AN ALTERNATIVE PERSPECTIVE ON FUZZY SET-BASED APPROXIMATE REASONING

Abstract

On the subject of fuzzy set-based approximate reasoning, this paper attempts to present a perspective that is both rigorously stated and different from the standard approach as stated by Mamdani and many others. Functionally speaking, this alternative perspective produces results essentially the same as the standard one, and in fact we intend to prove that subject to certain assumptions the results will be exactly die same. We feel however that the alternative perspective offers advantages in that it makes a more appropriate and more understandable use of such concepts as fuzzy relations, the extension principle, and fuzzy composition. If indeed it can lead to a clearer and more widespread understanding of the approximate reasoning formalism then this could conceivably spark broader interest in fuzzy control and other applications.     

Multi-scale qualitative location: A direction-based model

Qualitative locations describe the locations of spatial objects by relating them to a reference frame with qualitative relations. Existing models concerned with regional partitions are mainly topology-based and do not consider the effects of scale changes on locations. This study develops a direction-based multi-scale qualitative location (DMQL) model to fill this gap. First, a cell partition is defined by extending the borders of the minimum bounding rectangles of the regions in a regional partition. Relating spatial objects to all regions by a set of directions is equal to representing the objects as a set of cells in a cell partition. Second, due to the multiple cell representations of spatial objects and the changes in direction relations across scales, some approaches are presented to derive the direction changes between regions in different frames, between spatial objects and regions, and between spatial objects at different scales. Third, the location and relation consistencies of qualitative locations are evaluated based on the cell representations of spatial objects at multiple scales through a case study. The results indicate that the DMQL model can locate objects more precisely than the topology-based models.     

The Politics of US Military Research in Greenland in the Early Cold War

The focus of this article is US military research in Greenland and its role in Danish‐American political relations in the early Cold War period 1945–1968. This was a period of intense US research activity that aimed to overcome the hostile Greenlandic environment and harness it for military purposes. In the US‐Danish defense agreement on Greenland of 1951 the USA got a free hand to develop three so‐called defense areas for military purposes, while it had to seek Danish permission for research and other activities outside these areas. The two partners had differing, but mainly compatible, interests in this process. The US interest was freedom to do research on the gigantic Greenland Icecap, while the Danish authorities emphasized the protection of its sovereignty over Greenland. The article follows the US research programs in the 1950s and 1960s and Danish responses in some detail, including the intriguing and still mysterious Camp Century project and its relationship with the US Army's Iceworm plan to deploy strategic missiles beneath the surface of the Greenland Icecap.     

Poly(vinyl alcohol) functionalization with aldehydes in organic solvents: Shining properties of poly(vinyl acetals)

Poly(vinyl alcohol) has been functionalized with aldehydes in tetrahydrofuran (THF) with a good control of the grafting. A wide library of poly(vinyl acetals) could be obtained in order to study some structure/property correlations. The influence of the aldehyde nature on the functionalization rates has been studied, in particular for optical properties by measurement of the shininess for further applications in the cosmetic field. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014 , 131, 40677.     

FUZZIFYING THE “PRECISE”

Based on the fuzzy-integral model, methods and algorithms are developed for identifying the “input–output” operator of continuous and stationary discrete extremal fuzzy dynamic systems (EFDS). The EFDS “input–output” operator is restored by means of experimental data with possibilistic uncertainty, the source of which is extremal fuzzy time intervals. The regularization conditions for obtaining quasi-optimal estimates are substantiated by the proved theorems. The corresponding algorithms are provided. The results obtained are illustrated by examples in the case of a finite set of EFDS states.     

An improved convergence analysis for the Newton–Kantorovich method using recurrence relations

