YinYang bipolar dynamic organizational modeling for equilibrium-based decision analysis: Logical transformation of an indigenous philosophy to a global science

Abstract

While it is recognized that indigenous research on China is helpful if not essential, the essence of YinYang has never been made clear in logical forms. While indigenous research should be guided by a philosophy, it was widely believed that without a unique logical system China only had culture but no philosophy. Now, worldwide indigenous research on China is faced with tremendous difficulties due to the lack of principles, academic disciplines, and a scientific common ground even though the Chinese YinYang has been widely influential. Consequently, a unique formal logical foundation is imperative for a logical reincarnation of Chinese philosophy. It is shown in this work that a formal equilibrium-based and harmony-centered YinYang bipolar dynamic logic (BDL) can fill the gap. Based on BDL, bipolar dynamic organizational modeling (BDOM) is proposed for equilibrium-based decision analysis (EBDA). It is shown that BDOM/EBDA methodologies can integrate case study methods and grounded theory together into a holistic and dynamic management paradigm for global regulation. The three philosophies of metaphysics, dialectics and the Dao of YinYang are formally classified and distinguished. It is argued that with BDL YinYang is elevated to a formal logical system, and indigenous research on China is positioned in the context of a global science with a common philosophical ground of equilibrium, complementarity, and harmony. It is concluded that, with YinYang as a philosophical guiding light, not only is bipolar dynamic equilibrium-based indigenous research helpful but also fundamental and essential.

Appendices

Appendix 1. YinYang bipolar dynamic logic (BDL)

Figures 5, 6, and 7 show bipolar quantum sets, lattices, and bipolar interactions. Figure 8 provides the basic operations of BDL (Zhang, 2011). The laws in Fig. 9 hold on BDL. The zero order BDL has been extended to a 1st order formal system in which equilibrium-based bipolar predicates can be used similarly as truth-based predicates. An equilibrium-based axiomatization is shown in Fig. 10 which has been proven sound (Zhang, 2011). Bipolar universal modus ponens (BUMP) in Fig. 10 formally defines equilibrium-based bipolar causality with bipolar quantum entanglement. Given a bipolar relational matrix R (crisp or fuzzy), let R ²=R⊗R, the ⊕-⊗ bipolar transitive closure of R is the smallest bipolar transitive relation containing R. It has been proven that, let X = {x ₁ ,x ₂ ,…,x _n } be a finite bipolar set, the bipolar transitive closure ℜ of R in X exists, is unique (Zhang, 2003a),

$$ \Re ={R}^1\oplus {R}^2\oplus {R}^3\oplus \dots \oplus {R}^{2n}. $$

(1)

If a bipolar relation is symmetrical, reflexive, and transitive, it is defined as an equilibrium relation (Zhang, 2003a)—generalizations of equivalence relation and fuzzy similarity relation.

Fig. 5

Multidimensional equilibrium or non-equilibrium deconstructed to bipolar equilibria/non-equilibria

Fig. 6

Hasse diagrams of YinYang bipolar quantum lattices B₁, B_F, B_∞ in bipolar quantum geometry (BQG)

Fig. 7

Bipolar relativity: (a) Non-reciprocal bipolar interaction; (b) Reciprocal bipolar interaction; (c) Oscillation; (d) Bipolar entanglement

Fig. 8

Operations of (BDL)

Fig. 9

Laws of bipolar equilibrium/non-equilibrium

Fig. 10

Sound equilibrium-based vs. truth-based axiomatization

Appendix 2. Example of cognitive-map-based modeling

After the Cold War in the last century and before the 9-11 terrorist attack in 2001, the world enjoyed a harmonic environment for a while, and the global black-white partitioning of the Cold War era seemed to have lost its basis (Zhang, 2003b). As a result, most countries belong to a harmony cluster based on certain harmony criteria of common interest and conflict interests. In such an environment, bipolar clustering with equilibrium classes is more meaningful. Figure 11(a) and (b) show a bipolar fuzzy CM of international relations shortly after the Cold War of the last century.

