Sequences of refinements of rough sets: logical and algebraic aspects

In this thesis, a generalization of the classical Rough set theory is developed considering the so-called sequences of orthopairs that we define as special sequences of rough sets. Mainly, our aim is to introduce some operations between sequences of orthopairs, and to discover how to generate them starting from the operations concerning standard rough sets. Also, we prove several representation theorems representing the class of finite centered Kleene algebras with the interpolation property, and some classes of finite residuated lattices (more precisely, we consider Nelson algebras, Nelson lattices, IUML-algebras and Kleene lattice with implication) as sequences of orthopairs. Moreover, as an application, we show that a sequence of orthopairs can be used to represent an examiner's opinion on a number of candidates applying for a job, and we show that opinions of two or more examiners can be combined using operations between sequences of orthopairs in order to get a final decision on each candidate. Finally, we provide the original modal logic SOn with semantics based on sequences of orthopairs, and we employ it to describe the knowledge of an agent that increases over time, as new information is provided. Modal logic Son is characterized by the sequences (\u25a11,\u2026, \u25a1n) and (O1,\u2026, On) of n modal operators corresponding to a sequence (t1,\u2026, tn) of consecutive times. Furthermore, the operator \u25a1i of (\u25a11,\u2026, \u25a1n) represents the knowledge of an agent at time ti, and it coincides with the necessity modal operator of S5 logic. On the other hand, the main innovative aspect of modal logic SOn is the presence of the sequence (O1,\u2026, On), since Oi establishes whether an agent is interested in knowing a given fact at time ti

Sequences of refinements of rough sets: logical and algebraic aspects

In this thesis, a generalization of the classical Rough set theory is developed considering the so-called sequences of orthopairs that we define as special sequences of rough sets. Mainly, our aim is to introduce some operations between sequences of orthopairs, and to discover how to generate them starting from the operations concerning standard rough sets. Also, we prove several representation theorems representing the class of finite centered Kleene algebras with the interpolation property, and some classes of finite residuated lattices (more precisely, we consider Nelson algebras, Nelson lattices, IUML-algebras and Kleene lattice with implication) as sequences of orthopairs. Moreover, as an application, we show that a sequence of orthopairs can be used to represent an examiner's opinion on a number of candidates applying for a job, and we show that opinions of two or more examiners can be combined using operations between sequences of orthopairs in order to get a final decision on each candidate. Finally, we provide the original modal logic SOn with semantics based on sequences of orthopairs, and we employ it to describe the knowledge of an agent that increases over time, as new information is provided. Modal logic Son is characterized by the sequences (□1,…, □n) and (O1,…, On) of n modal operators corresponding to a sequence (t1,…, tn) of consecutive times. Furthermore, the operator □i of (□1,…, □n) represents the knowledge of an agent at time ti, and it coincides with the necessity modal operator of S5 logic. On the other hand, the main innovative aspect of modal logic SOn is the presence of the sequence (O1,…, On), since Oi establishes whether an agent is interested in knowing a given fact at time ti

Three-way Decisions with Evaluative Linguistic Expressions

We propose a linguistic interpretation of three-way decisions, where the regions of acceptance, rejection, and non-commitment are constructed by using the so-called evaluative linguistic expressions, which are expressions of natural language such as small, medium, very short, quite roughly strong, extremely good, etc. Our results highlight new connections between two different research areas: three-way decisions and the theory of evaluative linguistic expressions

