scholarly journals The Fuzzy Completeness Theory

2021 ◽  
Vol 4 (1) ◽  
pp. p52
Author(s):  
Hugh Ching
Keyword(s):  
Fuzzy Logic ◽  
Model Complexity ◽  
Impossibility Theorem ◽  
Human Knowledge ◽  
Demand Model ◽  
Empirical Verification ◽  
Kenneth Arrow ◽  
Incompleteness Theorems ◽  
Reliable Knowledge ◽  
Uncertain Future

The Two Incompleteness Theorems of Kurt Friedrich Gödel and the Impossibility Theorem of Kenneth Arrow claim that logic, the most reliable of human knowledge, is incomplete or can be inconsistent. The Fuzzy Completeness Theory states that the Fuzzy Logic of Lotfi A. Zadeh has resolved the incompleteness and impossibility in logic and made logic complete and knowledge reliable with the new concept of Range of Tolerance, within which logic is still complete and knowledge, valid. In the Age of Reason about 300 years ago just prior to the Age of Science, reasoning is free for all, without the constraint of the laws of nature, which would be discovered in the Age of Science. However, the Scientific Method of reasoning by empirical verification depends so much on faith that it is logically and empirically dismissed by mathematicians and logicians, especially, after the exposure by Thomas Kuhn and Paul Feyerabend that a scientific advancement is akin to a religious conversion. On the other hand, mathematicians and logicians have been working steadily to find the limit of reliable knowledge. In the current state of knowledge, Kurt Gödel has the last word with his Two Incompleteness Theorems, which conclude that the most reliable of human knowledge, logic, is incomplete, casting doubt whether knowledge is completely reliable. Gödel’s view is further supported by the Impossibility Theorem of Kenneth Arrow. However, Zadeh and the author of this paper extend Zadeh’s concept of Range of Value in Fuzzy Logic to that of Range of Tolerance. Accordingly, Fuzzy Logic deals with the sacrifice of precision in the process of expanding the Range of Tolerance of a creation in order for the creation to survive and flourish for all the possibility of an uncertain future. In knowledge, incompleteness in logic can be resolved by the Range of Tolerance covering the incomplete part or ignoring the infrequent impossibilities, and, thus, making logic valid, again. Knowledge is derived generally from reason. Technically, the Fuzzy Completeness Theory classifies 16 Methods of Reason. The 16 Methods are the combination of the 4 basic Methods of Reason: 1) Logic, 2) Mathematics, 3) Empirical Verification, and 4) Others, each of which has 2 forms: 1) Fuzzy and 2) Exact and two types: 1) Complete and 2) Incomplete. Gödel, Arrow, and the Author agree that no matter how rigorous is the Method of Reason the reason cannot be complete, when the reason is Exact. When a solution is newly defined as an answer within the Range of Tolerance of the solution, Fuzzy Logic resolves the incompleteness in logic and becomes the new foundation of knowledge, replacing Exact Logic. With this definition of a solution, Fuzzy Logic covers the incomplete or the impossible parts of the solution by expanding sufficiently the Range of Tolerance to make reason complete and knowledge reliable, but only within the Range of Tolerance. To summarize, even though the world’s leading intellectuals have proven, directly, that logic is incomplete and, indirectly, that knowledge is invalid, reality is still operating smoothly, and science has even demonstrated the power of knowledge. The conflict between the most reliable knowledge, namely, logic and the real world is resolved by Fuzzy Logic, which introduces the new concept of Range of Tolerance, within which reality can still operate in accordance with the laws discovered by knowledge. In sum, reality is fuzzy, not exact. The breakthrough impact of this paper centers around completeness theory and Fuzzy Logic. In the early 21st century, the mainstream knowledge is still not aware that the supply and demand model is incomplete, and that the DNA-protein system resembles computer science based on logic more than science based on experimentation. The current computer is based on exact logic and is designed for temporary existence, while the living system is design for permanent existence and must depend on the Range of Tolerance based on Fuzzy Logic to survive permanently in an uncertain future. Financial crises will be caused by the unstable investment return, which is the incomplete part in the supply demand model. Complexity crises will be caused by the lack of the requirement of permanence or complete automation, which is the ultimate solution to unlimited complexity. The 16 Methods of Reason correspond roughly to Culture Level Quotient (CLQ), which is a non-technical measure of a person, a people or a nation.