The countries in the fuzzy CM can be clustered into different coalition sets, conflict sets, and harmony sets based on different competition-cooperation criteria for focus generation, strategic decision analysis, and global regulation (Zhang, 2011: Ch. 11). Figure 11(c) shows some clusters in YinYang bipolar geometry. Figure 11(d) shows the negative-positive transitive paths for each bipolar relationship in the CM. The transitive paths as strongest chains provide focus of attentions, which can be linked to the ground - truth—the available data and information for decision support.

The clusters in Fig. 11(c) shows a possible view of the US on the world. In this last century CM, except North Korea (No. 10) and Cuba (No. 11), all the other countries are either on the main diagonal or on the positive side of the 2-D bipolar geometry. Therefore, to the interest of the US (No. 1), the 11 countries can be roughly clustered as

• (1) Cluster 1 = {10,11}; // This includes North Korea and Cuba—the countries on the negative side with more conflicts than common interests.

• (2) Cluster 2 = {1,2,3,4,5,8}; // This includes the allied countries of US, which are on the positive side with more common interests than conflicts.

• (3) Cluster 3 = {7,9}; // This includes China and Russia—the countries on the (harmonic) main diagonal with significant equal common interests and conflicts.

• (4) Cluster 4 = {6}; // This includes the countries on the (harmonic) main diagonal with less significant equal common interests and conflicts.

Such clusters can be used for strategic decision analysis and global regulation on cooperation and competition. It is shown in Fig. 11(b) that US and Cuba are related with predicted bipolar link weight (−0.9, +0.7) in the 1990s. At a first glance the positive weight might look nonsense in the last century. However, a meaningful explanation can be given by the corresponding transitive paths from Fig. 11(d). The paths are ((1 11)(1 9 1 11)). The negative side (1 11) indicates a direct negative link weight −0.9 between US (No. 1) and Cuba (No. 11). The positive link weight 0.7 is inferred through the chain (1 9 1 11). The cycle (1 9 1) indicates that the US-China-US cycle leads to the bipolar reflexivity (−0.8,1) of the US. Negative reflexivity suggests self-adjustability. Self-adjustability can find common interest from conflict interest. Therefore, the stronger the negative reflexivity of a symmetric bipolar relation R the more harmonic the equilibrium relation of R would be. The cycle (1 9 1) (US-China-US) has demonstrated such US self-adjustability. The equilibrium relationship (−0.9, 0.7) between US and Cuba suggests that, if the US really had strong conflict with Cuba, the US would find strong common interest with Cuba sooner or later in some way following the US-China-US case. On the other hand, if the conflict were trivial, there would be no basis for common interest. The normalization of US-China relation led to a more harmonic world. It is interesting to ask the question: Will the normalization of US-Cuba relation leads to a more harmonic environment in the Americas? (Note: The original CM was first constructed in 1996 as a qualitative simulation (Zhang, 2003a,b). Pope John Paul II visited Cuba in January 1998. Since then, US-Cuba relation improved slowly following the US-China case (1 9 1). Although its arrival is a bit late due to different factors, the predicted normalization arrived in 2015 when this paper was undergoing the 2nd round revision.)

Fig. 11

(a) A primary (incomplete) bipolar fuzzy CM after the cold war (Zhang, 2011); (b) ⊕-Δ Bipolar transitive equilibrium relation of (a); (c) A plot of equilibrium class clusters (relativity of US to the world); (d) Transitive paths (strongest paths)

It should be remarked that although global equilibrium and harmony are desired by humanity, local non-equilibrium and disharmony are unavoidable and natural. To the interest of different parties, the countries in an equilibrium class could be in different clusters. In reality, competition and cooperation are both necessary to achieve global equilibrium and harmony with different strategies such as

• Increase negative energy to strengthen competition within a conflict set.

• Increase positive energy to strengthen cooperation in a coalition set.

• Decrease negative energy for less conflict.

• Decrease positive energy for less cooperation.

