Solving sylvester matrix equations with LR bipolar triangular fuzzy numbers in electric circuits problems

Bipolar crisp numbers refer to two different functions and information in a given system, namely positive and negative components. Likelihood and unlikelihood information can be simultaneously represented by bipolar crisp numbers rather than classical crisp numbers. However, since bipolar crisp numbers are inadequate in dealing with uncertainty problem, bipolar fuzzy numbers (BFN) are used instead. BFN in Sylvester matrix equations (SME) plays an essential role in the control system such as in electrical controller. An electrical controller of RLC circuit consisting of resistor (R), inductor (L), and capacitor (C), is used to control the amount of electric currents flowing across the electric circuits. Besides, complex numbers which consist of real and imaginary parts are used in solving RLC circuit, where real numbers denote resistance, while imaginary numbers denote inductance or capacitance. To the best of our knowledge, the integration of SME with either BFN or complex BFN is not yet explored. Therefore, this study aims to construct analytical approaches in solving bipolar fuzzy Sylvester matrix equation (FSME), complex bipolar FSME, bipolar fully fuzzy Sylvester matrix equation (FFSME), and complex bipolar fully fuzzy linear system (FFLS) in left-right (LR) bipolar triangular fuzzy numbers. In order to obtain the solutions, bipolar FSME, complex bipolar FSME, and bipolar FFSME are converted into the bipolar linear system by utilizing Kronecker product and Vecoperator. Next, an equivalent bipolar linear system (EBLS), equivalent complex bipolar linear system (ECBLS), associated bipolar linear system (ABLS), and associated complex bipolar linear system (ACBLS) are established. Then, the final solutions of the constructed methods are obtained using inverse method. Therefore, four analytical approaches have been constructed in solving bipolar FSME, complex bipolar FSME, bipolar FFSME, and complex bipolar FFLS in LR forms. Several examples are presented to illustrate the constructed methods. Moreover, the application of RLC circuits with complex bipolar FSME and complex bipolar FFLS are also carried out. In conclusion, the new findings of analytical approaches add to the fuzzy equations body of knowledge with significant applications in bipolar electrical controllers

YinYang Bipolar Quantum Geometry and Bipolar Quantum Superposition Part I—A Background Independent Geometrical and Logical Exposition of Dirac 3-Polarizer Experiment

Bipolar quantum agent (BQA), bipolar quantum geometry (BQG) and bipolar dynamic logic (BDL) are introduced based on bipolar complementarity – a logical extension to Niels Bohr’s particle-wave YinYang duality principle. Complete geometrical background independence is proposed and BQG is proven completely background independent which leads to the notion of bipolar quantum superposition – an equilibrium-based logical approach to superposition. It is shown that the logical linearity of BDL can be unified with the physical nonlinearity of bipolar dynamic equilibrium. It is proven that a single polarized photon as a BQA can be logically channeled through the three polarizers in Dirac’s experiment with BDL regardless of quantum uncertainty. It is illustrated that BQG, BDL and bipolar probability adds analytical power to quantum mechanics. It is concluded that bipolar quantum superposition demystifies Schrödinger’s cat paradox from a weird quantum phenomenon to a logically comprehendible YinYang bipolar dynamic equilibrium interpretation of quantum superposition and leads to an analytical paradigm of quantum mechanics and quantum biology as presented in Part II of this work

Yin Yang Bipolar Atom - An Eastern Road toward Quantum Gravity

Based on bipolar dynamic logic and bipolar quantum linear algebra, a causal theory of YinYang bipolar atom is introduced in a completely background independent geometry that transcends spacetime. The causal theory leads to an equilibrium-based super symmetrical quantum cosmology of negative-positive energies. It is contended that the new theory has opened an Eastern road toward quantum gravity with bipolar logical unifications of particle and wave, matter and antimatter, relativity and quantum entanglement. Information recovery after a black hole is discussed. It is shown that not only can the new theory be applied in physical worlds but also in logical, mental, social and biological worlds. Falsifiability of the theory is discussed

YinYang Bipolar Quantum Geometry and Bipolar Quantum Superposition Part II—Toward an Equilibrium-Based Analytical Paradigm of Quantum Mechanics and Quantum Biology

In Part I of this paper, YinYang bipolar quantum agent (BQA), bipolar quantum geometry (BQG) and 2-dimensional generic bipolar quantum superposition are introduced with a geometrical and logical exposition of Dirac 3-polarizer experiment. While the exposition qualifies BQG as a geometry of light, it is shown in this paper that the logical exposition can be extended to an analytical paradigm of quantum mechanics and quantum biology. It is shown that BQG as the geometry of light is also the geometry of Nature with a logical unification of matter and antimatter atoms into a bipolar quantum cellular automaton (BQCA) through multidimensional YinYang bipolar quantum superposition using bipolar quantum linear algebra (BQLA). With the BQCA interpretation of quantum mechanics, it is shown that matter and antimatter self-organization and spacetime emergence is logically possible within BQG. A scalable BQCA model for biological repression activation and/or degeneration-regeneration is introduced. Bipolar cellular division and bipolar fractality are proposed. Background independent normal and abnormal bipolar fractal branching is proposed. A discussion on quantum gravity and mathematical abstraction is presented. A few challenges and predictions are posted. It is contended that this work leads to an analytical paradigm of quantum mechanics and quantum biology that may contribute to equilibrium-based analysis of quantum decoherence and collapse as associated with quantum measurement

