By Kofi Kissi Dompere
This monograph is a remedy on optimum fuzzy rationality as an enveloping of decision-choice rationalities the place restricted details, vagueness, ambiguities and inexactness are crucial features of our wisdom constitution and reasoning tactics. the quantity is dedicated to a unified process of epistemic versions and theories of decision-choice habit less than overall uncertainties composed of fuzzy and stochastic kinds. 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 technique. the reply to the query ends up in the transferring of the classical paradigm of reasoning to fuzzy paradigm. this is often through discussions and institution of the epistemic foundations of fuzzy arithmetic the place the character and function of data and information are explicated and represented.
The epistemic origin permits overall uncertainties that constrain decision-choice actions, wisdom company, good judgment and mathematical buildings 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 research and current versions and theories on decision-choice rationality and the wanted arithmetic for challenge formula, reasoning and computations. The epistemic constructions of 2 quantity structures made of classical numbers and fuzzy numbers are mentioned in terms of their transformations, similarities and relative relevance to decision-choice rationality. The houses of the 2 quantity platforms bring about the epistemic research of 2 mathematical platforms that permit the partition of the mathematical house in help of decision-choice area of data and non-knowledge construction into 4 cognitively separate yet interdependent cohorts whose houses are analyzed via the equipment and strategies of type conception. 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 house. the diversities within the epistemic foundations of the 2 mathematical structures are mentioned. The dialogue results in the institution of the necessity for fuzzy arithmetic and computing as a brand new process of reasoning in either specific and inexact sciences.
The mathematical constructions of the cohorts are imposed at the decision-choice procedure 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 buildings. The 4 groupings of versions and theories on decision-choice actions are then categorized as: 1) non-fuzzy and non-stochastic classification with distinct and entire information-knowledge constitution (no uncertainty), 2) non-fuzzy and stochastic category with certain and constrained information-knowledge constitution (stochastic uncertainty), three) fuzzy and non-stochastic type with complete and fuzzy information-knowledge constitution (fuzzy uncertainty) and four) Fuzzy and stochastic category with fuzzy and restricted information-knowledge constitution (fuzzy and stochastic uncertainties). a lot of these various periods of determination selection difficulties have their corresponding rationalities that are totally mentioned to give a unified logical process of theories on decision-choice procedure.
The quantity is concluded with epistemic discussions at the nature of contradictions and paradoxes considered as logical decision-choice difficulties within the classical paradigm, and the way those contradictions and paradoxes might be resolved via fuzzy paradigm and the tools and strategies of optimum fuzzy decision-choice rationality. The logical challenge of sorites paradox with its answer is given as an instance. viewers contains these operating within the parts of economies, decision-choice theories, philosophy of sciences, epistemology, arithmetic, desktop technology, engineering, cognitive psychology, fuzzy arithmetic and arithmetic of fuzzy-stochastic processes.