The starting point of the paper is the (well-known)observation that the “classical” Rough Set Theory as introduced by PAWLAK is equivalent to the S5 Propositional Modal Logic where the reachability relation is an equivalence relation. By replacing this equivalence relation by an arbitrary binary relation (satisfying certain properties, for instance, reflexivity and transitivity) we shall obtain...

In this paper, we investigate the properties of L-lower approximation operators as a generalization of fuzzy rough set in complete residuated lattices. We study relations lower (upper, join meet, meet join) approximation operators and Alexandrov L-topologies. Moreover, we give their examples as approximation operators induced by various L-fuzzy relations.

In multicriteria decision making, the study of attribute contributions is crucial to attain correct decisions. Fuzzy measures allow a complete description of the joint behavior of attribute subsets. However, the determination of fuzzy measures is often hard. A common way to identify fuzzy measures is HLMS (Heuristic Least Mean Squares) algorithm. In this paper, the convergence of the HLMS algor...

Fuzzy utility mining reflects fuzzy degrees of quantities and profits for high utility itemsets. In generally, transaction time is also concerned, and not all products sold are always on the shelf. Thus, in this paper we present an effective framework, which considers the transaction period of each product from the first transaction it appears to the last transaction in the whole database for m...

Designing the fuzzy controllers by using evolutionary algorithms and reinforcement learning is an important subject to control the robots. In the present article, some methods to solve reinforcement fuzzy control problems are studied. All these methods have been established by combining Fuzzy-Q Learning with an optimization algorithm. These algorithms include the Ant colony, Bee Colony and Arti...

Crisp and L-fuzzy ambiguous representations of closed subsets of one space by closed subsets of another space are introduced. It is shown that, for each pair of compact Hausdorff spaces, the set of (crisp or L-fuzzy) ambiguous representations is a lattice and a compact Hausdorff Lawson upper semilattice. The categories of ambiguous and L-ambiguous representations are defined and investigated.

Looking at decisiveness as crucial, we discuss the existence of an order-preserving function for the nontotal crisp preference relation naturally associated to a nontotal fuzzy preference relation. We further present conditions for the existence of an upper semicontinuous order-preserving function for a fuzzy binary relation on a crisp topological space.

The interstitial nucleus of Cajal (INC) is thought to control torsional and vertical head posture. Unilateral microstimulation of the INC evokes torsional head rotation to positions that are maintained until stimulation offset. Unilateral INC inactivation evokes head position-holding deficits with the head tilted in the opposite direction. However, the underlying muscle synergies for these oppo...

This study applies fuzzy set theory to the vulnerable Black-Scholes (1973) or Merton (1973) formula. Expectations of heterogeneity mean option prices are expected to be imprecise, thus making it natural to consider fuzziness to handle this. This article presents a fuzzy approach to value Black-Scholes options subject to non-identical rationality and correlated credit risk. Although no analytica...

In this paper, bi-level linear programming problem with multiple objectives at each level in intuitionistic fuzzy environment is studied and solved. In this problem, technological coefficients and resources are characterized by intuitionistic fuzzy numbers having linear membership and non-membership function. Intuitionistic fuzzy efficient solution is computed for the upper level by the propose...