This paper deals with ordinal sums of fuzzy implications. Some of the known constructions are recalled and new ways of generating fuzzy implications from given ones are proposed. Sufficient properties of fuzzy implications as summands for obtaining a fuzzy implication as a result are presented.

This paper deals with a new family of (A, N)-implications that derived from fuzzy negation and continuous monotone function, and some properties, like the left neutrally, the exchange principle, the ordering property and the laws of contraposition, of the proposed family of (A, N)-implications are studied. Moreover, the T-conditionality and the Modus tollens for the new family of (A, N)-i...

This paper presents an approach to building multi-input and single-output fuzzy models. Such a model is composed of fuzzy implications, and its output is inferred by simplified reasoning. The implications are automatically generated by the structure and parameter identification. In structure identification, the optimal or near optimal number of fuzzy implications is determined in view of valid ...

Bijective transformations play an important role in generating fuzzy implications from fuzzy implications. In [Representations through a Monoid on the set of Fuzzy Implications, Fuzzy Sets and Systems, 247, 5167], Vemuri and Jayaram proposed a monoid structure on the set of fuzzy implications, which is denoted by I, and using the largest subgroup S of this monoid discussed some group actions on...

Recently, Vemuri and Jayaram proposed a novel method of generating fuzzy implications, called the ~-composition, from a given pair of fuzzy implications (Vemuri and Jayaram, 2014). However, as with any generation process, the ~-composition does not always generate new fuzzy implications. In this work, we study the generative power of the ~-composition. Towards this end, we study some specific f...

In [14], we have presented a fuzzy forward reasoning methodology for rule-based systems using the functional representation of rules (fuzzy implications). In this paper, we extend methodology for selecting relevant fuzzy implications from [14] in backward reasoning. The proposed methodology takes full advantage of the functional representation of fuzzy implications and the algebraic properties ...

The main goal of this paper is to apply the method of extension of fuzzy connectives proposed in our previous work for fuzzy implications valued on a bounded lattice. Also we discuss about which properties of implications are preserved by this method and we prove some results involving extension and automorphisms. Finally, we investigate the behavior of the extensions of two special classes of ...

In this work, we show that single input single output (SISO) fuzzy inference systems based on Fuzzy Relational Inference (FRI) with implicative interpretation of the rule base are universal approximators under suitable choice of operations for the other components of the fuzzy system. The presented proofs make no assumption on the form or representations of the considered fuzzy implications and...

The main condition of the differently implicational inferencealgorithm is reconsidered from a contrary direction, which motivatesa new fuzzy inference strategy, called the double fuzzyimplications-based restriction inference algorithm. New restrictioninference principle is proposed, which improves the principle of thefull implication restriction inference algorithm. Furthermore,focusing on the ...