A Fuzzy Logic Trail Finding Algorithm Trained With Human Knowledge

2002 ◽  
Author(s):  
Charles Kinney ◽  
Dean B. Edwards
Keyword(s):  
Fuzzy Logic ◽  
Fuzzy Sets ◽  
Classical Logic ◽  
Fuzzy Logic System ◽  
Human Knowledge ◽  
Relationship Of ◽  
The Relationship ◽  
Logic System

This paper presents a method for developing a fuzzy logic trail finding algorithm using a technique called embedding human knowledge. The trail finding algorithm was trained to find the pixels in images that closely resemble those that were classified as belonging to a forest trail by a human analyst. The relationship of the fuzzy logic system to a classical logic system is discussed as a method for training the fuzzy sets to mimic a human. The results show that the method outlined in this paper reduced the error in the fuzzy logic system by 99%. More generally, this method can be applied to many different situations to find features in images quickly and effectively.

Fuzzy Analysis of Speech Metrics to Estimate Conductor Alertness

2009 ◽  
Author(s):  
Parham Shahidi ◽  
Steve C. Southward ◽  
Mehdi Ahmadian
Keyword(s):  
Mathematical Model ◽  
Fuzzy Logic ◽  
Rule Base ◽  
Mathematical Framework ◽  
Human Knowledge ◽  
Knowledge Based ◽  
Single Output ◽  
Output System ◽  
Alertness Level ◽  
Different Levels

A Fuzzy Logic-based algorithm has been developed for processing a series of speech metrics with the ultimate goal of estimating train conductor alertness. The output is a single metric, which directly quantifies the alertness level of the conductor. The metrics were selected based on their correlation to alertness through processed speech, but without any interpretation of the spoken words or phrases. Metrics that are used include: speech duration, silence duration, word production rate and word intensity. The assessment of these metrics is an experience and human knowledge based task, which generates the need for a mathematical model to accommodate this special circumstance. The algorithm developed here uses Fuzzy Logic to cast the human knowledge base into a mathematical framework for the alertness estimation analysis. The core of this fuzzy system is a rule base consisting of fuzzy IF-THEN rules, which are derived from the existing knowledge about the effects of sleep deprivation on alertness such as Furthermore, the rules were inferred from actual voice recordings that were taken on board a train. This data was then used to create a classification scheme to determine which pattern in the speech indicates different levels of alertness from anxiety to fatigue. The simplicity of the underlying mathematical model in this approach enables this system to compute and output an alertness metric in real-time. The nature of this algorithm allows for the use of an arbitrary number of rules to classify the alertness level and therefore provides the ability to continuously develop and extend the rule base as new knowledge emerges. The resulting algorithm is a fast, multi-input, single-output system that is able to quantify the train conductor’s alertness level anytime speech is produced.

How to Free Your Inner Mathematician

2020 ◽  
Author(s):  
Susan D'Agostino
Keyword(s):  
Fuzzy Logic ◽  
Mathematics Teaching ◽  
Knot Theory ◽  
Teaching Experience ◽  
Impossibility Theorem ◽  
Mathematics Students ◽  
Mathematical Content ◽  
Mathematical Background ◽  
Award Winning ◽  
Mathematical Success

How to Free Your Inner Mathematician: Notes on Mathematics and Life offers readers guidance in managing the fear, freedom, frustration, and joy that often accompany calls to think mathematically. With practical insight and years of award-winning mathematics teaching experience, DAgostino offers more than 300 hand-drawn sketches alongside accessible descriptions of fractals, symmetry, fuzzy logic, knot theory, Penrose patterns, infinity, the Twin Prime Conjecture, Arrows Impossibility Theorem, Fermats Last Theorem, and other intriguing mathematical topics. Readers are encouraged to embrace change, proceed at their own pace, mix up their routines, resist comparison, have faith, fail more often, look for beauty, exercise their imaginations, and define success for themselves. Mathematics students and enthusiasts will learn advice for fostering courage on their journey regardless of age or mathematical background. How to Free Your Inner Mathematician delivers not only engaging mathematical content but provides reassurance that mathematical success has more to do with curiosity and drive than innate aptitude.

