A temporal semantics for Nilpotent Minimum logic

In [Ban97] a connection among rough sets (in particular, pre-rough algebras) and three-valued {\L}ukasiewicz logic {\L}3 is pointed out. In this paper we present a temporal like semantics for Nilpotent Minimum logic NM ([Fod95, EG01]), in which the logic of every instant is given by {\L}3: a completeness theorem will be shown. This is the prosecution of the work initiated in [AGM08] and [ABM09], in which the authors construct a temporal semantics for the many-valued logics of G\"odel ([G\"od32], [Dum59]) and Basic Logic ([H\'aj98]).Comment: 19 pages, 2 table

Vagueness and Roughness

The paper proposes a new formal approach to vagueness and vague sets taking inspirations from Pawlak’s rough set theory. Following a brief introduction to the problem of vagueness, an approach to conceptualization and representation of vague knowledge is presented from a number of different perspectives: those of logic, set theory, algebra, and computer science. The central notion of the vague set, in relation to the rough set, is defined as a family of sets approximated by the so called lower and upper limits. The family is simultaneously considered as a family of all denotations of sharp terms representing a suitable vague term, from the agent’s point of view. Some algebraic operations on vague sets and their properties are defined. Some important conditions concerning the membership relation for vague sets, in connection to Blizard’s multisets and Zadeh’s fuzzy sets, are established as well. A classical outlook on a logic of vague sentences (vague logic) based on vague sets is also discussed

Rough Neutrosophic Multi-Attribute Decision-Making Based on Rough Accuracy Score Function

This paper presents multi-attribute decision making based on rough accuracy score function with rough neutrosophic attribute values. While the concept of neutrosophic sets is a powerful logic to handle indeterminate and inconsistent information, the theory of rough neutrosophic sets is also a powerful mathematical tool to deal with incompleteness. The rating of all alternatives is expressed with the upper and lower approximation operator and the pair of neutrosophic sets which are characterized by truth-membership degree, indeterminacy-membership degree, and falsity-membership degree

Rough Sets: a Bibliometric Analysis from 2014 to 2018

Along almost forty years, considerable research has been undertaken on rough set theory to deal with vague information. Rough sets have proven to be extremely helpful for a diversity of computer-science problems (e.g., knowledge discovery, computational logic, machine learning, etc.), and numerous application domains (e.g., business economics, telecommunications, neurosciences, etc.). Accordingly, the literature on rough sets has grown without ceasing, and nowadays it is immense. This paper provides a comprehensive overview of the research published for the last five years. To do so, it analyzes 4,038 records retrieved from the Clarivate Web of Science database, identifying (i) the most prolific authors and their collaboration networks, (ii) the countries and organizations that are leading research on rough sets, (iii) the journals that are publishing most papers, (iv) the topics that are being most researched, and (v) the principal application domains

Encapsulation of Soft Computing Approaches within Itemset Mining a A Survey

Data Mining discovers patterns and trends by extracting knowledge from large databases. Soft Computing techniques such as fuzzy logic, neural networks, genetic algorithms, rough sets, etc. aims to reveal the tolerance for imprecision and uncertainty for achieving tractability, robustness and low-cost solutions. Fuzzy Logic and Rough sets are suitable for handling different types of uncertainty. Neural networks provide good learning and generalization. Genetic algorithms provide efficient search algorithms for selecting a model, from mixed media data. Data mining refers to information extraction while soft computing is used for information processing. For effective knowledge discovery from large databases, both Soft Computing and Data Mining can be merged. Association rule mining (ARM) and Itemset mining focus on finding most frequent item sets and corresponding association rules, extracting rare itemsets including temporal and fuzzy concepts in discovered patterns. This survey paper explores the usage of soft computing approaches in itemset utility mining

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