We generate a sequence using the Newton–Kantorovich method in order to approximate a locally unique solution of an operator equation on a Banach space under Hölder continuity conditions. Using recurrence relations, Hölder as well as centre-Hölder continuity assumptions on the operator involved, we provide a semilocal convergence analysis with the following advantages over the elegant work by Hernánde? in (The Newton method for operators with Hölder continuous first derivative, J. Optim. Theory Appl. 109(3) (2001), pp. 631–648.) (under the same computational cost): finer error bounds on the distances involved, and a more precise information on the location of the solution. Our results also compare favourably with recent and relevant ones in (I.K. Argyros, Concerning the “terra incognita” between convergence regions of two Newton methods, Nonlinear Anal. 62 (2005), pp. 179–194; I.K. Argyros, Computational Theory of Iterative Methods, in Studies in Computational Mathematics, Vol. 15, C.K. Chui and L. Wuytack, eds., Elsevier Publ. Co., New York, USA, 2007; I.K. Argyros, On the gap between the semilocal convergence domain of two Newton methods, Appl. Math. 34(2) (2007), pp. 193–204; I.K. Argyros, On the convergence region of Newton's method under Hölder continuity conditions, submitted for publication; I.K. Argyros, Estimates on majorizing sequences in the Newton–Kantorovich method, submitted for publication; F. Cianciaruso and E. DePascale, Newton–Kantorovich approximations when the derivative is Hölderian: Old and new results, Numer. Funct. Anal. Optim. 24 (2003), pp. 713–723; F. Cianciaruso and E. DePascale, Estimates of majorizing sequences in the Newton–Kantorovich method, Numer. Funct. Anal. Optim. 27(5–6) (2006), pp. 529–538; F. Cianciaruso and E. DePascale, Estimates of majorizing sequences in the Newton–Kanorovich method: A further improvement, J. Math. Anal. Appl. 322 (2006), pp. 329–335; N.T. Demidovich, P.P. Zabreiko, and Ju.V. Lysenko, Some remarks on the Newton–Kantorovich mehtod for nonlinear equations with Hölder continuous linearizations, Izv. Akad. Nauk Belorus 3 (1993), pp. 22–26 (in Russian). (E. DePascale and P.P. Zabreiko, The convergence of the Newton–Kantorovich method under Vertgeim conditions, A new improvement, Z. Anal. Anwendvugen 17 (1998), pp. 271–280.) and (L.V. Kantorovich and G.P. Akilov, Functional Analysis in Normed Spaces, Pergamon Press, Oxford, 1982; J.V. Lysenko, Conditions for the convergence of the Newton–Kantorovich method for nonlinear equations with Hölder linearizations, Dokl. Akad. Nauk BSSR 38 (1994), pp. 20–24 (in Russian); B.A. Vertgeim, On some methods for the approximate solution of nonlinear functional equations in Banach spaces, Uspekhi Mat. Nauk 12 (1957), pp. 166–169 (in Russian); Amer. Math. Soc. Transl. 16 (1960), pp. 378–382. (English Trans.).)     

对实质蕴涵若干问题的思考

以实质蕴涵和逻辑蕴涵为对象,通过对郁慕镛教授和袁正校教授的观点进行比较,对逻辑学里的一个非常重要的概念——蕴涵进行了分析和讨论,澄清关于实质蕴涵和逻辑蕴涵的若干误解。     

UNIQUENESS CONDITIONS OF CL-STRUCTURES IN GL-STRUCTURE EQUIVALENCE CLASSES OF SYSTEM RECONSTRUCTABILITY ANALYSIS

This paper first introduces the basic notions of overall systems with logical relations, their subsystems, structure representation graphs, sets of H-structures and G-structures with logical relations S _H ^L and S _G ^L, immediate refinement and aggregate with logical relations, structure-graph mappings r_V ^L, r_G ^L, etc., and the notions of inclusiveness with logical relations, upper bounding and lower bounding with logical relations. Then it proves the sufficient conditions under which representation graphs R ^L form a lattice. By defining the least upper bound and largest lower bound of (R^L, ) and recommending a lemma on distributivity, this paper proves the sufficient conditions under which G-structures with logical relations form Boolean lattices. Finally after defining the M-structures and C-structures with logical relations, i.e. M-structures and C-structures, this paper proposes the sufficient conditions for the uniqueness of C-structures in G-structure equivalence classes, and proves that the C ^L-structure is the least refined GL-structure in equivalence class S _G ^L/r _G ^L.     

CHARACTERIZATION OF POLYMERS BY MEANS OF A STANDARD VISCOELASTIC MODEL AND FRACTIONAL DERIVATE CALCULUS

Polymeric materials are known to be more or less dispersive and absorptive. Dispersion has a consequence that the dynamic modulus is frequency dependent, and absorption is exhibited by the fact that these materials have the ability to absorb energy under vibratory motion. The phenomenon of dispersion in conjunction with the powerful notion of complex Modulus of Elasticity (MOE), permits to establish the relation between the real and the imaginary components of the MOE, that is, respectively the Storage and loss moduli. The loss factor is simply determined through taking the Ratio of these two MOE components. The theoretical background for the interrelations between the Storage modulus and the loss modulus is found in the Kramers-Kronig relations. However, due to the mathematical difficulties encountered in using the exact expressions of these relations, approximations are necessary for applications in practical situations. On the other hand, several simple models have been proposed to explain the viscoelastic behavior of materials, but all fail in giving a full account of the phenomenon. Among these models, the standard viscoelastic model, better known as the Zener model, is perhaps the most attractive. To improve the performance of this model, the concept of fractional derivates has been incorporated into it, which results in a four-parameter model. Applications have also shown the superiority of this model when theoretical predictions are compared to experimental data of different polymeric materials. The aim of this article is to present the results of applying this model to rubber, both natural and filled, and to some other selected more general polymer.