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By Kofi Kissi Dompere

This monograph is a remedy on optimum fuzzy rationality as an enveloping of decision-choice rationalities the place constrained info, vagueness, ambiguities and inexactness are crucial features of our wisdom constitution and reasoning tactics. the quantity is dedicated to a unified approach of epistemic versions and theories of decision-choice habit below overall uncertainties composed of fuzzy and stochastic forms. The unified epistemic research of decision-choice versions and theories starts off with the query of ways top to combine vagueness, ambiguities, restricted details, subjectivity and approximation into the decision-choice strategy. the reply to the query results in the moving of the classical paradigm of reasoning to fuzzy paradigm. this can be via discussions and institution of the epistemic foundations of fuzzy arithmetic the place the character and position of knowledge and data are explicated and represented.

The epistemic origin permits overall uncertainties that constrain decision-choice actions, wisdom firm, common sense and mathematical constructions as our cognitive tools to be mentioned in connection with the phenomena of fuzzification, defuzzification and fuzzy good judgment. The discussions on those phenomena lead us to investigate and current versions and theories on decision-choice rationality and the wanted arithmetic for challenge formula, reasoning and computations. The epistemic buildings of 2 quantity structures made from classical numbers and fuzzy numbers are mentioned on the subject of their alterations, similarities and relative relevance to decision-choice rationality. The homes of the 2 quantity structures result in the epistemic research of 2 mathematical platforms that let the partition of the mathematical area in help of decision-choice area of information and non-knowledge creation into 4 cognitively separate yet interdependent cohorts whose homes are analyzed by means of the equipment and methods of classification concept. The 4 cohorts are pointed out as non-fuzzy and non-stochastic, non-fuzzy and stochastic either one of which belong to the classical paradigm and classical mathematical house; and fuzzy and non-stochastic, and fuzzy and stochastic cohorts either one of which belong to the bushy paradigm and fuzzy mathematical area. the diversities within the epistemic foundations of the 2 mathematical platforms are mentioned. The dialogue ends up in the institution of the necessity for fuzzy arithmetic and computing as a brand new process of reasoning in either distinctive and inexact sciences.

The mathematical constructions of the cohorts are imposed at the decision-choice method to permit a grouping of decision-choice types and theories. The corresponding sessions of decision-choice theories have an analogous features because the logico-mathematical cohorts relative to the assumed information-knowledge constructions. The 4 groupings of versions and theories on decision-choice actions are then categorized as: 1) non-fuzzy and non-stochastic category with detailed and whole information-knowledge constitution (no uncertainty), 2) non-fuzzy and stochastic classification with precise and constrained information-knowledge constitution (stochastic uncertainty), three) fuzzy and non-stochastic category with complete and fuzzy information-knowledge constitution (fuzzy uncertainty) and four) Fuzzy and stochastic type with fuzzy and constrained information-knowledge constitution (fuzzy and stochastic uncertainties). these types of diversified sessions of selection selection difficulties have their corresponding rationalities that are totally mentioned to provide a unified logical approach of theories on decision-choice method.

The quantity is concluded with epistemic discussions at the nature of contradictions and paradoxes seen as logical decision-choice difficulties within the classical paradigm, and the way those contradictions and paradoxes will be resolved via fuzzy paradigm and the tools and methods of optimum fuzzy decision-choice rationality. The logical challenge of sorites paradox with its answer is given for example. viewers contains these operating within the parts of economies, decision-choice theories, philosophy of sciences, epistemology, arithmetic, laptop technological know-how, engineering, cognitive psychology, fuzzy arithmetic and arithmetic of fuzzy-stochastic processes.

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The pair { x*, µ ∆ ( x * )} thus defines a solution to optimal satisfactory decision-choice problem in knowledge production or social action. 2 concerns the fuzzification and defuzzification process of the clas- KNOWLEDGE SPACE CRISP VALUE EQUIVALENCE DEFUZZIFI CATION PROCESS INFORMATION SPACE ANALYSIS OF CONDITIONS OF FUZZINESS FUZZY ALGORHYTHMS FUZZY MODLING MODULES FUZZIFICATION PROCESS FUZZY SET EQUIVALENCE MODULE OF EXAMINATION OF FUZZY LOGICAL CONSISTENCY VALIDITY PROCESS Fig. 1. Geometry of General Fuzzification and Defuzzification Process for the Study of Fuzzy Optimal Rationality in Classical and Fuzzy Logical Spaces 36 2 The Rationality and Two Number Systems sical real number system in order to obtain fuzzy number system.

The use of higher order probability as a “covering” of vagueness or conditions of penumbral region has no logical justification. Given these criticisms certain problems arise as challenges to the fuzzy paradigm. The challenges include but are not limited to the following demands. 1. An explication and a measure of vagueness with clear conceptual meaning are required. 2. A development of an alternative to the classical logical system that can handle linguistic reasoning, vagueness of concepts, deductive and inductive approximations is needed.

90]. Precision and exactness of symbolic representation in logical constructs require extreme explication that devoices reasoning by symbolic language from reason from ordinary language of human thought process. The process of reconciling this criticism of the classical paradigm and the demands to shift the paradigm into fuzzy paradigm may be found in the following statement. 3]. A logical extension of the principle of non-acceptance of contradiction in the classical paradigm may be made to the rejection of the concept of creative destruction where conflicts between construction and destruction exist in the same entity that internally generates forces of its own destruction and reconstruction.

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