Revealing the Ubiquitous Effects of Quantum Entanglement-Toward a Notion of God Logic

Following Spinoza-Einstein’s interpretation of God or nature, the notion “God Logic” is proposed. This notion is to serve as an elicitation for a consistent set of necessary criteria for: 1) developing the logical foundation of quantum gravity as envisaged by Einstein, 2) revealing the ubiquitous effects of quantum entanglement as suggested by Roger Penrose, and 3) programming the universe as proposed by Seth Lloyd. An evolving set of eleven criteria is proposed for the notion. The possibility of inventing such a logical system is analyzed. A supersymmetrical candidate logic of negative-positive energy dynamic equilibrium is introduced and assessed against the set of criteria. It is shown that the first 10 criteria are met or partially met by the candidate. But the question whether the 11th criterion has been or can be met is left open for discussion and further research effort. The assessment leads to a few predictions. Notably, it is predicted that, should Boson-Fermion symmetry or broken symmetry be observed, it would be caused by bipolar symmetry or broken symmetry of negative-positive energies

Bipolar Quantum Logic Gates and Quantum Cellular Combinatorics – A Logical Extension to Quantum Entanglement

Based on bipolar dynamic logic (BDL) and bipolar quantum linear algebra (BQLA) this work introduces bipolar quantum logic gates and quantum cellular combinatorics with a logical interpretation to quantum entanglement. It is shown that: 1) BDL leads to logically definable causality and generic particle-antiparticle bipolar quantum entanglement; 2) BQLA makes composite atom-atom bipolar quantum entanglement reachable. Certain logical equivalence is identified between the new interpretation and established ones. A logical reversibility theorem is presented for ubiquitous quantum computing. Physical reversibility is briefly discussed. It is shown that a bipolar matrix can be either a modular generalization of a quantum logic gate matrix or a cellular connectivity matrix. Based on this observation, a scalable graph theory of quantum cellular combinatorics is proposed. It is contended that this work constitutes an equilibrium-based logical extension to Bohr’s particle-wave complementarity principle, Bohm’s wave function and Bell’s theorem. In the meantime, it is suggested that the result may also serve as a resolution, rather than a falsification, to the EPR paradox and, therefore, a equilibrium-based logical unification of local realism and quantum non-locality

Beyond Spacetime Geometry – The Death of Philosophy and Its Quantum Reincarnation

Contrary to the “end” and “death” assertions on philosophy, this paper predicts an equilibrium-based and harmony-centered scientific reincarnation of philosophy. Logically, the reincarnation is backed by a formal system and a background independent geometry that transcends spacetime. Physically, it is supported by definable quantum causality and bipolar logical unifications of matter and antimatter, particle and wave, big bang and black hole, relativity and quantum entanglement. Philosophically, it is distinguished from Western metaphysics and dialectics as well as the Dao of Laozi. It is named a quantum reincarnation for its central claim that YinYang bipolar quantum entanglement is the source of causality for the Being of beings following the 2nd law of thermodynamics. Thus, it presents a modest unification of science and philosophy for their reciprocal interaction (Note: Equilibrium subsumes non-equilibrium and quasi—equilibrium as local non-equilibriums can form global equilibrium or quasi-equilibrium)

Interval-valued and intuitionistic fuzzy mathematical morphologies as special cases of L-fuzzy mathematical morphology

Mathematical morphology (MM) offers a wide range of tools for image processing and computer vision. MM was originally conceived for the processing of binary images and later extended to gray-scale morphology. Extensions of classical binary morphology to gray-scale morphology include approaches based on fuzzy set theory that give rise to fuzzy mathematical morphology (FMM). From a mathematical point of view, FMM relies on the fact that the class of all fuzzy sets over a certain universe forms a complete lattice. Recall that complete lattices provide for the most general framework in which MM can be conducted. The concept of L-fuzzy set generalizes not only the concept of fuzzy set but also the concepts of interval-valued fuzzy set and Atanassov’s intuitionistic fuzzy set. In addition, the class of L-fuzzy sets forms a complete lattice whenever the underlying set L constitutes a complete lattice. Based on these observations, we develop a general approach towards L-fuzzy mathematical morphology in this paper. Our focus is in particular on the construction of connectives for interval-valued and intuitionistic fuzzy mathematical morphologies that arise as special, isomorphic cases of L-fuzzy MM. As an application of these ideas, we generate a combination of some well-known medical image reconstruction techniques in terms of interval-valued fuzzy image processing

Dynamic bipolar fuzzy aggregation operators: A novel approach for emerging technology selection in enterprise integration

Emerging technology selection is crucial for enterprise integration, driving innovation, competitiveness, and streamlining operations across diverse sectors like finance and healthcare. However, the decision-making process for technology adoption is often complex and fraught with uncertainties. Bipolar fuzzy sets offer a nuanced representation of uncertainty, allowing for simultaneous positive and negative membership degrees, making them valuable in decision-making and expert systems. In this paper, we introduce dynamic averaging and dynamic geometric operators under bipolar fuzzy environment. We also establish some of the fundamental crucial features of these operators. Moreover, we present a step by step mechanism to solve MADM problem under bipolar fuzzy dynamic aggregation operators. In addition, these new techniques are successfully applied for the selection of the most promising emerging technology for enterprise integration. Finally, a comparative study is conducted to show the validity and practicability of the proposed techniques in comparison to existing methods