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Fuzzy logic in its 50th year : new developments, directions and challenges
Kahraman C., Kaymak U., Yazici A., Springer International Publishing, New York, NY, 2016. 404 pp. Type: Book (978-3-319310-91-6)
Date Reviewed: Mar 17 2017

Lotfi Zadeh published his initial work on fuzzy set theory in 1965. This volume celebrates a half century of progress in the research and applications of fuzzy set theory and fuzzy logic. The 16 contributions in this volume are divided into four parts: (1) a historical review of the origins of both fuzzy sets as a concept and its uses in support of decision making, (2) the mathematical foundations of fuzzy sets including descriptions of extensions to fuzzy set theory by their originators, (3) applications in several sciences, and (4) applications emphasizing management and decision making in mainly business contexts. Ten of the 16 papers are on applications in the last two parts of the book.

The two papers in the first part on the history of fuzzy sets are related. The first paper, by Dubois and Prade, shows how fuzzy set theory emerged from independent scholarly threads of studies of multivalued logics, optimization of problems with multiple criteria, and investigations into vagueness in natural languages. The second paper, by Kahraman, Onar, and Öztaysi, focuses on the decision-making process in ordinary fuzzy set theory and in its intuitionistic, hesitant, and fuzzy-2 extensions. The four embodiments of fuzzy set theory are compared in an example of determining the locations of charging stations for electric automobiles given five different criteria.

Three of the four papers in the second part, on mathematical foundations, describe extensions to fuzzy set theory using full mathematical formulation: intuitionistic fuzzy sets (Atanassov), hesitant fuzzy sets (Rodríguez, Martínez, Herrera, and Torra), and type 1 and type 2 fuzzy sets (Zarandi, Gamasaee, and Castillo). The fourth paper is an essay on “computing with words” by Trillas and de Soto in which they describe a context for the scientific study of language and for the exploration and modeling of commonsense reasoning. Language is the key concept because it is used both for thinking and for representing facts and concepts in the mind.

The third part’s emphasis is on applications in the sciences. There are four papers in this part. Three are reviews in application areas. The paper on fuzzy sets in earth and space sciences (Otay and Kahraman) reviews the literature of applications of fuzzy sets in astronomy, astrophysics, geology, meteorology, and oceanography. The subject matter in these disciplines must often deal with uncertainty. Even more uncertainty is inherent in the human sciences (especially psychology, economics, anthropology, and medicine). Smithson reviews applications of fuzzy sets and fuzzy logic in these disciplines. Although there has been continual activity in these areas, Smithson is convinced that the potential of fuzzy set theory in these areas has not been met due to many reasons, but they seem to be grouped together due to the failure of potential users to employ fuzzy set theory carefully and critically. Agricultural applications of fuzzy sets (Papageorgiou, Kokkinos, and Dikopoulou) are natural since agriculture has many variables, constraints, and criteria subject to vagueness and ambiguity. They find success in the applications they reviewed. Another paper, by Carlsson, Heikkilä, and Mezei, deals with the specific problem of predictively identifying situations in which a maintenance intervention must be made interrupting a process when there is plenty of data from many sensors and the data itself may be imprecise, subject to error, or partially incomplete. They describe a model in which fuzzy sets are coupled with measures of entropy to identify appropriate situations in which maintenance needs to be performed. There were no examples from physics and chemistry. In physics, fuzzy logic has been closely associated with quantum mechanics. In chemistry, a classic 1997 book, Fuzzy logic in chemistry edited by Dennis Rouvray [1], is a good place to begin.

The fourth part contains more applications with a business flavor. Of the six papers, five describe applications in specific areas, and one is methodological. The five specific application areas are truck and trailer routing with fuzzy constraints (Torres, Rosete, Cruz, and Verdegay), health service network design under epistemic uncertainty (Mousazadeh, Torabi, and Pishvaee), robotics and control systems leading to autonomous robots (Zarandi and Mosadegh), socioecological systems with multiple fuzzy criteria (Ervural, Ervural, and Kahraman), and supply chain planning (Naderi, Pishvaee, and Torabi). The methodological paper by Ebrahimnejad and Verdegay is on fuzzy linear programming problems in which all four cases of crisp or fuzzy inequalities and objective functions are combined as separate cases.

All of the papers in this volume receive high marks for quality of presentation, critical analysis, careful mathematics, well-developed examples with sample data, and extensive review of the literature.

Reviewer:  Anthony J. Duben Review #: CR145127 (1706-0352)
1) Rouvray, D. H. Fuzzy logic in chemistry. Academic Press, San Diego CA, 1997.
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