Rationality, Morality, and Impossibility Theorems

1980 ◽  
Vol 74 (2) ◽  
pp. 373-384 ◽  
Author(s):  
Fred M. Frohock
Keyword(s):  
Political Thought ◽  
Impossibility Theorem ◽  
Collective Rationality ◽  
Arrow’S Theorem ◽  
Ranking Of Alternatives ◽  
Arrow's Theorem ◽  
Kenneth Arrow ◽  
Alternative Relationships

The impossibility theorem developed by Kenneth Arrow has implications for both rationality and morality in political thought. Transitivity in a collective ordering can be assured only with a decisive set, but this outcome is acknowledged as morally undesirable. The alternatives exhibited by the theorem thus seem to require a choice between rationality and morality. But exit routes can be cut out of this dilemma with the idea of a conditional ordering, one where warranting factors attach to a ranking of alternatives. Conditional orderings form two senses of collective rationality. One is represented by compound directives, which avoid the rational problems of the theorem by warranting local orderings. The second is moral fusion, which requires a reasoned dominance in collective outcomes. These two forms of conditional rationality put into relief the restricted scope of the composition rules and individualism of Arrow's theorem, and suggest alternative relationships of individual and social whole.

scholarly journals So how to make group decisions? Arrow's impossibility theorem 70 years after

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Hung T. Nguyen ◽  
Olga Kosheleva ◽  
Vladik Kreinovich
Keyword(s):  
Decision Making ◽  
Decision Theory ◽  
Group Decision Making ◽  
First Principles ◽  
Group Decision ◽  
Impossibility Theorem ◽  
Group Decisions ◽  
Content Type ◽  
Kenneth Arrow ◽  
Practical Recommendations

PurposeIn 1951, Kenneth Arrow proved that it is not possible to have a group decision-making procedure that satisfies reasonable requirements like fairness. From the theoretical viewpoint, this is a great result – well-deserving the Nobel Prize that was awarded to Professor Arrow. However, from the practical viewpoint, the question remains – so how should we make group decisions? A usual way to solve this problem is to provide some reasonable heuristic ideas, but the problem is that different seemingly reasonable idea often lead to different group decision – this is known, e.g. for different voting schemes.Design/methodology/approachIn this paper we analyze this problem from the viewpoint of decision theory, the basic theory underlying all our activities – including economic ones.FindingsWe show how from the first-principles decision theory, we can extract explicit recommendations for group decision making.Originality/valueMost of the resulting recommendations have been proposed earlier. The main novelty of this paper is that it provides a unified coherent narrative that leads from the fundamental first principles to practical recommendations.

The “Win-Win-Win Papakonstantinidis Model”: from Social Welfare’s Philosophy towards a Rural Development Concept by Rural Tourism Approach: The WERT Case Study

2017 ◽  
Vol 3 (1) ◽  
pp. 7-25 ◽  
Author(s):  
Papakonstantinidis L.A
Keyword(s):  
Rural Development ◽  
Social Welfare ◽  
Nash Bargaining Solution ◽  
Nash Bargaining ◽  
Impossibility Theorem ◽  
Bargaining Solution ◽  
Kenneth Arrow ◽  
Development Objectives

The article is dealing with two interconnected problems based on the conjectures: a) social welfare is a condition for rural development and not the prerequisite for it; b) shape a new landscape (the “win-win-win”) based on critique of the “Impossibility Theorem (Kenneth Arrow 1951) through the Nash Bargaining Solution (Nash, John 1950). Specifically, this article discusses and analyses social welfare and rural development objectives integrating elements from the impossibility theorem, the bargaining theory, and the theory of agency by (a) reviewing the literature on coordination “social welfare” and “rural development” (b) reversing the focus from “voting” to “bargaining” and (c) underlining that Social choice is the perquisite of social welfare, using the “win-win-win Papakonstantinidis model’s solution as the bridge between “voting”(Arrow) and “bargaining”(proposal). This solution highlights the Role of Rural Community as an “Aggregation” corresponding to its “sensitization process”.

