Fawad Hussain ¹, Muhammad Tahir ², Saleem Abdullah ², Nazia Sadiq ²

Affiliations
1 Department of Mathematics, Abbottabad University of Science and Technology, PK
2 Department of Mathematics, Hazara University Mansehra, PK

Abstract

The study of a seminear-ring was started in 1967. Seminear-ring is the generalization of semiring and nearing. It is known that in a semiring the quotient structure is constructed by congruence relations through c-ideals and homomorphisms. We apply the said congruence relations to a seminear-ring and get quotient structure of a seminear-ring. The aim of this paper is to discuss quotient seminear-rings in two different ways. We study congruence relations, homomorphisms and ideals. We show that each homomorphism and c-ideal define a congruence relation on seminear-rings. At the end, we discuss quotient seminear-rings.

Keywords

C-Ideals, Congruence Relation, Homomorphism, Seminear-Ring, Quotient Seminear-Ring.

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Mahmood Ashraf ¹, Rabia Shakir ¹, Mohammad Abrar ², Muhammad Tahir ³, Thabit Sabbah ⁴

Affiliations
1 Department of Computer Science, Federal Urdu University of Arts, Science and Technology, Islamabad, PK
2 Department of Computer Science, Bache Khan University, Charade, KPK, PK
3 University of Jeddah, SA
4 Al-Quads Open University, Ramallah, PS

Abstract

Objectives: To develop the physicality and usability guidelines to reduce the interaction complexities and the cognitive burden on the users. Methods/Statistical Analysis: The study is conducted on the kitchen appliances. Three case studies were conducted on different kitchen appliances. Forty to fifty participants were selected from different age group, qualification, and cities. The data were collected from the participant on the bases of pretest and posttest questionnaire and direct observation method. The study was divided into two phases i.e. formulation of guidelines and comparative analysis. The study I and study II were used for guideline formulation and study III provided a comparative analysis. The qualitative research paradigms were employed for data analysis. Findings: Based on the data analysis, the new guidelines were proposed and evaluated in terms of physicality principles and usability components. Subsequently, t-test was used to validate, evaluate, and compare the results against ISO and IEC. This research has showed that the proposed physicality and usability guidelines are helpful in overcoming interaction complexities, reducing cognitive burden, and saving time. Application/Improvements: The data analysis showed that the proposed guidelines will improve the user experience by 94% and 85% in the physicality and usability of the kitchen appliances, respectively. The proposed guidelines can be employed in improving the design of these appliances to overcome interaction complexities.

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