In this paper we investigate further properties of fuzzy ideals of a BL-algebra. The notions of fuzzy prime ideals, fuzzy irreducible ideals, and fuzzy Gödel ideals of a BL-algebra are introduced and their several properties are investigated. We give a procedure to generate a fuzzy ideal by a fuzzy set. We prove that every fuzzy irreducible ideal is a fuzzy prime ideal but a fuzzy prime ideal m...

This paper describes FPGA realization of a Fuzzy Temperature Controller (FTC) using VHDL intended for industrial application. The system is built up with four major modules namely fuzzification, inference, implication and defuzzification. The composition method selected for the fuzzy model is the MaxMin composition while the Mamdani Min operator is chosen as the implication method. Each module ...

Based on the concept of limit of prefilters and residual implication, several notions in fuzzy topology are fuzzyfied in the sense that, for each notion, the degree to which it is fulfilled is considered. We establish therefore theories of degrees of compactness and relative compactness, of closedness, and of continuity. The resulting theory generalizes the corresponding “crisp” theory in the r...

In our case study we look at one of the early papers that interrelates the concept of fuzzy set inclusion, power set and many-valued implication operators, namely the paper of Bandler and Kohout [3]. This is followed by discussion of the subsequent related work by the fuzzy community.

We explore how belief aggregation in the fuzzy framework can be molded into an optimization problem which helps avoid paradoxical outcomes without the fear of indecision. We further illustrate that depending on the choice of t -norm and fuzzy implication, we can find aggregation functions that produce collectively rational outcome without compromising on systematicity.

In this chapter, a new family of multifactorial function, called generalized additive weighted multifactorial function, is proposed and discussed in detail. First, its properties in n-dimensional space are discussed and then our results are extended to the infinite dimensional space. Second, the implication of its constant coefficients is explained by fuzzy integral. Finally, its application in...