Independence of Irrelevant Alternatives in Engineering Design

2014 ◽  
Author(s):  
Simon Li
Keyword(s):  
Engineering Design ◽  
Quality Function Deployment ◽  
Choice Function ◽  
Irrelevant Information ◽  
Borda Count ◽  
Impossibility Theorem ◽  
Independence Of Irrelevant Alternatives ◽  
Decision Methods ◽  
Consistency Property ◽  
Kenneth Arrow

When discussing Arrow’s Impossibility Theorem (AIT) in engineering design, we find that one condition, Independence of Irrelevant Alternatives (IIA), has been misunderstood generally. In this paper, two types of IIA are distinguished. One is based on Kenneth Arrow (IIA-A) that concerns the rationality condition of a collective choice rule (CCR). Another one is based on Amartya Sen (IIA-S) that is a condition for a choice function (CF). Through the analysis of IIA-A, this paper revisits three decision methods (i.e., Pugh matrix, Borda count and Quality Function Deployment) that have been criticized for their failures in some situations. It is argued that the violation of IIA-A does not immediately imply irrationality in engineering design, and more detailed analysis should be applied to examine the meaning of “irrelevant information”. Alternatively, IIA-S is concerned with the transitivity of CF, and it is associated with contraction consistency (Property α) and expansion consistency (Property β). It is shown that IIA-A and IIA-S are technically distinct and should not be confused in the rationality arguments. Other versions of IIA-A are also introduced to emphasize the significance of mathematical clarity in the discussion of AIT-related issues.

Fuzzy Logic–Based Travel Demand Model to Simulate Public Transport Policies

2015 ◽  
Vol 141 (4) ◽  
pp. 04014044 ◽  
Author(s):  
Sarada Pulugurta ◽  
Errampalli Madhu ◽  
Ravinder Kayitha
Keyword(s):  
Fuzzy Logic ◽  
Public Transport ◽  
Travel Demand ◽  
Demand Model ◽  
Travel Demand Model

scholarly journals South Africa’s rising logistics costs: An uncertain future

2014 ◽  
Vol 8 (1) ◽  
Author(s):  
Jan H. Havenga ◽  
Zane P. Simpson ◽  
Anneke De Bod ◽  
Nadia M. Viljoen
Keyword(s):  
Policy Instruments ◽  
Freight Transport ◽  
Cost Driver ◽  
Demand Model ◽  
Logistics System ◽  
The Road ◽  
Freight Logistics ◽  
Road Freight ◽  
Uncertain Future ◽  
The Cost

A country’s competitiveness can be severely hampered by an uncompetitive freight logistics system. During the first decade of the 21st century, two in-depth models were developed for South Africa which provide a framework for measuring and improving the country’s freight logistics system – the cost of logistics survey and the freight demand model. These models also allow for the development of scenarios for key identified risks. The objectives of this study were to provide an overview of South Africa’s surface freight transport industry,identify key risks to national competitiveness and suggest ways in which these risks could be mitigated. Freight flows were modelled by disaggregating the national input–output model into 372 origin–destination pairs and 71 commodity groups, followed by distance decay gravity-modelling. Logistics costs were calculated by relating commodity-level freight flows to the costs of fulfilling associated logistical functions. South Africa’s economy is highly transport intensive. Excessive dependence on road freight transport exacerbates this situation. Furthermore, the road freight transport’s key cost driver is fuel, driven in turn by the oil price. Scenario analysis indicated the risk posed by this rising and volatile input and should provide impetus for policy instruments to reduce transport intensity. As such, this study concluded that a reduction in freight transport intensity is required to reduce exposure to volatile international oil prices.

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