Fuzzy number

About: Fuzzy number is a research topic. Over the lifetime, 35606 publications have been published within this topic receiving 972544 citations.

Entropy of interval-valued fuzzy sets based on distance and its relationship with similarity measure

Abstract: This article proposes a new axiomatic definition of entropy of interval-valued fuzzy sets (IVFSs) and discusses its relation with similarity measure. First, we propose an axiomatic definition of entropy for IVFS based on distance which is consistent with the axiomatic definition of entropy of a fuzzy set introduced by De Luca, Termini and Liu. Next, some formulae are derived to calculate this kind of entropy. Furthermore we investigate the relationship between entropy and similarity measure of IVFSs and prove that similarity measure can be transformed by entropy. Finally, a numerical example is given to show that the proposed entropy measures are more reasonable and reliable for representing the degree of fuzziness of an IVFS.

A fuzzy-based decision-making procedure for data warehouse system selection

Abstract: The increase in the number of companies seeking data warehousing solutions, in order to gain significant business advantages, has created the need for a decision-aid approach in choosing appropriate data warehouse (DW) systems. Owing to the vague concepts frequently represented in decision environments, we have proposed a fuzzy multi-criteria decision-making procedure, to facilitate data warehouse system selection, with consideration given to both technical and managerial criteria. The procedure can systematically construct the objectives of DW systems selection to support the business goals and requirements of an organization, and identify the appropriate attributes or criteria for evaluation. In the fuzzy-based method, the weight of each criterion and the rating of each alternative are described using linguistic terms, which can also be expressed as triangular fuzzy numbers. The fuzzy algorithm aggregated the decision-makers' preference rating for criteria, and the suitability of data warehouse alternatives versus the selection criteria, to calculate fuzzy appropriateness indices, through which, the most suitable data warehouse system was determined. A case study of a Bar Code Implementation Project for Agricultural Products in Taiwan was conducted to illustrate this method's effectiveness.

Intuitionistic fuzzy rough sets: at the crossroads of imperfect knowledge

Abstract: Just like rough set theory, fuzzy set theory addresses the topic of dealing with imperfect knowledge. Recent investigations have shown how both theories can be combined into a more flexible, more expressive framework for modelling and processing incomplete information in information systems. At the same time, intuitionistic fuzzy sets have been proposed as an attractive extension of fuzzy sets, enriching the latter with extra features to represent uncertainty (on top of vagueness). Unfortunately, the various tentative definitions of the concept of an ‘intuitionistic fuzzy rough set’ that were raised in their wake are a far cry from the original objectives of rough set theory. We intend to fill an obvious gap by introducing a new definition of intuitionistic fuzzy rough sets, as the most natural generalization of Pawlak's original concept of rough sets.