Data Mining - Concepts and Techniques.

An intuitionistic fuzzy set, characterized by a membership function and a non-membership function, is a generalization of fuzzy set. In this paper, based on score function and accuracy function, we introduce a method for the comparison between two intuitionistic fuzzy values and then develop some aggregation operators, such as the intuitionistic fuzzy weighted averaging operator, intuitionistic fuzzy ordered weighted averaging operator, and intuitionistic fuzzy hybrid aggregation operator, for aggregating intuitionistic fuzzy values and establish various properties of these operators.

Intuitionistic Fuzzy Aggregation Operators

http://bcpw.bg.pw.edu.pl/Content/1968/Rudiments.pdf

Rudiments of rough sets

The weighted geometric (WG) operator and the ordered weighted geometric (OWG) operator are two common aggregation operators in the field of information fusion. But these two aggregation operators are usually used in situations where the given arguments are expressed as crisp numbers or linguistic values. In this paper, we develop some new geometric aggregation operators, such as the intuitionistic fuzzy weighted geometric (IFWG) operator, the intuitionistic fuzzy ordered weighted geometric (IFOWG) operator, and the intuitionistic fuzzy hybrid geometric (IFHG) operator, which extend the WG and OWG operators to accommodate the environment in which the given arguments are intuitionistic fuzzy sets which are characterized by a membership function and a non-membership function. Some numerical examples are given to illustrate the developed operators. Finally, we give an application of the IFHG operator to multiple attribute decision making based on intuitionistic fuzzy sets.

Some geometric aggregation operators based on intuitionistic fuzzy sets

In this paper, we apply the theory of soft sets to solve a decision making problem using rough mathematics.

An application of soft sets in a decision making problem

Fuzzy classification has become of great interest because of its ability to utilize simple linguistically interpretable rules and has overcome the limitations of symbolic or crisp rule based classifiers. This paper introduces an extension to fuzzy classifier: a neutrosophic classifier, which would utilize neutrosophic logic for its working. Neutrosophic logic is a generalized logic that is capable of effectively handling indeterminacy, stochasticity acquisition errors that fuzzy logic cannot handle. The proposed neutrosophic classifier employs neutrosophic logic for its working and is an extension of commonly used fuzzy classifier. It is compared with the commonly used fuzzy classifiers on the following parameters: nature of membership functions, number of rules and indeterminacy in the results generated. It is proved in the paper that extended fuzzy classifier: neutrosophic classifier; optimizes the said parameters in comparison to the fuzzy counterpart. Finally the paper is concluded with justifying that neutrosophic logic though in its nascent stage still holds the potential to be experimented for further exploration in different domains.

Neutrosophic classifier: An extension of fuzzy classifer

The conventional first-order computational homogenization framework is restricted to problems where the macro characteristic length scale is much larger than the underlying Representative Volume Element (RVE). In the absence of a clear separation of length scales, higher-order enrichment is required to capture the influence of the underlying rapid fluctuations, otherwise neglected in the first-order framework. In this contribution, focusing on matrix-inclusion composites, a novel computational homogenization framework is proposed such that standard continuum models at the micro-scale translate onto the macro-scale to recover a micromorphic continuum. Departing from the conventional FE 2 framework where a macroscopic strain tensor characterizes the average deformation within the RVE, our formulation introduces an additional macro kinematic field to characterize the average strain in the inclusions. The two macro kinematic fields, each characterizing a particular aspect of deformation within the RVE, thus provide critical information on the underlying rapid fluctuations. The net effect of these fluctuations, as well as the interactions between RVEs, are next incorporated naturally into the macroscopic virtual power statement through the Hill-Mandel condition. The excellent predictive capability of the proposed homogenization framework is illustrated through three benchmark examples. It is shown that the homogenized micromorphic model adequately captures the material responses, even in the absence of a clear separation of length scales between macro and micro.

A micromorphic computational homogenization framework for heterogeneous materials

Fretting fatigue stress analysis in heterogeneous material using direct numerical simulations in solid mechanics

Fuzzy inner product spaces and fuzzy norm functions

In the present paper, the bag structure viewed by Yager is studied. Complementation of bags and fuzzy bags is done, Cartesian product of bags is defined and some propositions are proved.

Ranjit Biswas

Papers

Neutrosophic classifier: An extension of fuzzy classifer

A micromorphic computational homogenization framework for heterogeneous materials

Fretting fatigue stress analysis in heterogeneous material using direct numerical simulations in solid mechanics

Fuzzy inner product spaces and fuzzy norm functions

On Yager's theory of bags and fuzzy bags