In this Chapter, invoking the notion of signed fuzzy number valued measures on the fuzzy set, we attempt to study the Lebesgue decompositions of a signed fuzzy number valued measures. We introduce in this Chapter a new notion called singular complements to the domain of fuzzy number valued measures and derive some consequential properties. The contents of this chapter form the material of the p...

In this paper, the authors propose a schema for a decision support system for basketball defense strategies using a fuzzy expert system. The authors introduce the original ideas for the proposed schema and the background of the basketball defense strategies. The authors also present the fuzzy input and output attributes for the fuzzy expert system according to the domain knowledge from the bask...

Coevolutionary algorithms have received increased attention in the past few years within the domain of evolutionary computation. In this paper we combine the search power of coevolutionary computation with the expressive power of fuzzy systems, presenting Fuzzy CoCo: Fuzzy Cooperative Coevolution. We demonstrate the efficacy of Fuzzy CoCo by applying it to two hard problems—plant classification...

Introducing rough sets in hesitant fuzzy set domain and using it for the various applications would open up new possibilities in rough set theory. For this purpose the notion of hesitant fuzzy relations is introduced. The foundation of equivalence hesitant fuzzy relation is laid. Definition of anti-reflexive kernel, symmetric kernel etc. is proposed and the formulae to evaluate them are derived...

Fuzzy{logic theory is a valuable tool to structure ad{hoc designs where model{based designs are not suitable or even not available. There exist numerous examples of industry proven fuzzy{logic solutions in the domain of control, pattern recognition and expert systems. The design of fuzzy systems demand a great deal of experience and intuition. Due to the many degrees of freedom in the design of...

For a mapping, fuzzy sets obtained by Zadeh's extension principle are images of other fuzzy sets on the domain of the mapping under the mapping. Some relationships between images of level sets of one or two fuzzy sets under a mapping and another fuzzy set obtained from the one or two fuzzy sets by Zadeh's extension principle are known. In the present paper, the known results are extended to mor...

For medical diagnosis, fuzzy Dempster-Shafer theory is extended to model domain knowledge under probabilistic and fuzzy uncertainty. However, there are some information loss using discrete fuzzy sets and traditional matching degree method. This study aims to provide a new evidential structure to reduce information loss. This paper proposes a new intuitionistic fuzzy evidential reasoning (IFER) ...

Since fuzzy controllers are nonlinear, it is more difficult to set the controller gains compared to proportional-integral-derivative (PID) controllers. This research paper proposes a design procedure and a tuning procedure that carries tuning rules from the PID domain over to fuzzy single-loop controllers. The idea is to start with a tuned, conventional PID controller, replace it with an equiva...

In many applications, spatial data often are prone to uncertainty and imprecision. To model this, fuzzy regions have been developed. Our initial model was a fuzzy set over a two dimensional domain, allowing for fuzzy regions and fuzzy points to be modelled. The model had some limitations: all points where treated independently, and it was not possible to group points together. Furthermore, it d...

This paper introduces a new approach to the theory of Ω-categories enriched by a frame. The approach combines ideas from various areas such as generalized ultrametric domains, Ω-categories, constructive analysis, and fuzzy mathematics. As the basic framework, we use the Wagner’s Ω-category [18,19] with a frame instead of a quantale with unit. The objects and morphisms in the category will be ca...