Classical automata, fuzzy automata, and rough automata with input alphabets as numbers or symbols are formal computing models with values. Fuzzy automata and rough automata are computation models with uncertain or imprecise information about the next state and can only process the string of input symbols or numbers. To process words and propositions involved in natural languages, we need a computation model to model real-world problems by capturing the uncertainties involved in a word. In this paper, we have shown that computing with word methodology deals with perceptions rather than measurements and allows the use of words in place of numbers and symbols while describing the real-world problems together with interval type-2 (IT2) fuzzy sets which have the capacity to capture uncertainties involved in word using its footprint of uncertainty. The rough set theory, which has potential of modeling vagueness in the imprecise and ill-defined environment, introduces a computation model, namely, IT2 fuzzy rough finite automata, which is efficient to process uncertainties involved in words. Further, we have shown the application of introduced IT2 fuzzy finite rough automaton in the medical diagnosis of COVID-19 patients.

The classical automata, fuzzy finite automata, and rough finite state automata are some formal models of computing used to perform the task of computation and are considered to be the input device. These computational models are valid only for fixed input alphabets for which they are defined and, therefore, are less user-friendly and have limited applications. The semantic computing techniques provide a way to redefine them to improve their scope and applicability. In this paper, the concept of semantically equivalent concepts and semantically related concepts in information about real-world applications datasets are used to introduce and study two new formal models of computations with semantic computing (SC), namely, a rough finite-state automaton for SC and a fuzzy finite rough automaton for SC as extensions of rough finite-state automaton and fuzzy finite-state automaton, respectively, in two different ways. The traditional rough finite-state automata can not deal with situations when external alphabet or semantically equivalent concepts are given as inputs. The proposed rough finite-state automaton for SC can handle such situations and accept such inputs and is shown to have successful real-world applications. Similarly, a fuzzy finite rough automaton corresponding to a fuzzy automaton is also failed to process input alphabet different from their input alphabet, the proposed fuzzy finite rough automaton for SC corresponding to a given fuzzy finite automaton is capable of processing semantically related input, and external input alphabet information from the dataset obtained by real-world applications and provide better user experience and applicability as compared to classical fuzzy finite rough automaton.

The present paper is focusing on the Mathematical concepts from Linear Algebra including Eigen values and eigen vectors and disgonalization to predict the genotype distribution. This paper is based on finding the genotype distribution for n th generation in Autosomal inheritance.

This work applies the bicategory-theoretic concepts in formation of minimal fuzzy realization for a given fuzzy behavior. The concept of derivative of fuzzy behavior is used for such construction.

This work is toward the study of theory of IF-automata based on residuated lattices ([Formula: see text]-automaton) and to use [Formula: see text]-topological concepts for study of algebraic concepts therein. We introduce the notion of [Formula: see text]-subsystems and strong [Formula: see text]-subsystems of an [Formula: see text]-automaton and show that these are precisely the [Formula: see text]-closed sets with respect to the [Formula: see text]-topologies introduced on state-set of an [Formula: see text]-automaton. Finally, we study the characterization of separated [Formula: see text]-subsystem for an [Formula: see text]-automaton.