46,734 research outputs found
Modeling group assessments by means of hesitant fuzzy linguistic term sets
Hesitant linguistic term sets have been introduced to capture the human way of reasoning using linguistic expressions involving different levels of precision. In this paper, a lattice structure is provided to the set of hesitant fuzzy linguistic term sets by means of the operations intersection and connected union. In addition, in a group decision making framework, hesitant fuzzy linguistic descriptions are defined to manage situations in which decision makers are assessing different alternatives by means of hesitant fuzzy linguistic term sets. Based on the introduced lattice structure, two distances between hesitant fuzzy linguistic descriptions are defined. These metric structures allow distances between decision makers to be computed. A centroid of the decision making group is proposed for each distance to model group representatives in the considered group decision making framework.Peer ReviewedPostprint (author's final draft
Reasoning with Non-Numeric Linguistic Variables
Where decisions are based on imprecise numeric data and linguistic variables, the development of automated decision aids presents particular difficulties. In such applications, linguistic variables often take their values from a pre-ordered set of vaguely defined linguistic terms. The mathematical structures that arise from the assumption that sets of linguistic terms are pair-wise tolerant are considered. A homomorphism between tolerance spaces, filter bases and fuzzy numbers is shown. A proposal for modeling linguistic terms with an ordered set of fuzzy numbers is introduced. A procedure for structured knowledge acquisition based on the topology of the term sets and the cognitive theory of prototypes is shown to give rise to sparse rule bases. Similarity as a function of “distance” between fuzzy numbers treated as tolerance mappings is used as an inference mechanism in sparse rule bases to give linguistically valued outputs. Measuring the “distance” between fuzzy sets to correspond to intuitive notions of nearness is not straightforward, since the usual metric axioms are not adequate. An alternative way of measuring “distance” between fuzzy numbers is introduced, which reduces to the usual one when applied to crisp numbers
FUZZY CONTROL CHARTS FOR VARIABLE AND ATTRIBUTE QUALITY CHARACTERISTICS
ABSTRACT. This paper addresses the design of control charts for both variable ( x chart) and attribute (u and c charts) quality characteristics, when there is uncertainty about the process parameters or sample data. Derived control charts are more flexible than the strict crisp case, due to the ability of encompassing the effects of vagueness in form of the degree of expert's presumption. We extend the use of proposed fuzzy control charts in case of linguistic data using a developed defuzzifier index, which is based on the metric distance between fuzzy sets
(Quantum) Space-Time as a Statistical Geometry of Fuzzy Lumps and the Connection with Random Metric Spaces
We develop a kind of pregeometry consisting of a web of overlapping fuzzy
lumps which interact with each other. The individual lumps are understood as
certain closely entangled subgraphs (cliques) in a dynamically evolving network
which, in a certain approximation, can be visualized as a time-dependent random
graph. This strand of ideas is merged with another one, deriving from ideas,
developed some time ago by Menger et al, that is, the concept of probabilistic-
or random metric spaces, representing a natural extension of the metrical
continuum into a more microscopic regime. It is our general goal to find a
better adapted geometric environment for the description of microphysics. In
this sense one may it also view as a dynamical randomisation of the causal-set
framework developed by e.g. Sorkin et al. In doing this we incorporate, as a
perhaps new aspect, various concepts from fuzzy set theory.Comment: 25 pages, Latex, no figures, some references added, some minor
changes added relating to previous wor
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