This study aims to present a new perspective for creating associative memories using incomplete data and project them into artificial neural networks to retrieve complete data from incomplete data.In previous studies, various approaches to construct associative memories and retrieval of stored data have been proposed.This paper attempts to pin point some of the limitations observed in the existing approaches and propose a way to get rid of that.In particular, a different perspective of comparing two incomplete patterns is proposed and based on that a flexible way of constructing associative patterns of a given input (partial) pattern is developed.Finally, the respective neural network architecture is proposed following similar construction reported in the existing research.

We present an approach based on the Interactive Granular Computing (IGrC) model as the basis for developing foundations of Complex Intelligent Systems, i.e., Intelligent Systems dealing with complex phenomena (IS's).The generalization of GrC to IGrC was proposed to support the design of IS's treated in IGrC as examples of complex granules (c-granules) with control.To make such systems successful, it is necessary to enable such systems to have continuous interaction with the physical world.The control of c-granules aims to properly implement the physical semantics of specified transformations of c-granules in the physical world.This implementation is based on the discovery of relevant configurations of physical objects, which provides the basis for perceiving relevant data about these objects and their interactions through the control of c-granules.Additionally, to create high-quality models that serve as the basis for the behavior of IS's, these configurations must be adaptively adjusted by control to allow for the perception of relevant data used to induce those models.Unlike information granules from GrC, the correct implementation of c-granule transformations cannot be restricted to the abstract space.An important property of the IS's discussed here is that they cannot be separated from interactions with the physical world.Hence, they cannot be confined to an abstract space.In particular, the relevance of IGrC in searching for rough computational building blocks for cognition is discussed.These computational building blocks are modeled by complex granules (c-granules) and their networks.It is also proposed to use IGrC as the basis for developing IS's grounded on cognitive computing.

The aim of this tutorial is to present a brief overview of the theory of rough sets from the perspective of its mathematical foundations, history of development as well as connections with other branches of mathematics and informatics.The content concerns both the theoretical and practical aspects of applications.The above mentioned target of the tutorial will be covered in two parts.In the first part we would aim to present the introduction to rough sets and the second part will focus on the connections with other branches of mathematics and informatics.

The paper presents an AI-based model which depending on the input of a woman for a finite number of menstrual cycles helps in determining the possible ovulation dates as well as possibility of some health risks e.g., Premenstrual Syndrome, Luteal Phase Defect etc.The architecture of the model consists of three layers, namely analyzing and detecting the features from a single cycle, analyzing cycle level concepts based on the analyzed features, and analyzing the user's health risks based on the cycle level concepts accumulated over a finitely many cycles.

Reaction system is a model of interactive computations which was motivated by the functioning of the living cell. It is an idealized mathematical model, also because it abstracts from the complex nature of the physical systems where only partial, incomplete information is available (e.g., about the ir states). The framework of rough sets was developed to deal with such incomplete information. In this paper we establish a connection between reaction systems and rough sets. This is done in a somewhat broader perspective of the relationship between “pure” mathematical models and “realistic models” that take into account the limitation of perceiving physical reality.

This paper is an attempt to introduce a notion of dialogue among different agents, e.g. a user or situation descriptor and an information provider or machine, to better understand a user’s need of information. When a user describes a concept through some keywords first the system needs to choose th e relevant attributes for initiating the search. Regarding this, a series of dialogues may help the system to better understand the user’s language of expresssion. After fixing the relevant attributes, the system needs to look at its repertoire of positive and negative cases of different concepts characterized with respect to this set of attributes. Then through a step-by-step process of matching and comparing similarity of user’s described situation with those positive and negative cases of a concept, incorporating several layers of dialogue, the system may provide information closer to the user’s need. The target of this paper is to develop a theoretical model, incorporating the above features, for characterizing one’s concern of concept based on dialogue and similarity based reasoning.

Introduction of rough sets by Professor Zdzisław Pawlak has completed 35 years. The theory has already attracted the attention of many researchers and practitioners, who have contributed essentially to its development, from all over the world. The methods, developed based on rough set theory alone or in combination with other approaches, found applications in many areas. In this article, we outline some selected past and present research directions of rough sets. In particular, we emphasize the importance of searching strategies for relevant approximation spaces as the basic tools in achieving computational building blocks (granules or patterns) required for approximation of complex vague concepts. We also discuss new challenges related to problem solving by intelligent systems (IS) or complex adaptive systems (CAS). The concern is to control problems using interactive granular computing, an extension of the rough set approach, for effective realization of computations realized in IS or CAS. These challenges are important for the development of natural computing too.

We present an extension of logical structures, called interactive logical structures, for reasoning about interactive computations performed by Intelligent Systems or Complex Adaptive Systems. Reasoning based on such structures is called adaptive judgment and it goes beyond deduction, induction, an d abduction. An extension of logical structures, based on complex granules, couples the abstract world and the physical world of an agent’s environment, and transmits the features of interactions of physical objects realized in the physical world to the abstract world. This allows us to consider the problems of perception and action.

Looking back to Prof. Zadeh’s paradigm of Computing with Words (CWW) [28, 29, 30], one can notice that the initial attempt of such an endeavour was to set up a basic vocabulary of linguistic words, and fix their semantics based on fuzzy sets. Then a grammar was proposed to generate compound linguis tic expressions based on the primitive ones, and simultaneously based on the semantic interpretations of those basic linguistic expressions a general scheme for the semantics of the rest of linguistic expressions were proposed. Sentences involving linguistic quantifiers and vague predicates constitute a fragment of natural language. In this paper, we choose this fragment of the natural language, and explore the semantics from the perspective of rough sets [13, 14, 16, 17, 18, 21]. We fix a set of basic crisp quantifiers, mainly of proportional kind. A set of vague quantifiers are proposed to lie in a close vicinity of those crisp quantifiers in the sense that a particular vague quantifier can be visualized as a blurred, may be called rough, image of a set of crisp quantifiers. Semantics of the rest of the vague quantifiers can be obtained based on the subjective perception of the interrelations among the (vague) quantifiers.

Fuzzy Logic a la Pavelka has been reintroduced here in terms of consequence relation instead of consequence operator. Metalogical notions like, consistency and inconsistency are proposed as graded notions. The relationship between consequence relation and inconsistency, both fuzzy here, is studied. Another metalogical notion viz., equivalence of two sets of formulae that originates from Tarski is defined and investigated in this context when the premise is a fuzzy set.