INTERVAL-VALUED REPRESENTABILITY OF QUALITATIVE DATA: THE CONTINUOUS CASE

2007 ◽  
Vol 15 (03) ◽  
pp. 299-319 ◽  
Author(s):  
GIANNI BOSI ◽  
MARIA JESÚS CAMPIÓN ◽  
JUAN CARLOS CANDEAL ◽  
ESTEBAN INDURÁIN
Keyword(s):  
Qualitative Data ◽  
Triangular Fuzzy Number ◽  
Continuous Case ◽  
Interval Order ◽  
Interval Orders ◽  
And Topology ◽  
Study Interval ◽  
Characteristic Interval ◽  
Interval Valued

In the framework of the representability of ordinal qualitative data by means of interval-valued correspondences, we study interval orders defined on a nonempty set X. We analyse the continuous case, that corresponds to a set endowed with a topology that furnishes an idea of continuity, so that it becomes natural to ask for the existence of quantifications based on interval-valued mappings from the set of data into the real numbers under preservation of order and topology. In the present paper we solve a continuous representability problem for interval orders. We furnish a characterization of the representability of an interval order through a pair of continuous real-valued functions so that each element in X has associated in a continuous manner a characteristic interval or equivalently a symmetric triangular fuzzy number.

scholarly journals Hereditary Semiorders and Enumeration of Semiorders by Dimension

10.37236/8140 ◽  
2020 ◽  
Vol 27 (1) ◽  
Author(s):  
Mitchel T. Keller ◽  
Stephen J. Young
Keyword(s):  
Generating Function ◽  
Generating Functions ◽  
Interval Order ◽  
Structural Description ◽  
Interval Orders ◽  
Structural Result ◽  
Forbidden Subposets ◽  
Open Question ◽  
Ascent Sequences

In 2010, Bousquet-Mélou et al. defined sequences of nonnegative integers called ascent sequences and showed that the ascent sequences of length $n$ are in one-to-one correspondence with the interval orders, i.e., the posets not containing the poset $\mathbf{2}+\mathbf{2}$. Through the use of generating functions, this provided an answer to the longstanding open question of enumerating the (unlabeled) interval orders. A semiorder is an interval order having a representation in which all intervals have the same length. In terms of forbidden subposets, the semiorders exclude $\mathbf{2}+\mathbf{2}$ and $\mathbf{1}+\mathbf{3}$. The number of unlabeled semiorders on $n$ points has long been known to be the $n$th Catalan number. However, describing the ascent sequences that correspond to the semiorders under the bijection of Bousquet-Mélou et al. has proved difficult. In this paper, we discuss a major part of the difficulty in this area: the ascent sequence corresponding to a semiorder may have an initial subsequence that corresponds to an interval order that is not a semiorder. We define the hereditary semiorders to be those corresponding to an ascent sequence for which every initial subsequence also corresponds to a semiorder. We provide a structural result that characterizes the hereditary semiorders and use this characterization to determine the ordinary generating function for hereditary semiorders. We also use our characterization of hereditary semiorders and the characterization of semiorders of dimension $3$ given by Rabinovitch to provide a structural description of the semiorders of dimension at most $2$. From this description, we are able to determine the ordinary generating function for the semiorders of dimension at most $2$.

scholarly journals From Academia to Start-up: A Case Study with Implications for Engineering Education

2014 ◽  
Vol 4 (1) ◽  
pp. 24
Author(s):  
Bill Williams ◽  
José Figueiredo
Keyword(s):  
Knowledge Production ◽  
Critical Analysis ◽  
Qualitative Data ◽  
Engineering Students ◽  
Role Play ◽  
Engineering Practice ◽  
Start Up ◽  
Mode 2

This study uses the characterization of contrasting modes of knowledge production to follow the activity of a group of engineers who migrated from an academic environment to a successful start-up firm. Qualitative data from interviews of two key members of the team were used to characterize their activities in the two settings. The authors relate the engineering practice described in the interviews to the Gibbons Mode 1 and Mode 2 knowledge production phases and note the importance of a phase change in the transition between the two modes. The resultant case-study contributes material for use in role-play activity with engineering students to help develop interdisciplinary skills. The study also presents a critical analysis to evaluate the merits of the Mode 1 and Mode 2 framework for analysis of engineering practice at the level of the firm.

