Bipolar-Valued Multi Fuzzy Subhemirings Of A Hemiring

Santhi, V. K.; Anbarasi, K.

doi:10.37622/afm/10.1.2015.55-62

Cited by 4 publications

(5 citation statements)

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“…The function η N = ðη 1N , η 2N , ⋯, η nN Þ is said to be a fuzzy multimembership function of a multifuzzy set N of dimension n. Definition 4. (see [65]). A bipolar-valued multifuzzy set B of dimension n over Π is given by the following structure: B = fðπ, η + 1B ðπÞ, η + 2B ðπÞ, ⋯, η + nB ðπÞ, η − 1B ðπÞ, η − 2B ðπÞ, ⋯, η − nB ðπÞÞ: π ∈ Πg, where for i = 1, 2, ⋯, n, we have η + iB : Π ⟶ ½0, 1 representing the positive membership degrees denoting the satisfaction degrees of π to some properties corresponding to B and η − iB : Π ⟶ ½−1, 0 representing the negative membership degrees denoting the satisfaction degrees of π to some implicit counter-properties of B.…”

Section: Preliminary Definitionsmentioning

confidence: 96%

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A Generalized Decision-Making Technique Based on Bipolar-Valued Multivague Soft Sets

Sakr

Muse²,

Aldallal

2022

Journal of Function Spaces

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The decision-making technique, launched by Roy and Maji, is considered an effective method to overcome uncertainty and fuzziness in decision-making problems, though, adapting it to reflect the problem parameters’ vagueness, as well as multibipolarity, is very difficult. So, in this article, the bipolarity is interpolated into the multivague soft set of order n . This gives a new more generalized, flexible, and applicable extension than the fuzzy soft model, or any previous hybrid model, which is the bipolar-valued multivague soft model of dimension n . Moreover, types of bipolar-valued multivague soft sets of dimension n , as well as some new associated concepts and operations, are investigated with examples. Furthermore, properties of bipolar-valued multivague soft sets of dimension n including absorption, commutative, associative, and distributive properties, as well as De Morgan’s laws, are provided in detail. Finally, a bipolar-valued multivague soft set-designed decision-making algorithm, as well as a real-life example, are discussed generalizing the Roy and Maji method.

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Section: Preliminary Definitionsmentioning

confidence: 96%

“…Furthermore, Santhi and Shyamala [65] defined the bipolar-valued multifuzzy set and made some notes on bipolar-valued multifuzzy subgroups of a group. Moreover, Yang et al [66] proposed the bipolar-valued multifuzzy soft set concept and introduced some decision-making applications using it.…”

Section: Introduction Motivation and Related Workmentioning

confidence: 99%

A Generalized Decision-Making Technique Based on Bipolar-Valued Multivague Soft Sets

Sakr

Muse²,

Aldallal

2022

Journal of Function Spaces

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“…These definitions are about the fuzzy set, bipolar-valued fuzzy set, multi-fuzzy set, bipolar-valued multi-fuzzy set, soft set, effective set, and effective fuzzy soft set. One can refer to [1,3,6,24,26,39] to find more detailed results and examples about those above concepts.…”

Section: Preliminariesmentioning

confidence: 99%

“…. , η nN ), the fuzzy multimembership function of a multi-fuzzy set N of dimension n. Definition 4 ((Bipolar-valued multi-fuzzy set) [26]). The following formula represents the bipolar-valued multi-fuzzy set B of dimension n over an initial universe Ξ:…”

Section: Preliminariesmentioning

confidence: 99%

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Medical Diagnosis under Effective Bipolar-Valued Multi-Fuzzy Soft Settings

Sakr,

Alyami,

Abd Elgawad

2023

Mathematics

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The Molodtsov-initiated soft set theory plays an important role as a powerful mathematical tool for handling uncertainty. As an extension of the soft set, the fuzzy soft set can be seen to be more generic and flexible than utilizing the soft set only that fails to represent problem parameters fuzziness. Through this progress, the fuzzy soft set theory cannot deal with decision-making problems involving multi-attribute sets, bipolarity, or some effective considered parameters. Therefore, the goal of this article is to adapt effectiveness and bipolarity concepts with the multi-fuzzy soft set of order n. One can see that this approach generates a novel, extended, effective decision-making environment that is more applicable than any previously introduced one. In addition, types, concepts, and operations of effective bipolar-valued multi-fuzzy soft sets of dimension n are provided, each with an example. Furthermore, properties like absorption, associative, distributive, commutative, and De Morgan’s laws of those new sets are investigated. Moreover, a decision-making methodology under effective bipolar-valued multi-fuzzy soft settings is established. This technique facilitates reaching the final decision that this student is qualified to take a certain education level, or this patient is suffering from a certain disease, etc. In addition, a case study represented in a medical diagnosis example is discussed in detail to make the proposed algorithm clearer. Applying matrix techniques in this example as well as using MATLAB®, not only makes it easier and faster in doing calculations, but also gives more accurate, optimal, and effective decisions. Finally, the sensitivity analysis, as well as a comparison with the existing methods, are conducted in detail and are summarized in a chart to show the difference between them and the current one.

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An inventory model for the association between retailer and supplier for a finite planning horizon with carbon emission-dependent demand

Mishra,

Ranu

2023

The Fourth Scientific Conference for Electrical Engineering Techniques Research (Eetr2022)

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Bipolar-Valued Multi Fuzzy Subhemirings Of A Hemiring

Cited by 4 publications

References 0 publications

A Generalized Decision-Making Technique Based on Bipolar-Valued Multivague Soft Sets

A Generalized Decision-Making Technique Based on Bipolar-Valued Multivague Soft Sets

Medical Diagnosis under Effective Bipolar-Valued Multi-Fuzzy Soft Settings

An inventory model for the association between retailer and supplier for a finite planning horizon with carbon emission-dependent demand

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