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Über dieses Buch

The book offers a comprehensive survey of intuitionistic fuzzy logics. By reporting on both the author’s research and others’ findings, it provides readers with a complete overview of the field and highlights key issues and open problems, thus suggesting new research directions. Starting with an introduction to the basic elements of intuitionistic fuzzy propositional calculus, it then provides a guide to the use of intuitionistic fuzzy operators and quantifiers, and lastly presents state-of-the-art applications of intuitionistic fuzzy sets. The book is a valuable reference resource for graduate students and researchers alike.



Chapter 1. Elements of Intuitionistic Fuzzy Propositional Calculus

In classical logic (e.g., [1–4]), to each proposition (sentence) we juxtapose its truth value: truth – denoted by 1, or falsity – denoted by 0. In the case of fuzzy logic [5], this truth value is a real number in the interval [0, 1] and it is called “truth degree” or “degree of validity”.

Krassimir T. Atanassov

Chapter 2. Intuitionistic Fuzzy Predicate Logic

The idea for evaluation of the propositions was extended for predicates (see Barwise (Handbook of mathematical logic, 1989, [1]), Crossley et al. (What is mathematical logic? 1972, [2]), van Dalen (Logic and structure, 2013, [3]), Ebbinghaus et al. (Mathematical logic, 1994, [4]), Mendelson (Introduction to mathematical logic, 1964, [5]), Shoenfield (Mathematical logic, 2001, [6]) as follows (see, e.g., Atanassov (Intuitionistic fuzzy sets, 1999, [7]), Atanassov (Modern approaches in fuzzy sets, intuitionistic fuzzy sets, generalized nets and related topics, 2014, [8]), Atanassov and Gargov (Elements of intuitionistic fuzzy logic I, 1998, [9]), Gargov and Atanassov (Two results in intuitionistic fuzzy logic, 1992, [10]).

Krassimir T. Atanassov

Chapter 3. Intuitionistic Fuzzy Modal Logics

The first step of the development of the idea of intuitionistic fuzziness (see [1]), was related to introducing an intuitionistic fuzzy interpretation of the classical (standard) modal operators “necessity” and “possibility” (see, e.g., [2–5]). In the period 1988–1993, we defined eight new operators, extending the first two ones. In the end of last and in the beginning of this century, a lot of new operators were introduced. Here, we discuss the most interesting ones of them and study their basic properties.

Krassimir T. Atanassov

Chapter 4. Temporal and Multidimensional Intuitionistic Fuzzy Logics

The first results in temporal intuitionistic fuzzy logic appeared in 1990 (see Atanassov, Remark on a temporal intuitionistic fuzzy logic, 1990, [1]) on the basis of ideas from Karavaev (Foundations of temporal logic, 1983, [2]). However, the first example for their application was only proposed as early as 15 years later, in Atanassov (On intuitionistic fuzzy sets theory, 2012, [3]). The concept of the temporal IFL was extended to the concept of multidimensional intuitionistic fuzzy logic in a series of papersSzmidt, E.Kacprzyk, J. of the author together with E. Szmidt and J. Kacprzyk.

Krassimir T. Atanassov

Chapter 5. Conclusion

In the book, the author has collected his basic results related to intuitionistic fuzzy logics.

Krassimir T. Atanassov


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