scholarly journals A Functional Representation Model Facilitating Design Space Expansion

2013 ◽  
Vol 2013 ◽  
pp. 1-15
Author(s):  
Wei Xu ◽  
Ke Zhao ◽  
Yatao Li ◽  
Peitao Cheng

This paper addresses the functional representation based on the event model. In the event model, the ontology is defined based on the theory of propositional logic to describe the connotation of the event, and the variant is defined based on the theories of domain relational calculus and set theory to express the variation range of the event, which is alterable part of the event under the constraints of the ontology. Function is an important concept in conceptual design and has its connotation and extension. The functional representation is proposed based on the event model. The ontology of event is used to describe the connotation of function and to reflect the stability of function. The variant of the event is used to represent the extension and to incarnate the variety of function. The extension of function is the change range of function under the constraints of the connotation. The proposed functional representation divides the function into the immutable part and the alterable part, facilitating the expansion of design space. A functional reasoning model is also put forward based on the event model to support the function reasoning on the computers. Finally, a simple case validates the feasibility of the model.

1975 ◽  
Vol 4 (2) ◽  
Author(s):  
Bruno Meile

AbstractThe author tries to establish a formal-descriptive model for group-dynamic concepts in related logical terms and set theory. Cybernetics form the basic frame of reference. Herewith some fundamental principles such as ‘group’, ‘group structure’ and ‘change of group structure’ are defined exactly. - The consequences for empirical group research are shown by some examples: (1) a possible way out of the ‘methodological dilemma’ in sociometry,(2) a design for empirical description of the changes in group structure, (3) the formalization of a group-dynamic theorem, whereby groups of friends form according to the principle of individuals who share the same attributes. (4) The reshaping of the theorem allows the deduction of exact terminological hypotheses. New hypotheses, concerning the stability of group structure, can be gained through consideration of the cybernetic implications.


Pragmatics ◽  
2006 ◽  
Vol 16 (1) ◽  
pp. 103-138 ◽  
Author(s):  
Pieter A.M. Seuren

This paper aims at an explanation of the discrepancies between natural intuitions and standard logic in terms of a distinction between NATURAL and CONSTRUCTED levels of cognition, applied to the way human cognition deals with sets. NATURAL SET THEORY (NST) restricts standard set theory cutting it down to naturalness. The restrictions are then translated into a theory of natural logic. The predicate logic resulting from these restrictions turns out to be that proposed in Hamilton (1860) and Jespersen (1917). Since, in this logic, NO is a quantifier in its own right, different from NOT-SOME, and given the assumption that natural lexicalization processes occur at the level of basic naturalness, single-morpheme lexicalizations for NOT-ALL should not occur, just as there is no single-morpheme lexicalization for NOT-SOME at that level. An analogous argument is developed for the systematic absence of lexicalizations for NOT-AND in propositional logic.


Author(s):  
Claudius Wagemann

Qualitative Comparative Analysis (QCA) is a method, developed by the American social scientist Charles C. Ragin since the 1980s, which has had since then great and ever-increasing success in research applications in various political science subdisciplines and teaching programs. It counts as a broadly recognized addition to the methodological spectrum of political science. QCA is based on set theory. Set theory models “if … then” hypotheses in a way that they can be interpreted as sufficient or necessary conditions. QCA differentiates between crisp sets in which cases can only be full members or not, while fuzzy sets allow for degrees of membership. With fuzzy sets it is, for example, possible to distinguish highly developed democracies from less developed democracies that, nevertheless, are rather democracies than not. This means that fuzzy sets account for differences in degree without giving up the differences in kind. In the end, QCA produces configurational statements that acknowledge that conditions usually appear in conjunction and that there can be more than one conjunction that implies an outcome (equifinality). There is a strong emphasis on a case-oriented perspective. QCA is usually (but not exclusively) applied in y-centered research designs. A standardized algorithm has been developed and implemented in various software packages that takes into account the complexity of the social world surrounding us, also acknowledging the fact that not every theoretically possible variation of explanatory factors also exists empirically. Parameters of fit, such as consistency and coverage, help to evaluate how well the chosen explanatory factors account for the outcome to be explained. There is also a range of graphical tools that help to illustrate the results of a QCA. Set theory goes well beyond an application in QCA, but QCA is certainly its most prominent variant. There is a very lively QCA community that currently deals with the following aspects: the establishment of a code of standards for QCA applications; QCA as part of mixed-methods designs, such as combinations of QCA and statistical analyses, or a sequence of QCA and (comparative) case studies (via, e.g., process tracing); the inclusion of time aspects into QCA; Coincidence Analysis (CNA, where an a priori decision on which is the explanatory factor and which the condition is not taken) as an alternative to the use of the Quine-McCluskey algorithm; the stability of results; the software development; and the more general question whether QCA development activities should rather target research design or technical issues. From this, a methodological agenda can be derived that asks for the relationship between QCA and quantitative techniques, case study methods, and interpretive methods, but also for increased efforts in reaching a shared understanding of the mission of QCA.


