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Roughness of a set by $$(\alpha , \beta )$$-indiscernibility of Bipolar fuzzy relation
Computational and Applied Mathematics, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Rizwan Gul, Muhammad Shabir
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On fuzzy bipolar soft sets, their algebraic structures and applications
Journal of Intelligent & Fuzzy Systems, 2014We have defined fuzzy bipolar soft sets and basic operations of union, intersection and complementation for fuzzy bipolar soft sets. The algebraic properties of fuzzy bipolar soft sets are discussed. The concept of bipolar fuzzy soft set is also given and the equivalence of both structures is established.
Munazza Naz, Muhammad Shabir
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(Yin) (Yang) bipolar fuzzy sets
1998 IEEE International Conference on Fuzzy Systems Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98CH36228), 2002A bipolar fuzzy set theory is introduced in the space {/spl forall/(x,y)|(x,y)/spl isin/[-1,0]/spl times/[0,1]}. Two types of bipolar /spl alpha/-cuts are proposed. Resolutions of bipolar level sets and their relationships are established. The bipolar fuzzy set theory combines both polarity and fuzziness into a unified model and therefore, provides a ...
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Complex Bipolar Multi-Fuzzy Sets
UncertaintyConvey human being's information to a mathematical formula and vice versa by a proper tool, is considered a first step to solve the problem of assigning a membership degree (suitable value) of an object to a set by decision-makers. Different information with its periodic circumstances highlighted the need for an extra variable to be built into the ...
Abd Ulazeez Alkouri +2 more
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The novel WASPAS method for roughness of bipolar fuzzy sets based bipolar fuzzy covering
Physica ScriptaAbstract The research employs Covering-based Rough Set and Fuzzy Set theories to handle uncertainty in data analysis. However, when dealing with data uncertainty and bipolarity in various scenarios, the Bipolar Fuzzy Set (BFS) theory proves advantageous by simultaneously managing positive and negative information.
Faiza Tufail, Muhammad Shabir
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SymmetryThis study introduces a novel mathematical tool for representing imprecise and ambiguous data: the multi-q cubic bipolar fuzzy soft set. Building upon established bipolar fuzzy sets and soft sets, this paper fist defines the concept of multi-q cubic ...
Khawla Abdullah Alqablan +1 more
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Mathematical morphology and spatial reasoning: fuzzy and bipolar setting
2021Summary: This paper summarizes the mathematical aspects of fuzzy and bipolar mathematical morphology and shows how morphological operators can be applied to define spatial relations, and then used for spatial reasoning. Fuzzy sets are useful both at representation level and at reasoning level, and contribute to establish links between various areas of ...
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Fuzzy Bipolar Mathematical Morphology: A General Algebraic Setting
2011Bipolar information is an important component in information processing, to handle both positive information (e.g. preferences) and negative information (e.g. constraints) in an asymmetric way. In this paper, a general algebraic framework is proposed to handle such information using mathematical morphology operators, leading to results that apply to ...
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An Approach to Select the Investment Based on Bipolar Picture Fuzzy Sets
International Journal of Fuzzy Systems, 2021Agha Kashif, Tabasam Rashid
exaly