scholarly journals STYLE AND SUBSTANCE: A QUALITATIVE CHARACTERIZATION OF DEMENTIA CAREGIVING MANAGEMENT STYLES

2019 ◽  
Vol 3 (Supplement_1) ◽  
pp. S594-S595
Author(s):  
Amanda N Leggett ◽  
Benjamin Bugajski ◽  
Breanna Webster ◽  
Brianna Broderick ◽  
Daphne Watkins ◽  
...  
Keyword(s):  
Lived Experience ◽  
Family Caregivers ◽  
Care Management ◽  
Qualitative Data ◽  
Management Style ◽  
Management Styles ◽  
Caregiver Interventions ◽  
Future Direction ◽  
Primary Family

Abstract Caring for a person living with dementia (PLWD) can take a physical and emotional toll, but understudied is the process of how family caregivers actually provide care (caregiver management styles). We interviewed 100 primary family caregivers regarding management of a recently experienced care challenge and values held which might impact care management decisions. Watkins’ (2017) rigorous and accelerated data reduction (RADaR) technique was used to analyze qualitative data through open/focused coding, determining commonalities of style components/themes, and finally defining caregiving management styles. Style for a given caregiver emerged from enacted care strategies, caregiver’s internal stances which informed their use of strategies, and broader engagement (or lack thereof) with the PLWD’s lived experience/reality. Styles emerging from the analysis will be described including the direct, rigid “Just do it” style, and the flexible, empathic “Teamwork” style. Individualizing caregiver interventions and supports based on caregiver management style is an important future direction.

Characterization of regular LA-semigroups by interval-valued $$(\overline{\alpha },\overline{\beta })$$ -fuzzy ideals

2013 ◽  
Vol 25 (3) ◽  
pp. 501-518 ◽  
Author(s):  
Muhammad Aslam ◽  
Saleem Abdullah ◽  
Samreen Aslam
Keyword(s):  
Interval Valued

scholarly journals A characterization of interval-valued residuated lattices

2008 ◽  
Vol 49 (2) ◽  
pp. 478-487 ◽  
Author(s):  
B. Van Gasse ◽  
C. Cornelis ◽  
G. Deschrijver ◽  
E.E. Kerre
Keyword(s):  
Residuated Lattices ◽  
Interval Valued

scholarly journals Characterization of the Geometry and Topology of DNA Pictured As a Discrete Collection of Atoms

2012 ◽  
Vol 8 (3) ◽  
pp. 1092-1107 ◽  
Author(s):  
Nicolas Clauvelin ◽  
Wilma K. Olson ◽  
Irwin Tobias
Keyword(s):  
And Topology

scholarly journals A characterization of normed M-spaces

1983 ◽  
Vol 24 (1) ◽  
pp. 89-92 ◽  
Author(s):  
Garfield C. Schmidt
Keyword(s):  
Linear Space ◽  
Linear Structure ◽  
Topological Spaces ◽  
Intrinsic Properties ◽  
Small Step ◽  
Linear Lattice ◽  
Linear Spaces ◽  
And Topology ◽  
Necessary And Sufficient

Linear spaces on which both an order and a topology are defined and related in various ways have been studied for some time now. Given an order on a linear space it is sometimes possible to define a useful topology using the order and linear structure. In this note we focus on a special type of space called a linear lattice and determine those lattice properties which are both necessary and sufficient for the existence of a classical norm, called an M-norm, for the lattice. This result is a small step in a program to determine which intrinsic order properties of an ordered linear space are necessary and sufficient for the existence of various given types of topologies for the space. This study parallels, in a certain sense, the study of purely topological spaces to determine intrinsic properties of a topology which make it metrizable and the study of the relation between order and topology on spaces which have no algebraic structure, or. algebraic structures other than a linear one.

scholarly journals Fuzzy Alexandrov Topologies Associated to Fuzzy Interval Orders

2020 ◽  
pp. 1-6
Author(s):  
Gianni Bosi ◽  
Chiaramaria Panozzo ◽  
Magal`ı Ernestine Zuanon
Keyword(s):  
Partial Order ◽  
Interval Order ◽  
Interval Orders ◽  
The Family ◽  
Fuzzy Interval

We characterize the fuzzy T0 - Alexandrov topologies on a crisp set X, which are associated to fuzzy interval orders R on X. In this way, we generalize a well known result by Rabinovitch (1978), according to which a crisp partial order is a crisp interval order if and only if the family of all the strict upper sections of the partial order is nested.

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