An Interval Type-2 Possibilistic C-Means Clustering Algorithm and Its Application

In this paper, we aim at the fuzzy uncertainty caused by noise in pattern data. The advantages of PCM algorithm to deal with noise and interval type-2 fuzzy sets to deal with high-order uncertainties are used, respectively. An interval type-2 probability C-means clustering (IT2-PCM) based on penalty factor is proposed. The performance of the algorithm is evaluated by two sets of data sets and two groups of images segmentation experiments. The results show that IT2-PCM algorithm can assign proper membership degrees to clustering samples with noise, and it can detect noise points effectively, and it has good performance in image segmentation.

Fuzzy Simheuristics for Optimizing Transportation Systems: Dealing with Stochastic and Fuzzy Uncertainty

In the context of logistics and transportation, this paper discusses how simheuristics can be extended by adding a fuzzy layer that allows us to deal with complex optimization problems with both stochastic and fuzzy uncertainty. This hybrid approach combines simulation, metaheuristics, and fuzzy logic to generate near-optimal solutions to large scale NP-hard problems that typically arise in many transportation activities, including the vehicle routing problem, the arc routing problem, or the team orienteering problem. The methodology allows us to model different components–such as travel times, service times, or customers’ demands–as deterministic, stochastic, or fuzzy. A series of computational experiments contribute to validate our hybrid approach, which can also be extended to other optimization problems in areas such as manufacturing and production, smart cities, telecommunication networks, etc.

On the fuzzy interval equal surplus sharing solutions

PurposeThis paper deals with cooperative games whose characteristic functions are fuzzy intervals, i.e. the worth of a coalition is not a real number but a fuzzy interval. This means that one observes a lower and an upper bound of the considered coalitions. This is very important, for example, from a computational and algorithmic viewpoint. The authors notice that the approach is general, since the characteristic function fuzzy interval values may result from solving general optimization problems.Design/methodology/approachThis paper deals with cooperative games whose characteristic functions are fuzzy intervals, i.e. the worth of a coalition is not a real number but a fuzzy interval. A situation in which a finite set of players can obtain certain fuzzy payoffs by cooperation can be described by a cooperative fuzzy interval game.FindingsIn this paper, the authors extend a class of solutions for cooperative games that all have some egalitarian flavour in the sense that they assign to every player some initial payoff and distribute the remainder of the worth v(N) of the grand coalition N equally among all players under fuzzy uncertainty.Originality/valueIn this paper, the authors extend a class of solutions for cooperative games that all have some egalitarian flavour in the sense that they assign to every player some initial payoff and distribute the remainder of the worth v(N) of the grand coalition N equally among all players under fuzzy uncertainty. Examples of such solutions are the centre-of-gravity of the imputation-set value, shortly denoted by CIS value, egalitarian non-separable contribution value, shortly denoted by ENSC value and the equal division solution. Further, the authors discuss a class of equal surplus sharing solutions consisting of all convex combinations of the CIS value, the ENSC value and the equal division solution. The authors provide several characterizations of this class of solutions on variable and fixed player set. Specifications of several properties characterize specific solutions in this class.