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2023

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Beyond Negation And Excluded Middle: An Exploration To Embrace The Otherness Beyond Classical Logic System And Into Neutrosophic Logic, Florentin Smarandache, Victor Christianto Jan 2023

Beyond Negation And Excluded Middle: An Exploration To Embrace The Otherness Beyond Classical Logic System And Into Neutrosophic Logic, Florentin Smarandache, Victor Christianto

Branch Mathematics and Statistics Faculty and Staff Publications

As part of our small contribution in dialogue toward better peace development and reconciliation studies, and following Toffler & Toffler’s War and Antiwar (1993), the present article delves into a realm of logic beyond the traditional confines of negation and the excluded middle principle, exploring the nuances of "Otherness" that transcend classical and Nagatomo logics. Departing from the foundational premises of classical Aristotelian logic systems, this exploration ventures into alternative realms of reasoning, specifically examining Neutrosophic Logic and Klein bottle logic (cf. Smarandache, 2005). The study challenges conventional boundaries and explores the implications of embracing paradoxes and self-reference in logic …

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Superhyperfunction, Superhyperstructure, Neutrosophic Superhyperfunction And Neutrosophic Superhyperstructure: Current Understanding And Future Directions, Florentin Smarandache Jan 2023

Superhyperfunction, Superhyperstructure, Neutrosophic Superhyperfunction And Neutrosophic Superhyperstructure: Current Understanding And Future Directions, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The n-th PowerSet of a Set {or Pn(S)} better describes our real world, because a system S (which may be a company, institution, association, country, society, set of objects/plants/animals/beings, set of concepts/ideas/propositions, etc.) is formed by sub-systems, which in their turn by sub-sub-systems, and so on. We prove that the SuperHyperFunction is a generalization of classical Function, SuperFunction, and HyperFunction. And the SuperHyperAlgebra, SuperHyperGraph are part of the SuperHyperStructure. Almost all structures in our real world are Neutrosophic SuperHyperStructures since they have indeterminate/incomplete/uncertain/conflicting data.

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Graphical Method For Solving Neutrosophical Nonlinear Programming Models, Maissam Ahmad Jdid, Florentin Smarandache Jan 2023

Graphical Method For Solving Neutrosophical Nonlinear Programming Models, Maissam Ahmad Jdid, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

One important method for finding the optimal solution for linear and nonlinear models is the graphical method, which is used if the linear or nonlinear mathematical model contains one, two, or three variables. Models that contain only two variables are models for which the optimal solution has been obtained graphically, whether these models are linear or non-linear in references that rely on classical logic. In this research, we present a study through which we present the graphical method for solving nonlinear neutrosophical models in the following case: (1) The objective function is a nonlinear function, and the constraints are linear …

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On Characterizing Efficient And Properly Efficient Solutions For Multi- Objective Programming Problems In A Complex Space, Alhanouf Alburaikan, Hamiden Abd El-Wahed Khalifa, Florentin Smarandache Jan 2023

On Characterizing Efficient And Properly Efficient Solutions For Multi- Objective Programming Problems In A Complex Space, Alhanouf Alburaikan, Hamiden Abd El-Wahed Khalifa, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, a complex non- linear programming problem with the two parts (real and imaginary) is considered. The efficient and proper efficient solutions in terms of optimal solutions of related appropriate scalar optimization problems are characterized. Also, the Kuhn-Tuckers' conditions for efficiency and proper efficiency are derived. This paper is divided into two independently parts: The first provides the relationships between the optimal solutions of a complex single-objective optimization problem and solutions of two related real programming problems. The second part is concerned with the theory of a multi-objective optimization in complex space.

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