Different strategies may lead to different actions, and different actions may lead to new CMs for new situations. Before a decision is made, current and future CMs can facilitate strategic decision analysis with WHAT-IF scenarios. Together with its supporting data and knowledge, a CM provides an equilibrium-based, holistic and integrated picture for BDOM, strategic decision, coordination, conflict resolution and global regulation. It is a fact that a CM alone is not sufficient for decision analysis. Without a CM, however, the holistic and integrated picture would be missing, and decision makers could be lost in the ground truths scattered around. It demonstrates the fact that truth exists as part of a dynamic equilibrium and the two are complementary to each other in BDOM and EBDM.

Appendix 3. Case studies of integrated modeling

Application Example 1: Supply-production rebalancing, optimization, and operation

To illustrate the applicability of Methodology-NP, we first show a simulated capacity rebalancing and optimization example in a supply-production or input-output network among three divisions of a company as shown in Fig. 12(a).

Fig. 12

Supply-production optimization: (a) Bipolar CM; (b) 1st rebalancing (in decimal); (c) Bipolar curves; (d) Curves transformed to YinYang bipolar geometry; (e) 2nd rebalancing (in percentage)

The rebalancing task is to meet an average of production capacity of 80% with the conditions that division e1 can get a minimum of 40% of its supply from e2 and another 40% from e3 which constitute 40% production from e2 and another 40% from e3, respectively; division e2 needs at least 30% supply from e3 but e3 may provide a minimum of 20%. The exact capacity of each division is uncertain until they are determined, and there is no guarantee for the consistency and completeness of the cognitive map. Even at such small scale the problem is challenging both cognitively and computationally for a number of reasons, three of them are:

• (1) The information involved in the management decision is uncertain, incomplete and even inconsistent;

• (2) Without direct bipolarity, it is impossible to represent the information in a holistic, dynamic, and equilibrium-based mathematical representation using truth-based models;

• (3) Without the unique integrated Methodology-NP, no computational method can be used to conduct the holistic, dynamic and equilibrium-based mathematical computation systematically step by step, not even by any of the component methodologies when being used alone.

With Methodology-NP, however, the problem can be approximately solved with relative ease in a systematic way with four steps.

In Step1, bipolar socio-psychiatric modeling results in a set of three divisions e1, e2, and e3, each with a desired 80% production capacity (−0.8 +0.8).

In Step2, bipolar cognitive mapping results in the cognitive map C(t) as shown in Fig. 12(a).

In Step3, bipolar quantum modeling converts C(t) to an energy conservational bipolar quantum logic gate (matrix) M(t) through a linear normalization scheme (Zhang, 2016b). In this case,

$$ \mathrm{M}\left(\mathrm{t}\right) = \left[\begin{array}{ccc}\hfill \left(-0,+0\right)\hfill & \hfill \left(-0, + 0.571\right)\hfill & \hfill \left(-0, + 0.667\right)\hfill \\ {}\hfill \left(-0.5,+0\right)\hfill & \hfill \left(-0,+0\right)\hfill & \hfill \left(-0, + 0.333\right)\hfill \\ {}\hfill \left(-0.5,+0\right)\hfill & \hfill \left(-0.429, + 0\right)\hfill & \hfill \left(-0,+0\right)\hfill \end{array}\right]. $$

M(t) can serve as a regulatory center for equilibrium-based rebalancing. Based on M(t), we can calculate E(t+1) = M(t) × E(t) for N iterations until E(t+1) = E(t) (see Fig. 12(b)). The simulation result is curved in Fig. 12(c,d).

In Step4, management decision analysis can be performed based on the result from the early steps. It can be verified that the condition of an average of 80% production capacity is met by the quantum model because the normalized matrix M(t) enforces energy conservation in the rebalancing process from iteration to iteration in absolute total with certain specified precision. The result shows that, with an average of 80% capacity, e1 may exceed 80% denoted (−0.800 0.800) and stabilize at 92% (−0.920 0.920); e2 and e3 may run below the planned 80% capacity and stabilize at 71.5% and 76.6%, respectively. The average is (92+71.5+76.6)/3 = 240.1/3 = 80.0%.

