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FUZZY REASONING BASED ON CONCEPT OF SIMILARITY
Published in Kumar S. Ray, Soft Computing and Its Applications, Volume Two, 2014
Due to the essential vagueness and approximation of human thinking, the logical treat-ment of uncertainty is of increasing importance in artificial intelligence and related research. Nowadays, a considerable number of logical systems have been carried out as formalizations of vague concepts and AR (for example, seeGarrgov, Gerla, Goguen, Hajek, Lano, Marquis, Novak, Pavelka, Takeuti, and Titani). However, reasoning in these logics is still exact, that is in order to apply an inference rule, the antecedent clauses of this rule must be equal either to some premises or to logical axioms or previously proven formulas. Recently, Using proposed a new approach, in which we can really make ARs, that is, it is possible to allow the antecedent clauses of a rule to match its premises (or logical axioms of previously proven formulas) only approximately. The starting point is a similarity R defined in the set of propositional variables and its “natural” extension R to the whole set of propositional formulas. Subsequently, Biacino and Gerla generalized the definition of an approximate consequence operator given and clarified its connection with Pavelka’s logic.
FUZZY LOGIC
Published in Kumar S. Ray, Soft Computing and Its Applications, Volume One, 2014
Fuzzy Logic is not an appropriate tool for a complete formalization of NL. The aspect of vagueness and the relaxations of classical logical truth can only be handled by Fuzzy Logic. In the essay Vagueness: An Exercise in Logical Analysis (1937), Max Black first proposed the idea of vague sets and talked about three kinds of imprecision in NL: the generally, the ambiguity, and the vagueness. The generality is the power of a word to refer to a lot of things which can be very different each other. The ambiguity is the possibility of a linguistic expression to have many different meanings. The vagueness is the absence of precise confines in the reference of a lot of adjective and common names of human language, for example, "table", "house", "tall", "rich", "strong", "young", and so on. More precisely, vagueness is an approximate relation between a common name or a quantitative adjective and the objects of the world which can be referred by this name or predicated of this adjective. By the term "quantitative adjective" we mean an adjective which refers to qualities which have variable intensities, that is qualities which can be predicated of the subject more or less. Fuzzy Logic can completely handle the linguistic vagueness.
Function Optimization Using IBM Q
Published in Siddhartha Bhattacharyya, Mario Köppen, Elizabeth Behrman, Ivan Cruz-Aceves, Hybrid Quantum Metaheuristics, 2022
Siddhartha Bhattacharyya, Mario Köppen, Elizabeth Behrman, Ivan Cruz-Aceves
Most natural language is fuzzy, which involves vagueness and imprecision. A fuzzy logic proposition is a linguistic statement relating some perception without clearly defined boundaries. In other words, all truths in fuzzy logic are partial or approximate. Linguistic statements that tend to express subjective ideas and that can be interpreted slightly differently by various individuals typically involve fuzzy propositions. Fuzzy propositions are assigned to fuzzy sets. The objective and constraint functions are characterized by the membership functions in a fuzzy system, where membership in a classical subset, of a classical crisp sets of objects.
A novel decision-making method using fuzzy DEA credibility constrained and RC index
Published in Cogent Engineering, 2021
Rahmad Wisnu Wardana, Ilyas Masudin, Dian Palupi Restuputri, Adhi Nugraha
Decision-making based on expert’s opinion by data envelopment analysis (DEA) model requires crisp number. Vagueness is the main source of uncertainty because the assumption of the experts might not always be accurate. Vagueness refers to fuzzy input and output data from experts. To solve this problem, the integration of fuzzy DEA credibility constrained and relative closeness (RC) index is introduced. This approach transforms the traditional DEA models to be fuzzy events by using credibility measure. RC index was used to increase the discrimination power of traditional DEA. The credibility level of the proposed approach provides the flexibility for decision-maker to set their own acceptable credibility level in making decision. Moreover, the efficiency score of each DMU is decreased by increasing the credibility level. The preserved output data applying by the integration of RC index and credibility level are the cause of the discrimination power improvement.
A Fuzzy Semantic for BDI Logic
Published in Fuzzy Information and Engineering, 2021
Anderson Cruz, André V. dos Santos, Regivan H. N. Santiago, Benjamin Bedregal
On the other hand, the classical formal semantics is founded under the principles of bivalence, i.e. sentences are either true or false, and truth functionality which means that the truth value of logically complex sentences are given in function of the truth values of their subsentences [14]. Historically, problems that arise from these two notions when dealing with some incomparable information have motivated to discard the principle of bivalence and consider three values or, more generically, many truth values [15]. The set of these truth values can be finite as in [16] or infinite as proposed by Lotfi Zadeh when introduced the Fuzzy logic in [17]. Fuzzy logics model the uncertainty, vagueness, and ambiguity present in the real world by mapping sentences to truth degrees of the real interval [0; 1] and by the basis for the approximate reasoning, i.e. methods and methodologies to reasoning with imprecise inputs to obtain meaningful outputs. Inference in approximate reasoning has strong and important differences with the inference in classical logic. Indeed, in the former, the consequences of a set of fuzzy propositions depend on the underlying meaning of such fuzzy propositions. Thus, inference in approximate reasoning is a computation with the possible fuzzy sets which give meaning to the set of fuzzy propositions [18]. Thereby, one way to overcome the limitations of BDI is to fuzzify the BDI logic, i.e. consider a fuzzy semantics for it. Also contributed to the employment of the Approximate Reasoning in the BDI model. The approximate reasoning becomes the BDI model more faithful to the human being reasoning representation and maintains the model capable of reasoning about simpler rational agency.
Present and future of semantic web technologies: a research statement
Published in International Journal of Computers and Applications, 2021
The Semantic Web data space is distributed, dynamic, incoherent, and very sensitive to privacy issues. There are three domains that help in furthering the growth of the semantic web. The first domain is computational Intelligence, the second one is Evolutionary and Swarm Computing, and the last is knowledge representation methods. With the help of swarm computing we store large-scale data and provide reasoning over the web. Computational intelligence provides the methods for handling vagueness and uncertainty issues. Knowledge representation methods help store the data in a consistent and coherent manner.