The objective of this work is to present a triangular interval type-2 (TIT2) intuitionistic fuzzy sets and their corresponding aggregation operators, namely, TIT2 intuitionistic fuzzy weighted averaging, TIT2 intuitionistic fuzzy ordered weighted averaging and TIT2 intuitionistic fuzzy hybrid averaging based on Frank norm operation laws. Furthermore, based on these operators, an approach to mul...

There are two equivalent de nitions of a fuzzy right ideal, fuzzy left ideal, fuzzy bi-ideal or fuzzy quasi-ideal f of an ordered semigroup (or a semigroup) S in the bibliography. The rst one is based on the fuzzy subset f itself, the other on the multiplication of fuzzy sets and the greatest fuzzy subset of S. Investigations in the existing bibliography are based on the rst de nition. The pres...

An multi-polar fuzzy set is a robust mathematical model to examine multipolar, multiattribute, and multi-index data. The sets was created as useful mechanism portray uncertainty in multiattribute decision making. In this article, we consider the theoretical applications of sets. We present notion ordered semihypergroups define hyperideals (bi-hyperideals, quasi hyperideals) an semihypergroup. R...

We introduce tuple cryptanalysis, a variant of structural cryptanalysis techniques as square, saturation, integral, internal collision, or multiset cryptanalysis, the main difference being that tuple cryptanalysis considers ordered rather than unordered multisets. This allows cryptanalysts to better trace structural properties within a cipher’s internal state. Unlike previous works that focus o...

This report is based on the default integration for Description Logics (DL) presented by Quantz and Royer at KR’92. We specify the general framework for Preferential Default Description Logics (PDDL), and present various alternative PDDL, addressing issues like implicit objects, priorization between defaults, and maximization of default application. We show that all PDDL satisfy the formal prop...

This paper is about partially ordered multisets (pomsets for short). We investigate a particular class of pomsets that we call order-deterministic, properly including all partially ordered sets, which satisfies a number of interesting properties: among other things, it forms a distributive lattice under pomset prefix (hence prefix closed sets of order-deterministic pomsets are prime algebraic),...

The total voice leading between sets X and Y is defined as the complete collection of ordered pc intervals formed between the pcs in X and the pcs in Y. These interval multisets (imultisets) describe the sonic signature of the motion from X to Y, and they always have the property of transpositional combination. In some cases, the same total voice leading may be produced by different pairs of X ...