The bipolar quantum logic gate matrix M(t) holds the regulatory information for the rebalancing and optimization. Based on the regulatory information, e2 and e3 can actually supply 57.1% and 66.7% of their productions to e1, respectively, that constitute 100% of e1’s demand after rebalancing; e3 can actually supply 33.3% of its production to e2 that constitutes 42.9% of e2’s demand. The remaining output of e2 and e3 have to match other demands. On the other hand, the output of e1 has to find its demand and the unmet supplies to e2 and e3 have to find their sources.

If a decision can be reached based on the above (1st round) result, the EBDA process can stop; if not, a 2nd round EBDA can be started with Methodology-NP. In the 2nd round, the planned average 80% capacity can be adjusted higher or lower and the link weights in the cognitive map can be adjusted as well. The process can then be repeated to produce alternative solutions for a better decision. For instance, based on the result from the 1st round, if the 80% capacity needs to be adjusted to (80+60+70)/3 = 70% for some reason, Methodology-NP will produce the result as shown in Fig. 12(e). The figure shows that the adjusted plan matches the conditions very well with small deviations as highlighted, namely, (80.433+62.549+67.018)/3 = 210,000/3 = 70.000%. Thus, an optimized decision can be reached in an adaptive decision process through multiple rounds of rebalancing. (Note: While this is an example of rebalancing with energy conservation, energy regeneration and degeneration will lead to supply-production growth and decline, respectively.)

The example illustrates the practical utility and operationalizability of the equilibrium-based approach to holistic rebalancing and optimization. While three divisions are used for simplicity in the illustration, more divisions are logically the same for a computer to perform the task but practically impossible for a decision maker to carry out the task without automated decision support using Methodology-NP. It is contended that a bipolar cognitive map can never be unitarily represented as a single holistic picture without bipolar complementarity (Zhang, 2011; Zhang et al, 1989, 1992). It is interesting to ask whether there is any other better methodology for solving the same problem systematically without YinYang bipolarity.

Application Example 2: International trade rebalancing and regulation

While Example1 shows that, with an incomplete, uncertain or even inconsistent cognitive map, Methodology-NP can be applied in supply-production rebalancing and optimization, a complete and consistent bipolar cognitive map, on the other hand, can be used for equilibrium-based international trade analysis and import–export prediction.

Equilibrium-based trade analysis

Here we ask the question: “Based on the international trade data what is the individual trade percentage of the total trade volume among any trade group of N partners?” Here N could be any finite number greater than one. Taken the super trade group of US-China-EU as an example, we get the 3-partner import–export data for 2014 which are shown in Fig. 13(a) in million Euros. Using bipolar quantum computing, accurate calculation can be carried out following the equation E(t+1) = M(t) × E(t) based on a column-normalized bipolar quantum logic gate matrix M(t) starting with a bipolar column vector E(t) = [(−40,+40) (−30,+30) (−30,+30)]^T where 40+30+30 = 100 (%) is merely an initial rough estimate, which can be rebalanced to the exact percentages. The matrix M(t) is based on the normalization of the ground truth for 2014.

$$ \mathrm{C}\left(\mathrm{t}\right)=\left[\begin{array}{ccc}\hfill \left(0,\ 0\right)\ \hfill & \hfill \left(-420,079, + 111,308\right)\hfill & \hfill \left(-311,035, + 206,127\right)\hfill \\ {}\hfill \left(-111,308, + 420,079\right)\hfill & \hfill \left(0,\ 0\right)\hfill & \hfill \left(-164,777, + 302,049\right)\hfill \\ {}\hfill \left(-206,127, + 311,035\right)\hfill & \hfill \left(-302,049, + 164,777\right)\hfill & \hfill \left(0,\ 0\right)\hfill \end{array}\right]. $$

The transpose of C(t) is used to obtain M(t)—a an energy/information conservational bipolar quantum logic gate matrix resulted from a linear normalization.

