A Modern Syllogistic Method in Intuitionistic Fuzzy Logic with Realistic Tautology

Rushdi, Ali Muhammad Ali; Zarouan, Mohamed; Alshehri, Taleb; Rushdi, Muhammad A.

doi:10.1155/2015/327390

Cited by 8 publications

(7 citation statements)

References 59 publications

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“…In computing the complete sum all don't-care configurations are considered asserted. There are many algorithmic ways to compute the complete sum (Muroga, 1979;Brown, 1990;Rushdi and Al-Yahya, 2001b;Rushdi et al, 2015a;2015b). The CKM is not particularly convenient for computing the complete sum (Muroga, 1979) since it is possible that some prime implicants might be overlooked.…”

Section: The Complete Sum Versus the Minimal Summentioning

confidence: 99%

Utilization of Karnaugh Maps in Multi-Value Qualitative Comparative Analysis

Rushdi¹

2018

Int J Math, Eng, Manag Sci

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A recent debate in the literature of Qualitative Comparative Analysis (QCA) concerns the potentials and pitfalls of the multi-value variant (mvQCA) in comparison with the more established crisp-set QCA (csQCA) and fuzzy-set QCA (fsQCA) variants. So far, the mvQCA methodology has been implemented either algebraically or via specific software tools such as TOSMANA. The main goal of this paper is to enhance the mvQCA methodology through the utilization of several varieties of Karnaugh maps including (a) the Conventional Karnaugh Map (CKM), (b) the Multi-Valued Karnaugh Map (MVKM), and (c) the Variable-Entered Karnaugh Map (VEKM). The paper offers a tutorial exposition of each of these maps in terms of two recently-published problems concerning the legal provision (introduction) and implementation of party bans in sub-Saharan Africa. Results obtained via various map techniques agree exactly among themselves, and are generally more compact than those obtained earlier via elementary algebraic manipulations, or even via software tools. We show, by way of example, that coding multi-valued variables by binary ones has a harmful primary effect of increasing the input domain. This effect is partially counterbalanced by a (contrarily to common belief) beneficial secondary effect of introducing genuine don’t-care configurations. We also address the issue of unresolved contradictory configurations, and propose two strategies to cope with them. The maps used tackle seven binary variables (or their equivalent), a number beyond the typical map limit of six variables. They are used to produce not only the minimal sum of a Boolean function but the complete sum as well. Though this paper is basically intended as a contribution to mvQCA methodology, it is also of significant utility in any field that demands the use of the Karnaugh map. It serves as a unification/exposition of three fundamental variants of the map, and has a definite pedagogical advantage for the wide spectrum of map users.

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Section: The Complete Sum Versus the Minimal Summentioning

confidence: 99%

Utilization of Karnaugh Maps in Multi-Value Qualitative Comparative Analysis

Rushdi¹

2018

Int J Math, Eng, Manag Sci

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“…Correspondingly, its complement, the Boolean function of failure is given by [12, [29][30][31][32] ( , , , ,…”

Section: A) the Unit-gap Methodsmentioning

confidence: 99%

Reliability Analysis of a Home-scale Microgrid Based on a Threshold System

Hidayat

Rushdi

2021

JENRR

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The reliability of a microgrid power system is an important aspect to analyze so as to ascertain that the system can provide electricity reliably over a specified period of time. This paper analyzes a home-scale model of a microgrid system by using the threshold system model (inadvertently labeled as the weighted k-out-of-n:G system model), which is a system whose success is treated as a threshold switching function. To analyze the reliability of the system, we first proved that its success is a coherent threshold function, and then identified possible (non-unique) values for its weights and threshold. Two methods are employed for this. The first method is called the unity-gap method and the second is called the fair-power method. In the unity-gap method, we utilize certain dominations and symmetries to reduce the number of pertinent inequalities (turned into equations) to be solved. In the fair-power method, the Banzhaf index is calculated to express the weight of each component as its relative power or importance. Finally, a recursive algorithm for computing system reliability is presented. The threshold success function is verified to be shellable, and the non-uniqueness of the set of weights and thresholds is demonstrated to be of no detrimental consequence, as different correct sets of weights and threshold produce equivalent expressions of system reliability.

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“…Complementing both sides of (9), we obtain the system failure as a product of four sums (which, when multiplied out, and after absorbing all subsuming terms, yields a disjunction of all prime implicants of system failure) Using intelligent multiplication [40,42,[44][45][46][47][48][49][50][51][52] { ∨ ∨ = ∨ }, we multiply out the first two terms in (10) to obtain ( 7 < 3 ∨ 2 < 3 3 < 3 ) ( 5 < 3 ∨ 8 < 3 ∨ 2 < 3 3 < 3 ) = 7 < 3 ( 5 < 3 ∨ 8 < 3 ) ∨ 2 < 3 3 < 3 = 7 < 3 5 < 3 ∨ 7 < 3 8 < 3 ∨ 2 < 3 3 < 3…”

Section: Suppliers Transfer Centers Marketmentioning

confidence: 99%

Derivation of Minimal Cutsets from Minimal Pathsets for a Multi-State System and Utilization of Both Sets in Checking Reliability Expressions

Rushdi

Amashah

2021

JERR

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This paper addresses two important useful extensions of binary reliability techniques to multi-state reliability techniques, namely: (a) the problem of complementation or inversion of the function of system success to that of system failure (or equivalently, of deriving the logical minimal cutsets in terms of the logical minimal paths), and (b) the associated problem of hand-checking of a symbolic reliability expression. The paper deals specifically with the reliability of a multi-state delivery network. It presents two complementation procedures, one via the application of multi-state De Morgan’s rules, and the other via the multi-state Boole-Shannon expansion. The paper also illustrates one case in which this complementation is needed, as it outlines a method for checking the reliability of the multi-state system in terms of its logical minimal paths and logical minimal cutsets.

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A Modern Syllogistic Method in Intuitionistic Fuzzy Logic with Realistic Tautology

Cited by 8 publications

References 59 publications

Utilization of Karnaugh Maps in Multi-Value Qualitative Comparative Analysis

Utilization of Karnaugh Maps in Multi-Value Qualitative Comparative Analysis

Reliability Analysis of a Home-scale Microgrid Based on a Threshold System

Derivation of Minimal Cutsets from Minimal Pathsets for a Multi-State System and Utilization of Both Sets in Checking Reliability Expressions

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