Sequences of refinements of rough sets: logical and algebraic aspects

In this thesis, a generalization of the classical Rough set theory is developed considering the so-called sequences of orthopairs that we define as special sequences of rough sets. Mainly, our aim is to introduce some operations between sequences of orthopairs, and to discover how to generate them starting from the operations concerning standard rough sets. Also, we prove several representation theorems representing the class of finite centered Kleene algebras with the interpolation property, and some classes of finite residuated lattices (more precisely, we consider Nelson algebras, Nelson lattices, IUML-algebras and Kleene lattice with implication) as sequences of orthopairs. Moreover, as an application, we show that a sequence of orthopairs can be used to represent an examiner's opinion on a number of candidates applying for a job, and we show that opinions of two or more examiners can be combined using operations between sequences of orthopairs in order to get a final decision on each candidate. Finally, we provide the original modal logic SOn with semantics based on sequences of orthopairs, and we employ it to describe the knowledge of an agent that increases over time, as new information is provided. Modal logic Son is characterized by the sequences (□1,…, □n) and (O1,…, On) of n modal operators corresponding to a sequence (t1,…, tn) of consecutive times. Furthermore, the operator □i of (□1,…, □n) represents the knowledge of an agent at time ti, and it coincides with the necessity modal operator of S5 logic. On the other hand, the main innovative aspect of modal logic SOn is the presence of the sequence (O1,…, On), since Oi establishes whether an agent is interested in knowing a given fact at time ti

Refinements of Orthopairs and IUML-algebras

In this paper we consider sequences of orthopairs given by refinement sequences of partitions of a finite universe. While operations among orthopairs can be fruitfully interpreted by connectives of threevalued logics, we describe operations among sequences of orthopairs by means of the logic IUML of idempotent uninorms having an involutive negation

Finite IUML-algebras, Finite Forests and Orthopairs

We show that finite IUML-algebras, which are residuated lattices arising from an idempotent uninorm, can be interpreted as algebras of sequences of orthopairs whose main operation is defined starting from the three-valued Soboci\u144ski operator between rough sets. Our main tool is the representation of finite IUML-algebras by means of finite forests

Context-aware advertisment recommendation on twitter through rough sets

The main, if not the only, income for social networks is from advertising. Social media platforms like Twitter have become a main stream communication medium to disseminate information and capture the interest of potential customers. So, it is crucial that the policy implemented to decide which ads to show in proximity of which user's posts, is the most profitable one: the ads shown should be as much as possible targeted to the user's interests. In this paper, we propose a context-aware advertising recommendation system that, analyzing the users' tweets during the timeline, interpretes the personal interests of users through orthopairs (they are equivalent to rough sets) to meet ads and users' interests at the right time

Context-aware advertisment recommendation on twitter through rough sets

The main, if not the only, income for social networks is from advertising. Social media platforms like Twitter have become a main stream communication medium to disseminate information and capture the interest of potential customers. So, it is crucial that the policy implemented to decide which ads to show in proximity of which user's posts, is the most profitable one: the ads shown should be as much as possible targeted to the user's interests. In this paper, we propose a context-aware advertising recommendation system that, analyzing the users' tweets during the timeline, interpretes the personal interests of users through orthopairs (they are equivalent to rough sets) to meet ads and users' interests at the right time

Antiproliferative, Proapoptotic, Antioxidant and Antimicrobial Effects of <em>Sinapis nigra </em>L. and <em>Sinapis alba</em> L. Extracts

High Brassicaceae consumption reduces the risk of developing several cancer types, probably due to high levels of glucosinolates. Extracts from Sinapis nigra L. (S. nigra) and Sinapis alba L. (S. alba) have been obtained from leaves and seeds under different conditions using ethanol/water mixtures because their glucosinolates are well accepted by the food industry. The EtOH/H2O 8:2 mixture gives better yields in glucosinolate amounts from ground seeds, mainly, sinalbin in S. alba and sinigrin in S. nigra. The highest antiproliferative activity in both non-tumor and tumor cell lines was induced by S. alba seeds extract. To evaluate whether the effect of Sinapis species (spp) was only due to glucosinolate content or whether it was influenced by the extracts’ complexity, cells were treated with extracts or glucosinolates, in the presence of myrosinase. Pure sinigrin did not modify cell proliferation, while pure sinalbin was less effective than the extract. The addition of myrosinase increased the antiproliferative effects of the S. nigra extract and sinigrin. Antiproliferative activity was correlated to Mitogen-Activated Protein Kinases modulation, which was cell and extract-dependent. Cell-cycle analysis evidenced a proapoptotic effect of S. alba on both tumor cell lines and of S. nigra only on HCT 116. Both extracts showed good antimicrobial activity in disc diffusion tests and on ready-to-eat fresh salad. These results underline the potential effects of Sinapis spp in chemoprevention and food preservation