Fuzzy classification rules allow the definition of readable and interpretable rule bases. Nevertheless, the shape of the resulting class borders of fuzzy classification rules depends to a great part on the used tnorm and t-conorm and can sometimes even be counter-intuitive. In this paper we discuss the shape of class borders between overlapping rules under consideration of different t-norms and...

A generalization of bags is proposed and fundamental operations are described. That is, a real-valued bag is proposed which is a straightforward generalization of the traditional bags, but is necessary for complementation, and s-norm and t-norm operations. We mainly describe how complementation and s-norms are related. As a result a duality theorem between s-norm and t-norm is obtained. R-bag r...

In this paper, we introduce concept of possibility neutrosophic soft set and define some related concepts such as possibility neutrosophic soft subset, possibility neutrosophic soft null set, and possibility neutrosophic soft universal set. Then, based on definitions of n-norm and n-conorm, we define set theoretical operations of possibility neutrosophic soft sets such as union, intersection an...

Soft sets have been regarded as a useful mathematical tool to deal with uncertainty. In recent years, many scholars have shown an intense interest in soft sets and extended standard soft sets to intuitionistic fuzzy soft sets, interval-valued fuzzy soft sets, and generalized fuzzy soft sets. In this paper, hesitant fuzzy soft sets are defined by combining fuzzy soft sets with hesitant fuzzy set...

In this study, we present a continuous-valued logical approach to generalize the sigmoid function. Our starting point is kappa function, which known as unary operator in logic. First extend function (a,b) interval, and then interpret generalized limit of extended when b tend negative positive infinity, respectively. Since induced by an additive generator strict t-norm or t-conorm, dependent. Ba...

This paper is devoted to the research of full implication triple I method under Pythagorean fuzzy environment. We first propose concepts t-norm, t-conorm, residual operator (RPFIO) and biresiduum. The for modus ponens (PFMP) tollens (PFMT) are also established. In addition, properties PFMP PFMT models including robustness, continuity reversibility analyzed. Finally, a practical problem discusse...

A contribution of this article is to introduce new q-rung Orthopair fuzzy (q-ROF) aggregation operators (AOs) as the consequence Aczel–Alsina (AA) t-norm (TN) (AATN) and t-conorm (TCN) (AATCN) their specific advantages in handling real-world problems. In beginning, we a few q-ROF numbers (q-ROFNs) operations, including sum, product, scalar power operations based on AATN AATCN. At that point, co...

In this paper we present the N-norms/N-conorms in neutrosophic logic and set as extensions of T-norms/T-conorms in fuzzy logic and set. Also, as an extension of the Intuitionistic Fuzzy Topology we present the Neutrosophic Topologies. 1. Definition of the Neutrosophic Logic/Set: Let T, I, F be real standard or non-standard subsets of ]0, 1[, with sup T = t_sup, inf T = t_inf, sup I = i_sup, inf...

Uninorms as binary operations on the unit interval have been widely applied in the fuzzy set theory. This paper presents some 7 properties of uninorm-like operations for which the underlying operations are given by ordinal sums. If the underlying operations of a uninorm are given by ordinal sums, then the Cartesian product of the union of two arbitrary intervals (one in [0, e] and the other in ...

In classical (two-valued) logic, CNF and DNF forms of each propositional formula are equivalent to each other. In fuzzy logic, CNF and DNF forms are not equivalent, they form an interval that contains the fuzzy values of all classically equivalent propositional formulas. If we want to select a single value from this interval, then it is natural to select a linear combination of the interval's e...