Höhle and A. Šostak, we introduce a category >HŠ-SL-FilGrp, of stratified lattice-valued filter groups, and study its relationship with other categories so far achieved in this paper.

In this paper, we define the notion of a mapping on soft classes and study several properties of images and inverse images of soft sets supported by examples and counterexamples. Finally, these notions have been applied to the problem of medical diagnosis in medical expert systems.

Plasmodium of Physarum polycephalum is a large single cell capable for distributed sensing, information processing, decentralized decision-making and collective action. In the paper, we interpret basic features of the plasmodium foraging behavior in terms of process calculus and spatial logic and show that this behavior could be regarded as one of the natural implementations of spatial logic without modal operators.

In this paper, the concept of intuitionistic fuzzy sets is applied to residuated lattices. The notion of intuitionistic fuzzy filters of a residuated lattice is introduced and some related properties are investigated. The characterizations of intuitionistic fuzzy filters are obtained. We show that the set of all the intuitionistic fuzzy filters of a residuated lattice forms a complete lattice and we find the distributive sublattices of it. Finally, the correspondence theorem for intuitionistic fuzzy filters is established.

As an emerging approach to explore the dynamics of voter preference, agent-based modeling (ABM) highlights new opportunities for intellectual exchange across disciplines, such as mathematics, political science, communication studies, and computer science. By aiming to contribute to cross-disciplinary communication for a better application of this approach, this paper summarizes what scholars have done about internal and external validation and presents a comparison between statistical analysis based on datasets generated in a laboratory and analysis based on corresponding empirical datasets. The results of the comparison suggest that, although there is no perfect matching, the comparison reveals some similarities in terms of increase or decrease in the proportion of different types of agents. This result further implies that an internally valid ABM model may lead to a certain level of external validity.

Rough set theory was originally proposed for analyzing data gathered in data tables, often referred to as information systems. The lower and upper approximations introduced within this theory are known as the very useful concepts. The theory as a whole now becomes a recognized foundation for granular computing. This paper investigates the rough set-based issues for analyzing table data with uncertainty. In reality, tables with non-deterministic information are focused on instead of tables with deterministic information, and several mathematical properties are examined. Especially, decision rule generation from tables with non-deterministic information is highlighted. This investigation is also applied to tables with uncertain numerical data. As a result, a new mathematical framework for analyzing tables with uncertain information is formalized.