Article history: Received 15 November 2012 Received in revised form 3 January 2014 Accepted 1 February 2014 Available online 10 February 2014

In this paper, we derive innerand outer-bound sets for the type-reduced set of an interval type-2 fuzzy logic system (FLS), based on a new mathematical interpretation of the Karnik–Mendel iterative procedure for computing the type-reduced set. The bound sets can not only provide estimates about the uncertainty contained in the output of an interval type-2 FLS, but can also be used to design an ...

In interval type-2 fuzzy logic controllers (IT2-FLCs), the output processing includes type reduction and defuzzification. Recently, researchers have proposed many efficient type reduction algorithms, but there are no effective schemes to improve the output of defuzzification. This paper presents a geneticalgorithm-based type reduction algorithm, which reduces the type of an interval type-2 fuzz...

it is well known fact that binary relations are generalized mathematical functions. contrary to functions from domain to range, binary relations may assign to each element of domain two or more elements of range. some basic operations on functions such as the inverse and composition are applicable to binary relations as well. depending on the domain or range or both are fuzzy value fuzzy set, i...

The design of weight is one of the important parts in fuzzy decision making, as it would have a deep effect on the evaluation results. Entropy is one of the weight measure based on objective evaluation. Non--probabilistic-type entropy measures for fuzzy set and interval type-2 fuzzy sets (IT2FS) have been developed and applied to weight measure. Since the entropy for (IT2FS) for decision making...

the purpose of this paper is to develop a methodology for solving a new type of matrix games in which payoffs are expressed with triangular intuitionistic fuzzy numbers (tifns). in this methodology, the concept of solutions for matrix games with payoffs of tifns is introduced. a pair of auxiliary intuitionistic fuzzy programming models for players are established to determine optimal strategies...

If all we know about normalized fuzzy sets is which set is a subset of which, will we be able to detect crisp sets? It is known that we can do it if we allow all possible fuzzy sets, including non-normalized ones. In this paper, we show that a similar detection is possible if we only allow normalized fuzzy sets. We also show that we can detect type-1 fuzzy sets based on the subsethood ordering ...