In this paper the solution of a second order linear differential equations with intuitionistic fuzzy boundary value is described. It is discussed for two different cases: coefficient is positive crisp number and coefficient is negative crisp number. Here fuzzy numbers are taken as generalized trapezoidal intutionistic fuzzy numbers (GTrIFNs). Further a numerical example is illustrated.

In this paper we study the L-fuzzy hyperoperation t, which generalizes the crisp Nakano hyperoperation t1. We construct t using a family of crisp tp hyperoperations as its p-cuts. The hyperalgebra (X,t,∧) can be understood as an L-fuzzy hyperlattice. AMS Classification: 06B99, 06D30, 08A72, 03E72, 20N20.

One of the main challenges of fuzzy community detection problems is to be able to measure the quality of a fuzzy partition. In this paper, we present an alternative way of measure the quality of a fuzzy community detection output based on n-dimensional grouping and overlapping functions that generalize the classical modularity for crisp community detection problems and also for crisp overlappin...

The existing Data Envelopment Analysis models for evaluating the relative eciency of a set of decision making units by using various inputs to produce various outputs are limited to crisp data in crisp production possibility set. In this paper, rst of all the production possibility set is extended to the fuzzy production possibility set by extension principle in constant return to scale, and th...

A new approach for deriving priorities from fuzzy pairwise comparison judgements is proposed, based on -cuts decomposition of the fuzzy judgements into a series of interval comparisons. The assessment of the priorities from the pairwise comparison intervals is formulated as an optimisation problem, maximising the decision-maker’s satisfaction with a speci4c crisp priority vector. A fuzzy prefer...

Fuzzy Description Logics (FDLs) generalize crisp ones by providing membership degree semantics. To offer efficient query answering for FDLs it is desirable to extend the rewriting-based approach for DL-Lite to its fuzzy variants. For answering conjunctive queries over fuzzy DL-LiteR ontologies we present an approach, that employs the crisp rewriting as a black-box procedure and treats the degre...

The fuzzy numbers arise in decision making, control theory, fuzzy systems and approximate reasoning problems. The operations on them are becoming more and more popular. The aim of this paper is to present the fuzzy arithmetic operations on fuzzy numbers in a new way, using the horizontal membership functions (HMFs). The horizontal membership functions enable to introduce uncertain, interval or ...

In this paper, we consider a time-optimal control problem with uncertainties. Dynamics of controlled object is expressed by crisp linear system of differential equations with fuzzy initial and final states. We introduce a notion of fuzzy optimal time and reduce its calculation to two crisp optimal control problems. We examine the proposed approach on an example.

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.