Fuzzy orderings with reference to an underlying context of similarity were first defined by Höhle and Blanchard [9]. Since then, several authors have contributed to the development of this class of fuzzy relations, both from the theoretical and the practical side (e.g. [1–4, 7, 8]). Two problems remained open throughout several years: how to define strict fuzzy orderings and how to define lexic...

Among the many desirable properties of fuzzy inference systems not all of them are known to co-exist. For instance, a system based on a monotone fuzzy rule base need not be monotonic and interpolative simultaneously. Recently, Štěpnička and De Baets have investigated and shown the co-existence of the above two properties in the case of a fuzzy relational inference systems and the single-input-s...

This paper analyzes a single-period inventory model of profit maximization with a reordering strategy in an imprecise environment. The entire period is divided into two slots and the customer demand is considered as a fuzzy number in situations where the demand in each slot is linguistic in nature and characterized as ‘demand is about d’. The reordering is to be done during the mid-season after...

This paper proposes a novel approach for smoothing surfaces represented by triangular meshes. The proposed method is a two-step procedure: surface normal smoothing through fuzzy vector median (FVM) filtering followed by vertex position update based on the least square error criteria. This paper applies the fuzzy ordering theory to the vector based data and introduces the fuzzy vector median. Th...

The Critical Path Method (CPM) is useful for planning and control of complex projects. The CPM identifies the critical activities in the critical path of an activity network. The successful implementation of CPM requires the availability of clear determined time duration for each activity. However, in practical situations this requirement is usually hard to fulfill since many of activities will...

Hesitant fuzzy linguistic decision making is a focus point in linguistic decision making, in which the main method is based on preference ordering. This paper develops a new hesitant fuzzy linguistic TOPSIS method for group multi-criteria linguistic decision making; the method is inspired by the TOPSIS method and the preference degree between two hesitant fuzzy linguistic term sets (HFLTSs). To...

Quantitative assessment is the most important means to identify hazard potential and manage risk for an industrial process. The implement of quantitative assessment in the early stage will help to develop inherently safer process, eliminating the hazard and reduce the possibility of accidental chain events and the magnitude of consequences. In this paper, after reviewing the presently available...

Fuzzy sets are naturally ordered by the subsethood relation A ⊆ B. If we only know which set which fuzzy set is a subset of which – and have no access to the actual values of the corresponding membership functions – can we detect which fuzzy sets are crisp? In this paper, we show that this is indeed possible. We also show that if we start with interval-valued fuzzy sets, then we can similarly d...

In this paper we prove some stochastic comparisons results for progressive type II censored order statistics. The problem of stochastically comparing concomitants of the two progressive type II censored order statistics with possibly different schemes, under different kinds of dependence between X and Y is considered and it is proved that if Y is stochastically increasing (decreasing) in X, ...