A binary intuitionistic fuzzy relation: some new results, a general factorization, and two properties of strict components.
A characterization of tribes with respect to the Łukasiewicz -norm
We give a complete characterization of tribes with respect to the Łukasiewicz -norm, i. e., of systems of fuzzy sets which are closed with respect to the complement of fuzzy sets and with respect to countably many applications of the Łukasiewicz -norm. We also characterize all operations with respect to which all such tribes are closed. This generalizes the characterizations obtained so far for other fundamental -norms, e. g., for the product -norm.
A characterization of uninorms on bounded lattices via closure and interior operators
Uninorms on bounded lattices have been recently a remarkable field of inquiry. In the present study, we introduce two novel construction approaches for uninorms on bounded lattices with a neutral element, where some necessary and sufficient conditions are required. These constructions exploit a t-norm and a closure operator, or a t-conorm and an interior operator on a bounded lattice. Some illustrative examples are also included to help comprehend the newly added classes of uninorms.
A connection between Computer Science and Fuzzy Theory: Midpoints and running time of computing.
A contour view on uninorm properties
Any given increasing function is completely determined by its contour lines. In this paper we show how each individual uninorm property can be translated into a property of contour lines. In particular, we describe commutativity in terms of orthosymmetry and we link associativity to the portation law and the exchange principle. Contrapositivity and rotation invariance are used to characterize uninorms that have a continuous contour line.
A discussion on aggregation operators
It has been lately made very clear that aggregation processes can not be based upon a unique binary operator. Global aggregation operators have been therefore introduced as families of aggregation operators , being each one of these the -ary operator actually amalgamating information whenever the number of items to be aggregated is . Of course, some mathematical restrictions can be introduced, in order to assure an appropriate meaning, consistency and key mathematical capabilities. In this...
A fuzzy approach to option pricing in a Levy process setting
In this paper the problem of European option valuation in a Levy process setting is analysed. In our model the underlying asset follows a geometric Levy process. The jump part of the log-price process, which is a linear combination of Poisson processes, describes upward and downward jumps in price. The proposed pricing method is based on stochastic analysis and the theory of fuzzy sets. We assume that some parameters of the financial instrument cannot be precisely described and therefore they are...
A fuzzy logic approach to assembly line balancing.
This paper deals with the use of fuzzy set theory as a viable alternative method for modelling and solving the stochastic assembly line balancing problem. Variability and uncertainty in the assembly line balancing problem has traditionally been modelled through the use of statistical distributions. This may not be feasible in cases where no historical data exists. Fuzzy set theory allows for the consideration of the ambiguity involved in assigning processing and cycle times and the uncertainty contained...
A fuzzy modification of the category of linearly ordered spaces
A general approach to decomposable bi-capacities
We propose a concept of decomposable bi-capacities based on an analogous property of decomposable capacities, namely the valuation property. We will show that our approach extends the already existing concepts of decomposable bi-capacities. We briefly discuss additive and -additive bi-capacities based on our definition of decomposability. Finally we provide examples of decomposable bi-capacities in our sense in order to show how they can be constructed.
A new approach for studying fuzzy functional equations.
A new approach to construct uninorms via uninorms on bounded lattices
In this paper, on a bounded lattice , we give a new approach to construct uninorms via a given uninorm on the subinterval (or ) of under additional constraint conditions on and . This approach makes our methods generalize some known construction methods for uninorms in the literature. Meanwhile, some illustrative examples for the construction of uninorms on bounded lattices are provided.
A new definition of the fuzzy set
The present fuzzy arithmetic based on Zadeh's possibilistic extension principle and on the classic definition of a fuzzy set has many essential drawbacks. Therefore its application to the solution of practical tasks is limited. In the paper a new definition of the fuzzy set is presented. The definition allows for a considerable fuzziness decrease in the number of arithmetic operations in comparison with the results produced by the present fuzzy arithmetic.
A nonstandard approach to fuzzy set theory
A note about operations like (the weakest -norm) based addition on fuzzy intervals
We investigate a relation about subadditivity of functions. Based on subadditivity of functions, we consider some conditions for continuous -norms to act as the weakest -norm -based addition. This work extends some results of Marková-Stupňanová [15], Mesiar [18].
A note on -algebras.
A note on connectedness in intuitionistic fuzzy special topological spaces.
A note on fuzzy cardinals
A note on -norm-based operations on fuzzy intervals
A possibilistic view on set and multiset comparison