Kankana Chakrabarty

NOTION OF FUZZY IC-BAGS

In the present paper, the author introduces the notion of fuzzy IC-bags and does some characterizations of them. The concepts of fuzzy base sets, base equivalent fuzzy IC-Bags, cardinally equispaced fuzzy IC-Bags, and cardinally equivalent fuzzy IC-Bags have been developed. The types of peak elements, and the concerned types of peak membership grades have been discussed. It is observed that the collection of any particular type of peak elements together with their membership grades actually form fuzzy bags. A set of operations on fuzzy IC-Bags have been defined and some propositions have been proved. We note that under the conditions of uncertainty, where the counts of objects are not fixed, then the interval counts can occur with different fuzzy membership grades for each particular object in the collection, and the framework for fuzzy IC-Bags provides us with the opportunity to justify and model the organized complexity as a part of the associated intolerance embedded in the subjective patterns.

A note on the effect of knowledge refinement on bag structures

In this paper, the author discusses the notion of bags and describes a conceptual model of an information system where the effect of knowledge refinement on bag structure can be clearly observed. In this context, the indiscernibility relation is defined over one or more attribute(s) of a collection of objects of the same type. Here the author further define attributive indiscernibility relations and their types.

IF-Bags and Knowledge Representation in Soft Decision Analysis

The concept of IF-Bags was introduced by the author as a generalization of the notion of fuzzy bags. In case of IF-Bags, each element is associated with a crisp bag drawn from the Cartesian product I×I of the unit interval I = [0, 1]. This paper introduces a method for quantitatively measuring the similarity between two IF-Bags. As a consequence, the notions of a measure of coherence and a measure of hesitancy between two IF-Bags are also introduced. It is observed that the measure of coherence and the measure of hesitancy between the IF-Bags can be regarded as crucial factors in case of scenario evaluation as well as grading that relates to knowledge representation in soft decision analysis problems.

A note on knowledge representation using B B -mappings

In this paper, we discuss some knowledge representation scenarios where it is necessary to define the types of correspondence between the objects contained in bags. In this regard, we define BB mappings and study some of their characteristics.

On M-type bag structures

In this paper, the author introduces a structure called M-type bag structure which can be defined on a non-empty set associated with an indiscernibilty relation. It can be observed that an M-type bag structure represents a bag if the indiscernibility relation be defined in such a way that any two elementsof the set are indiscernible under a given set of criteria that considers the values of some predefined attribute set. This paper further studies some algebraic properties of M-type bag structures.

On B-groups

The notion of bags play an essential role in dealing with knowledge representation problems where object classes allow repeated occurrence of elements. Sometimes bags with some special conditions can be drawn from a given set. Under these situations, is possible to define some algebraic structures on the given set.The present paper considers the situation when some bags with special conditions are drawn from a set, which, under a given operation, forms a group. Consequently, it demonstrates how an existing group structure defined on a given set can induce special structures on some bags drawn from this set. Hence, the notions of induced B-groups, induced abelian B-groups, and induced semi B-groups are introduced and discussed. Further, some characteristics of B-groups, abelian B-groups, and semi B-Groups are studied.

A new intuitionitic Fuzzy Cognitive Maps building method

When modeling complex systems, conventional methodologies are recognized to be limited. Because of their fuzzy feedback structure of causality, Fuzzy Cognitive Maps (FCMs) have been seen as a promising alternative in multiple domains as a support for decision making and systems modeling. In an attempt to improve this framework, we extend it by considering both determinacy and indeterminacy of experts when assigning weights to causal relations between concepts such that a new initutionistic fuzzy method for constructing FCMs is considered. The proposed method largely improves the accuracy of evaluating weights of edges in the FCM models and avoids subjectiveness and indeterminacy while experts are designing the models.

Functional independence of elements and perceptual confidence factors

In this paper, we introduce the notions of functional independence of elements and perceptual confidence factors of experts with reference to some specific action taken within the framework of a given knowledge domain. Consequently we propose perceptual zero as a measure of belongingness of an object to a collection in whole in case of soft decision modeling. We discuss the underlying concept of zero as a precise numerical value and the concept of perceptual zero as an approximation towards the conceptual grading between belongingness and non-belongingness in case of knowledge representation under uncertainty. Considering the notion of functional independence of elements, we define the degree of coherence of opinions of the set of n experts regarding the objects in a collection. The degree of coherence of opinions is a probabilistic measure and it is observed that it increases with the increase in the value of the cardinality of the set of functionally independent elements.

A note on fixed point theorem for fuzzy mappings

This paper explores Heilperns notions of fuzzy mapping and the fixed point theorem for fuzzy mappings. The fixed point theorem for fuzzy mappings as introduced by Heilpern has been generalized and some characterizations are done in this context.