Please use this identifier to cite or link to this item: http://prr.hec.gov.pk/jspui/handle/123456789/18741
Title: Application of bipolar fuzzy (soft) set in ordered semigroups
Authors: Ibrar, Muhammad
Keywords: Physical Sciences
Mathematics
Issue Date: 2021
Publisher: Abdul Wali Khan University, Mardan
Abstract: In this research, the ideal theory of ordered semigroups in the framework of bipolar fuzzy sets (briefly BFSs) is expended. The main idea defined in this thesis are that of bipolar fuzzy left (right) ideal (briefly BFL(R)I) in ordered semigroups, bipolar fuzzy interior ideal (briefly BFII) in ordered semigroups, bipolar fuzzy generalized bi-ideal (briefly BFGBI) in ordered semigroups and bipolar fuzzy bi-ideal (briefly BFBI) in ordered semigroups. We also generalize BFL(R)I as (𝛼, 𝛽)- BFL(R)I, BFII as (𝛼, 𝛽)-BFII, BFGBI as (𝛼, 𝛽)-BFGBI and BFBI as (𝛼, 𝛽)-BFBI in ordered semigroups. We also generalize BFII as (𝛼1, 𝛼2; 𝛽1, 𝛽2 )-BFII in ordered semigroups. We examine these newly defined notions in regular, intra-regular and semi-prime ordered semigroups. These classes of ordered semigroups are characterized in framework of the newly defined notions. As soft sets plays a vital role to deal with uncertainty in the data and has many applications in decisions making problem, we utilize the concept of bipolar fuzzy soft sets (briefly BFSSs) in decision making as well. Decision makings schemes based on fuzzy parameterized bipolar fuzzy soft expert sets and possibility bipolar fuzzy soft expert sets have been examined. Key Words: Bipolar Fuzzy Set; Bipolar Fuzzy Ideal; Bipolar Fuzzy Interior Ideal; Bipolar Fuzzy Generalized Bi-Ideal; Bipolar Fuzzy Bi-Ideal; Bipolar Fuzzy Soft Expert Set; Fuzzy Parameterized Bipolar Fuzzy Soft Expert Set; Possibility Bipolar Fuzzy Soft Expert Set; Decision making
Gov't Doc #: 22531
URI: http://prr.hec.gov.pk/jspui/handle/123456789/18741
Appears in Collections:PhD Thesis of All Public / Private Sector Universities / DAIs.

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