Research Article A New Approach to Study h-Hemiregular Hemirings in terms of Bipolar Fuzzy h-Ideals Shahida Bashir , 1 Ahmad N. Al-Kenani, 2 Rabia Mazhar, 1 and Zunaira Pervaiz 1 1 Department of Mathematics, University of Gujrat, Gujrat 50700, Pakistan 2 Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80219, Jeddah 21589, Saudi Arabia Correspondence should be addressed to Shahida Bashir; shahida.bashir@uog.edu.pk Received 6 January 2022; Revised 7 February 2022; Accepted 2 March 2022; Published 15 April 2022 Academic Editor: Mingwei Lin Copyright©2022ShahidaBashiretal.isisanopenaccessarticledistributedundertheCreativeCommonsAttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. is paper provides a generalized form of ideals, that is, h-ideals of hemirings with the combination of a bipolar fuzzy set (BFS). e BFS is an extension of the fuzzy set (FS), which deals with complex and vague problems in both positive and negative aspects. e basic purpose of this paper is to introduce the idea of (α, β)−bipolar fuzzy h-subhemirings (h-BFSHs), (α, β)−bipolar fuzzy h-ideals (h-BFIs), and (α, β)−bipolar fuzzy h-bi-ideals (h-BFbIs) in hemirings by applying the definitions of belongingness (∈) and quasicoincidence (q) of the bipolar fuzzy point. We will also focus on upper and lower parts of the h-product of bipolar fuzzy subsets (BFSSs) of hemirings. In the end, we have characterized the h-hemiregular and h-intrahemiregular hemirings in terms of the (∈, ∈∨q)−h-BFIs and (∈, ∈∨q)−h-BFbIs. 1.IntroductionandMotivation In 1994, Zhang [1] introduced bipolar fuzzy set theory which is an inflation of fuzzy set theory. Bipolarity is an important idea that is mostly used in our daily life. In a lot of disciplines such as decision making, algebraic structures, graph theory, and medical science, bipolar valued fuzzy sets have become a significant research work. In real life, it is noticed that people may have a different response at a time for the same qualities of an item or a plan. One may have a positive response, and theotheronemayhaveanegativeresponse;forexample,$100 is a big amount for a needy person, but at the same time, this amount may have less value for a rich man. Similarly, sweetness and sourness of a food, effects and side effects of medicines, good and bad human behavior, happiness and sadness, thin and thick fluid, and honesty and dishonesty all are two-sided aspects of an object or situation. See [2–10] for examples and results which are relevant to bipolar fuzzy sets. In 1965, Zadeh [11] introduced the concept of fuzzy set theory which deals with the uncertain and complex problems in decision-making theory, medical science, engineering, automata theory, and graph theory [12–16]. e right place of entries to fuzzy set is indicated by a membership degree. In [0, 1] interval, perimeter point 0 shows no fuzzy set acceptability and 1 shows the fuzzy set acceptance. Also, (0, 1) defines the fuzzy collection to be partially belonging. If the membership degree is any property, then 1 describes that the element satisfiesthepropertyand0describesthattheelementdoesnot satisfy the property. Interval (0, 1) shows the midway con- dition. But, there was a difficulty to deliberate the irrelevancy of data to the fuzzy set. e FS is extended to BFS to tackle such situations. In 1934, Vandiver [17] firstly familiarized the theory of semiring. In 1935, Von Neumann introduced the idea of regularity in rings and showed that for any nonempty set R, if the semigroup (R, ·)isregular,thenthering(R,+, ·)isalso regular [18]. In 1951, Bourne showed if for all r ∈ R there exist x,y ∈ R such that r + rxr � ryr, then semiring (R, +, ·)is also regular [19]. Hemirings (semirings with zero and commutative addition) are studied in the theory of automata and formal languages [20–22]. Algebraic patterns are very important in mathematics. Hemiring is also a useful alge- braic structure. It is very useful in functional analysis, physics, computation, coding, topological space, automata theory, formal language theory, mathematical modelling, and graph theory. Hindawi Mathematical Problems in Engineering Volume 2022, Article ID 2766254, 11 pages https://doi.org/10.1155/2022/2766254