Kumar Sankar Ray
We mimic the cognitive ability of Human perception, based on Bayesian hypothesis, to recognize view-based 3D objects. We consider approximate Bayesian (Empirical Bayesian) for perceptual inference for recognition. We essentially handle computation with perception.
Litan Kumar Das, Kumar Sankar Ray, Prakash Chandra Mali
The paper aims to develop a framework for coalgebraic fuzzy geometric logic by adding modalities to the language of fuzzy geometric logic. Using the methods of coalgebra, the modal operators are introduced in the language of fuzzy geometric logic. To define the modal operators, we introduce a notion of fuzzy-open predicate lifting. Based on coalgebras for an endofunctor $T$ on the category $\textbf{Fuzzy-Top}$ of fuzzy topological spaces and fuzzy continuous maps, we build models for the coalgebraic fuzzy geometric logic. Bisimulations for the defined models are discussed in this work.
Mainak Sen, Kumar Sankar Ray, Amlan Chakrabarti
Phishing detection systems are predominantly rely on statistical machine learning models, which often lack contextual reasoning and are vulnerable to adversarial manipulation. In this work, we propose a hybrid framework that integrates machine learning classifiers with non-monotonic reasoning using Answer Set Programming (ASP) to enable context-aware decision refinement. The proposed post-hoc reasoning layer incorporates expert knowledge to revise classifier predictions through formal belief revisions. Experimental results indicate that the reasoning module modifies 5.08\% of classifier outputs, leading to improved decision consistency. A key advantage is that new domain knowledge can be incorporated into the reasoning layer in $\mathcal{O}(n)$ time, eliminating the need for model retraining.
Kumar Sankar Ray, Sandip Paul, Diganta Saha
A belief base revision is developed. The belief base is represented using Unified Answer Set Programs which is capable of representing imprecise and uncertain information and perform nonomonotonic reasoning with them. The base revision operator is developed using Removed Set Revision strategy. The operator is characterized with respect to the postulates for base revisions operator satisfies.
Sandip Paul, Kumar Sankar Ray, Diganta Saha
To deal with uncertainty in reasoning, interval-valued logic has been developed. But uniform intervals cannot capture the difference in degrees of belief for different values in the interval. To salvage the problem triangular and trapezoidal fuzzy numbers are used as the set of truth values along with traditional intervals. Preorder-based truth and knowledge ordering are defined over the set of fuzzy numbers defined over $[0,1]$. Based on this enhanced set of epistemic states, an answer set framework is developed, with properly defined logical connectives. This type of framework is efficient in knowledge representation and reasoning with vague and uncertain information under nonmonotonic environment where rules may posses exceptions.
Litan Kumar Das, Kumar Sankar Ray
In this paper, we investigate a bitopological duality for algebras of Fitting's multi-valued logic. We also extend the natural duality theory for $\mathbb{ISP_I}(\mathcal{L})$ by developing a duality for $\mathbb{ISP}(\mathcal{L})$, where $\mathcal{L}$ is a finite algebra in which underlying lattice is bounded distributive.
Sandip Paul, Kumar Sankar Ray, Diganta Saha
An interval-valued fuzzy answer set programming paradigm is proposed for nonmonotonic reasoning with vague and uncertain information. The set of sub-intervals of $[0,1]$ is considered as truth-space. The intervals are ordered using preorder-based truth and knowledge ordering. The preorder based ordering is an enhanced version of bilattice-based ordering. The system can represent and reason with prioritized rules, rules with exceptions. An iterative method for answer set computation is proposed. The sufficient conditions for termination of iterations are identified for a class of logic programs using the notion of difference equations.
Srikanta Kolay, Kumar Sankar Ray, Abhoy Chand Mondal
K-means (MacQueen, 1967) [1] is one of the simplest unsupervised learning algorithms that solve the well-known clustering problem. The procedure follows a simple and easy way to classify a given data set to a predefined, say K number of clusters. Determination of K is a difficult job and it is not known that which value of K can partition the objects as per our intuition. To overcome this problem we proposed K+ Means algorithm. This algorithm is an enhancement over K-Means algorithm.
Kumar Sankar Ray, Sandip Paul, Diganta Saha
Bilattice-based triangle provides an elegant algebraic structure for reasoning with vague and uncertain information. But the truth and knowledge ordering of intervals in bilattice-based triangle can not handle repetitive belief revisions which is an essential characteristic of nonmonotonic reasoning. Moreover the ordering induced over the intervals by the bilattice-based triangle is not sometimes intuitive. In this work, we construct an alternative algebraic structure, namely preorder-based triangle and we formulate proper logical connectives for this. It is also demonstrated that Preorder-based triangle serves to be a better alternative to the bilattice-based triangle for reasoning in application areas, that involve nonmonotonic fuzzy reasoning with uncertain information.
Kumar Sankar Ray, Mandrita Mondal
In this paper we propose a wet lab algorithm for prediction of radiation fog by DNA computing. The concept of DNA computing is essentially exploited for generating the classifier algorithm in the wet lab. The classifier is based on a new concept of similarity based fuzzy reasoning suitable for wet lab implementation. This new concept of similarity based fuzzy reasoning is different from conventional approach to fuzzy reasoning based on similarity measure and also replaces the logical aspect of classical fuzzy reasoning by DNA chemistry. Thus, we add a new dimension to existing forms of fuzzy reasoning by bringing it down to nanoscale. We exploit the concept of massive parallelism of DNA computing by designing this new classifier in the wet lab. This newly designed classifier is very much generalized in nature and apart from prediction of radiation fog this methodology can be applied to other types of data also. To achieve our goal we first fuzzify the given observed parameters in a form of synthetic DNA sequence which is called fuzzy DNA and which handles the vague concept of human reasoning.