Search results for "Fuzzy set"
showing 10 items of 197 documents
On the imprecision of consumer's spatial preferences
1978
Faced with a set of needs of different intensities and which he perceives more or less indistinctly, a consumer is not normally capable of selecting among the elements belonging to his set of possible consumptions, those he prefers or is indifferent to and those from which he is likely to derive utility. Moreover the goods and services are attainable to different degrees (available in supply space) and his knowledge is perfect only in border-line cases with the result that his world is generally imprecise. Even someone with an exceptional gift for discrimination is not capable of formulating for any pair of goods, his preference or indifference according to binary logic. The purpose of this…
Ajuste familiar durante la pandemia de la COVID-19: un estudio de díadas
2020
The global pandemic of COVID-19 has brought a host of vital changes to society Families and their children have had to adapt to new routines and situations, which may have increased or aggravated the suffering of emotional symptoms However, the presence of resilience and positive emotional regulation strategies can cushion this impact on families with young children The aim of the present study is to know the variables that explained the problems of family emotional adjustment to the COVID-19 pandemic, considering the dyads of parents and their adolescent children Thirty-one dyads of adolescents between 11 and 19 years old (M = 13 90;SD = 1 85) and their main caregivers participated, 93 50%…
On the Evaluation of Images Complexity: A Fuzzy Approach
2006
The inherently multidimensional problem of evaluating the complexity of an image is of a certain relevance in both computer science and cognitive psychology. Computer scientists usually analyze spatial dimensions, to deal with automatic vision problems, such as feature-extraction. Psychologists seem more interested in the temporal dimension of complexity, to explore attentional models. Is it possible, by merging both approaches, to define an more general index of visual complexity? We have defined a fuzzy mathematical model of visual complexity, using a specific entropy function; results obtained by applying this model to pictorial images have a strong correlation with ones from an experime…
Measure-free conditioning and extensions of additive measures on finite MV-algebras
2010
Using the well known representation of any finite MV-algebra as a product of finite MV-chains as factors, we obtain a representation of its canonical extension as a Girard algebra product of the canonical extensions of the MV-chain factors. Based on this representation and using the results from our last paper, we characterize the additive measures on any finite MV-algebra resp. the weakly and the strongly additive measures on its canonical Girard algebra extension, and that as convex combinations of the corresponding measures on the respective factors. After that we apply the results to measure-free defined conditional events which for this reason are considered as elements of the canonica…
Degree of monotonicity in aggregation process
2010
In this paper we introduce a fuzzy order relation notion in the description of aggregation process. Namely, we use the fuzzy order relation to define the degree of monotonicity, which is equal to 1 for a monotone function with respect to a crisp order relation. In that case, integration of fuzzy order relation allows us to generalize the notion of monotonicity and we try to investigate the benefits of using fuzzy relations instead of a crisp relation. Further we illustrate this definition by examples and study the properties of aggregation functions which have a certain degree of monotonicity.
Fuzzy functions: a fuzzy extension of the category SET and some related categories
2000
<p>In research Works where fuzzy sets are used, mostly certain usual functions are taken as morphisms. On the other hand, the aim of this paper is to fuzzify the concept of a function itself. Namely, a certain class of L-relations F : X x Y -&gt; L is distinguished which could be considered as fuzzy functions from an L-valued set (X,Ex) to an L-valued set (Y,Ey). We study basic properties of these functions, consider some properties of the corresponding category of L-valued sets and fuzzy functions as well as briefly describe some categories related to algebra and topology with fuzzy functions in the role of morphisms.</p>
Decomposable Measures and Measures of Information for Crisp and Fuzzy Sets
1983
Abstract There exist bijections between the decomposable informations of Kampe de Feriet and Forte (1967a) and the decomposable measures of Weber (1982). Using integrals for Archimedean decomposable operations, introduced by Weber (1982), informations and measures of this type are extended from crisp to fuzzy sets. For ∨-decomposable measures, Sugeno’s (1974) integral is used. For ∧-decomposable informations, Nguyen’s (1977) construction and a modification are discussed.
L -valued bornologies on powersets
2016
In M. Abel and A. ostak (2011) [1], the concept of an L-fuzzy bornology was introduced. Actually, an L-fuzzy bornology on a set X is a certain ideal in the family LX of L-fuzzy subsets of a set X. Here we propose an alternative approach to fuzzification of the concept of bornology. We define an L-valued bornology on a set X as an L-fuzzy subset B of the powerset 2X satisfying L-valued analogues of the axioms of a bornology. Basic properties of L-valued bornological spaces are studied. Our special interest concerns L-valued bornologies induced by fuzzy metrics and relative compactness-type L-valued bornologies in ChangGoguen L-topological spaces.
Extremal problems of approximation theory in fuzzy context
1999
Abstract The problem of approximation of a fuzzy subset of a normed space is considered. We study the error of approximation, which in this case is characterized by an L -fuzzy number. In order to do this we define the supremum of an L -fuzzy set of real numbers as well as the supremum and the infimum of a crisp set of L -fuzzy numbers. The introduced concepts allow us to investigate the best approximation and the optimal linear approximation. In particular, we consider approximation of a fuzzy subset in the space L p m of differentiable functions in the L q -metric. We prove the fuzzy counterparts of duality theorems, which in crisp case allows effectively to solve extremal problems of the…
On another approach to the definition of an L-fuzzy valued integral
2011
We continue to develop a construction of an L-fuzzy valued measure extending a crisp measure defined on a σ-algebra of crisp sets to an L-fuzzy valued measure defined on a T M -tribe. We describe two equivalent approaches to define an L-fuzzy valued integral of non-negative measurable functions.