Finite dimensional intuitionistic fuzzy normed linear space.
Finite-to-one fuzzy maps and fuzzy perfect maps
In this paper we define, for fuzzy topology, notions corresponding to finite-to-one and -to-one maps. We study the relationship between these new fuzzy maps and various kinds of fuzzy perfect maps. Also, we show the invariance and the inverse inveriance under the various kinds of fuzzy perfect maps (and the finite-to-one fuzzy maps), of different properties of fuzzy topological spaces.
Fixed points of fuzzy monotone maps
The existence of fixed points for monotone maps on the fuzzy ordered sets under suitable conditions is proved.
Fixed points of fuzzy monotone multifunctions
Under suitable conditions we prove the existence of fixed points of fuzzy monotone multifunctions.
Fixed points theorems for -fuzzy monotone maps.
Fixed points theorems of non-expanding fuzzy multifunctions
We prove the existence of a fixed point of non-expanding fuzzy multifunctions in -fuzzy preordered sets. Furthermore, we establish the existence of least and minimal fixed points of non-expanding fuzzy multifunctions in -fuzzy ordered sets.
From an alternative model of rough sets to fuzzy sets
From computing with numbers to computing with words - From manipulation of measurements to manipulation of perceptions
Computing, in its usual sense, is centered on manipulation of numbers and symbols. In contrast, computing with words, or CW for short, is a methodology in which the objects of computation are words and propositions drawn from a natural language, e.g., small, large, far, heavy, not very likely, the price of gas is low and declining, Berkeley is near San Francisco, it is very unlikely that there will be a significant increase in the price of oil in the near future, etc. Computing with words is inspired...
Function spaces and application to fuzzy analysis
Fundamentals of a mathematical theory of fuzzy sets
Fuzzy sets establish a mapping from the interval of values of a criterial function onto a system of subsets of a basic set. In the paper, a system of definitions and theorems is introduced, which is aimed at an adequate expression of this point of view. The criterial function, with an arbitrary interval of values, serves for expressing the really existing objective property, forming the basis for defining a fuzzy set.
Further development of Chebyshev type inequalities for Sugeno integrals and T-(S-)evaluators
In this paper further development of Chebyshev type inequalities for Sugeno integrals based on an aggregation function and a scale transformation is given. Consequences for T-(S-)evaluators are established.
Fuzziness and fuzzy equality
Fuzzy BCI-subalgebras with interval-valued membership functions.
Fuzzy Boolean algebras and Łukasiewicz logic.
Fuzzy concepts defined via residuated maps
Fuzzy data in statistics
The development of effective methods of data processing belongs to important challenges of modern applied mathematics and theoretical information science. If the natural uncertainty of the data means their vagueness, then the theory of fuzzy quantities offers relatively strong tools for their treatment. These tools differ from the statistical methods and this difference is not only justifiable but also admissible. This relatively brief paper aims to summarize the main fuzzy approaches to vague data...
Fuzzy distances
In the paper, three different ways of constructing distances between vaguely described objects are shown: a generalization of the classic distance between subsets of a metric space, distance between membership functions of fuzzy sets and a fuzzy metric introduced by generalizing a metric space to fuzzy-metric one. Fuzzy metric spaces defined by Zadeh’s extension principle, particularly to are dealt with in detail.
Fuzzy equality and convergences for -observables in -quantum spaces
We introduce a fuzzy equality for -observables on an -quantum space which enables us to characterize different kinds of convergences, and to represent them by pointwise functions on an appropriate measurable space.
Fuzzy ideals in Laskerian rings
Fuzzy Markov chains: uncertain probabilities.
We consider finite Markov chains where there are uncertainties in some of the transition probabilities. These uncertainties are modeled by fuzzy numbers. Using a restricted fuzzy matrix multiplication we investigate the properties of regular, and absorbing, fuzzy Markov chains and show that the basic properties of these classical Markov chains generalize to fuzzy Markov chains.