2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Fuxing Yang ◽  
Leilei Zhao ◽  
Yuewei Yu ◽  
Changcheng Zhou

To improve comfort, a nonlinear suspension system is proposed on the basis of the nonlinear vibration isolation theory and the installation space of the cab suspension system for trucks. This system is suitable for all-floating cabs. For easy matching and design, the static and stability characteristics of the suspension system were analyzed, respectively, and the boundary condition for the stability of the system was given. Moreover, the cab simulation model was established, and the dynamic simulation was conducted. The stability analysis shows that the smaller the vibration excitation of the cab system, the higher its stability is. The dynamic simulation results show that the acceleration of the cab with the nonlinear suspension system is effectively suppressed; the dynamic deflection of the suspension is kept within a certain range, and the design space of the suspension stroke can be effectively utilized. Compared with the traditional linear suspension system, the nonlinear suspension system has better vibration isolation characteristics and can effectively improve ride comfort.


1992 ◽  
Vol 34 (3) ◽  
pp. 301-307 ◽  
Author(s):  
L. P. Belluce ◽  
A. Di Nola ◽  
A. Lettieri

MV-algebras were introduced by C. C. Chang [3] in 1958 in order to provide an algebraic proof for the completeness theorem of the Lukasiewicz infinite valued propositional logic. In recent years the scope of applications of MV-algebras has been extended to lattice-ordered abelian groups, AF C*-algebras [10] and fuzzy set theory [1].


2021 ◽  
Vol 1 ◽  
pp. 691-700
Author(s):  
Marija Majda Perisic ◽  
Mario Štorga ◽  
John S. Gero

AbstractWhen observing a design space expansion during teamwork, several studies found that cumulative solution-related issues' occurrence follows a linear trend. Such findings contradict the hypothesis of solution-related issues being characteristic for the later design stages. This work relies on agent-based simulations to explore the emerging patterns in design solution space expansion during teamwork. The results demonstrate trends that accord with the empirical findings, suggesting that a cognitive effort in solution space expansion remains constant throughout a design session. The collected data on agents' cognitive processes and solution space properties enabled additional insights, which led to the detection of four distinct regimes of design solution space expansion.


2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Xiongrui Wang ◽  
Ruofeng Rao ◽  
Shouming Zhong

Linear matrices inequalities (LMIs) method and the contraction mapping theorem were employed to prove the existence of globally exponentially stable trivial solution for impulsive Cohen-Grossberg neural networks (CGNNs). It is worth mentioning that it is the first time to use the contraction mapping theorem to prove the stability for CGNNs while only the Leray-Schauder fixed point theorem was applied in previous related literature. An example is given to illustrate the effectiveness of the proposed methods due to the large allowable variation range of impulse.


Filomat ◽  
2015 ◽  
Vol 29 (5) ◽  
pp. 1137-1148 ◽  
Author(s):  
Reza Saadati ◽  
Yeol Cho ◽  
John Rassias

In this paper, we establish the stability result for the k-cubic functional equation 2[kf (x+ky)+f (kx-y)]=k(k2+1)[f(x+y)+f(x-y)] + 2(k4-1) f(y), where k is a real number different from 0 and 1, in the setting of various L-fuzzy normed spaces that in turn generalize a Hyers-Ulam stability result in the framework of classical normed spaces. First we shall prove the stability of k-cubic functional equations in the L-fuzzy normed space under arbitrary t-norm which generalizes previous works. Then we prove the stability of k-cubic functional equations in the non- Archimedean L-fuzzy normed space. We therefore provide a link among different disciplines: fuzzy set theory, lattice theory, non-Archimedean spaces and mathematical analysis.


2021 ◽  
Author(s):  
Vasil Dinev Penchev

The paper investigates the understanding of quantum indistinguishability afterquantum information in comparison with the “classical” quantum mechanics based on theseparable complex Hilbert space. The two oppositions, correspondingly “distinguishability/ indistinguishability” and “classical / quantum”, available implicitly in the concept of quantumindistinguishability can be interpreted as two “missing” bits of classical information, whichare to be added after teleportation of quantum information to be restored the initial stateunambiguously. That new understanding of quantum indistinguishability is linked to thedistinction of classical (Maxwell-Boltzmann) versus quantum (either Fermi-Dirac orBose-Einstein) statistics. The latter can be generalized to classes of wave functions (“empty” qubits) and represented exhaustively in Hilbert arithmetic therefore connectible to the foundations of mathematics, more precisely, to the interrelations of propositional logic and set theory sharing the structure of Boolean algebra and two anti-isometric copies of Peano arithmetic.


Author(s):  
Zequn Wang ◽  
Narendra Patwardhan

Abstract Despite the numerous advances, reinforcement learning remains away from widespread acceptance for autonomous controller design as compared to classical methods due to lack of ability to effectively tackle uncertainty. The reliance on absolute or deterministic reward as a metric for optimization process renders reinforcement learning highly susceptible to changes in problem dynamics. We introduce a novel framework that effectively quantify the uncertainty in the design space and induces robustness in controllers by switching to a reliability-based optimization routine. A model-based approach is used to improve the data efficiency of the method while predicting the system dynamics. We prove the stability of learned neuro-controllers in both static and dynamic environments on classical reinforcement learning tasks such as Cart Pole balancing and Inverted Pendulum.


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