$$ \mathrm{M}\left(\mathrm{t}\right) = \mathrm{normalize}\left({\mathrm{C}}^{\mathrm{T}}\left(\mathrm{t}\right)\right) = \left[\begin{array}{ccc}\hfill \left(0.000\ 0.000\right)\ \hfill & \hfill \left(-0.112\ 0.421\right)\hfill & \hfill \left(-0.209\ 0.316\right)\hfill \\ {}\hfill \left(-0.401\ 0.106\right)\hfill & \hfill \left(0.000\ 0.000\right)\hfill & \hfill \left(-0.307\ 0.167\right)\hfill \\ {}\hfill \left(-0.297\ 0.197\right)\hfill & \hfill \left(-0.165\ 0.303\right)\hfill & \hfill \left(0.000\ 0.000\right)\hfill \end{array}\right]. $$

The result is shown in Fig. 13(b) where the initial rough estimate 40+30+30 = 100 (%) is rebalanced to the exact percentages 34.597+32.936+32.467 = 100 (%) for US, China, and EU, respectively. The result is validated with truth-based calculation as shown in Fig. 13(c). While using truth-based computing we need to repeat the calculation N times for N partners, using equilibrium-based quantum rebalancing we can obtain all the percentages through bipolar interactions for all partners in one iterative procedure in parallel based on E(t+1) = M(t) × E(t) in a completely different approach regardless of the size of the group. This provides a computational basis for equilibrium-based and harmony-centered prediction and global regulation.

It should be remarked that equilibrium-based bipolar complementarity and causality enabled the holistic many-party prediction using one single year data as shown in Fig. 13(b) solely based on total trading volume without taking trade surplus and deficit into consideration. Thus, the above predicted higher percentage for US is due to its higher trading volume. If trade deficit and surplus rebalancing is taken into effect, the percentage distribution will have significant changes.

Fig. 13

a Bipolar cognitive map of 2014 US-China-EU trade (unit in million Euros); (b) Percentage calculation with equilibrium-based bipolar rebalancing; (c) Percentage calculation with usual truth-based sequential calculation

Equilibrium-based trade prediction and global regulation

Based on the above analysis, we have the question: If all parties of an international trade group of N partners are to balance their import–export to certain harmony level h > (|ε|(e) − |ε _imb (e)|)/|ε|(e) ( Zhang, 2016b ), what would be the expected individual trade percentage of the expected total trade volume among the trade group?” The answer of this question depends on the harmony level and global regulation policy. Given h = 1.0, two extreme cases are:

• Case1. Balance each partner’s trade based on the lower of its import and export volumes to (−min(|import|,|export|); +min(|import|,|export|)) (Fig. 14(a));

• Case2. Balance each partner’s trade based on the upper of its import and export volumes to (−max(|import|,|export|); +max(|import|,|export|)) (Fig. 14(b)).

Case1 would lead to much lower total trade volume and the individual percentages 32.914, 28.627, and 38.459 for US, China, and EU respectively, where 32.914 + 28.627 + 38.459 = 100 (%) (see Fig. 14(c)); Case2 would lead to much higher total trade volume and the individual percentages 35.382, 34.847, and 29.670 for US, China, and EU, respectively, where 35.382 + 34.847 + 29.670 = 100 (%) (see Fig. 14(d)). Case1 is evidently unreasonable and Case2 is desirable but might be unrealistic for a short time. They do, however, provide boundary conditions for equilibrium-based harmony-centered trade rebalancing and global regulation. Based on the boundary analysis, the harmony condition could be adjusted to suitable levels for smooth rebalancing. For instance, by setting the harmony level h to a moderate range of 0.5–1.0, realistic stepwise rebalancing strategies can be devised for a smooth transition to more balanced import-export while avoiding the economic damage caused by a drastic regulation decision.

It should be noted that the equation E(t+1) = M(t) × E(t) can also be used to rebalance actual trade volumes to an equilibrium state. For instance, we have the question “How can the 2014 import-export volumes of US-China-EU trade partners be self-balanced?” One possible answer to the question is given in Fig. 14(e). In this figure the actual 2014 trade volumes for the three partners are used as the initial input vector E(1), which is self-rebalanced by its own energy/information conserving quantum logic gate M(t) to a perfect bipolar equilibrium E(22) step by step. The rebalancing is curved in Fig. 14(f). Although a perfect equilibrium-state is neither practical nor desirable, the equilibrium-based self-rebalancing case can be studied together with energy/information regeneration or degeneration and optimized for management decision and global regulation. This is left for future investigation.

The above equilibrium-based and harmony-centered approach to rebalancing works with many trade partners based on a single year data. It is well-known that statistical prediction needs data from multiple years and does not support equilibrium-based holistic rebalancing. Further study on this topic may find possible integration of statistical prediction and other data mining methods into methodology-NP for better decision support. For instance, statistical analysis may suggest more suitable harmony levels for stepwise global regulation.

Fig. 14

(a) Hypothetical balanced CM of Case1; (b) Hypothetical balanced CM of Case2; (c) Expected trade volume percentages of Case1; (d) Expected trade volume percentages of Case2; (e) Self-rebalancing to equilibrium with actual data; (f) Normalized curves of self-rebalancing

Energy/information conservation for stability

Free trade among economic powers can translate to a harmonic economic competition-cooperation network (see Rule 6 in Fig. 3(b)). Fig. 15(a) shows such a harmonic cognitive map of US-China-EU bilateral free trade. The harmony is a dynamic equilibrium, not a static one. The economic harmony in the map can be compromised sometimes by political conflict because international trade can be used as a leverage for political gains. This leads to another question: “If US-China free trade relation were compromised by a political conflict, what should each side do?” Fig. 15(b) shows a hypothetical scenario where the harmonic economic relation between US and China cooled down by (−0.5, +0.5) from (−1, +1) to (−0.5, +0.5). The cool-down can be characterized by an average 16.667% = 1/6 total energy/information (absolute values of link weights) drop as we have |ε|(−0.5,+0.5)/|ε|[(−1,+1) + (−1,+1) + (−1,+1)] = 1/6 = 16.667%. It is thus expected to cause an average 16.667% drop of the trading volumes of the three partners.

In reality, such a hypothetical cool-down could lead to different consequences. A worst scenario could be that the cool-down triggers avalanche or domino effects with bipolar equilibrium energy/information degeneration (Fig. 15(c,d,e)) (Zhang, 2016a). ure. 15(c) shows that each iteration results in a nonlinear average of 16.667% drop in trade volume. For instance, in the first iteration, US-China-EU trade volumes dropped 25%, 25%, and 0%, respectively, the average is 50/3 = 16.667%. This could lead to significant decrease of import–export among all related parties, translate to the loss of jobs in large numbers worldwide, cause psychological panic on the stock market, and result in a global economic recession.

A less serious scenario could be that both US and China would successfully find EU (or other parties) to fill the trading gap, remedy the damage and maintain the same level of total trading energy/information (see Fig. 15(f, g, h)). In approximate percentage (assuming each side has the same average trading volume), this scenario could result in a short term 16.667% (100%–83.333%) estimated drop for US and China import-export complemented by a 33.333% (133.333%–100%) increase of EU volume where 16.667% + 16.667% = 33.333% (see 1st iteration in Fig. 15(f, g, h)). After a period of fluctuation the drop and increase would eventually stabilize at 10% and 20%, respectively, assuming the total energy/information is maintained at 100%.

Based on the above EBDA, an answer to the 2nd question is that “If US-China trade relation were compromised by a political conflict, the trading partners should manage to find the 3rd party EU (or other parties) to fill in the trading gap with equilibrium-based rebalancing.” In either case it indicates that a strong harmonic competition-cooperation relation between US and China can contribute to the global economy while maintaining a bilateral win-win scenario; an energy/information degeneration, on the other hand, could lead to a global disaster, which should be prevented through equilibrium-based rebalancing with 3rd party cooperation and global regulation—a theme of BDOM for EBDA.

Fig. 15

a Bipolar cognitive map of harmonic competition-cooperation; (b) Bipolar cognitive map of hypothetical cool-down; (c) Possible avalanche effects; (d) Curves of the avalanche effects; (e) Avalanche effects in YinYang bipolar geometry; (f) Rebalancing with 3rd party to fill the gap; (g) Curves of the rebalancing; (h) Curves of the rebalancing in YinYang bipolar geometry