Lotfi A. Zadeh: On the man and his work

AbstractZadeh is one of the most impressive thinkers of the current time. An engineer by formation, although the range of his scientific interests is very broad, this paper only refers to his work towards reaching computation, mimicking ordinary reasoning, expressed in natural language, namely, with the introduction of fuzzy sets, fuzzy logic, and soft computing, as well as more recently, computing with words and perceptions

Some geometrical methods for constructing contradiction measures on Atanassov's intuitionistic fuzzy sets

Trillas et al. (1999, Soft computing, 3 (4), 197–199) and Trillas and Cubillo (1999, On non-contradictory input/output couples in Zadeh's CRI proceeding, 28–32) introduced the study of contradiction in the framework of fuzzy logic because of the significance of avoiding contradictory outputs in inference processes. Later, the study of contradiction in the framework of Atanassov's intuitionistic fuzzy sets (A-IFSs) was initiated by Cubillo and Castiñeira (2004, Contradiction in intuitionistic fuzzy sets proceeding, 2180–2186). The axiomatic definition of contradiction measure was stated in Castiñeira and Cubillo (2009, International journal of intelligent systems, 24, 863–888). Likewise, the concept of continuity of these measures was formalized through several axioms. To be precise, they defined continuity when the sets ‘are increasing’, denominated continuity from below, and continuity when the sets ‘are decreasing’, or continuity from above. The aim of this paper is to provide some geometrical construction methods for obtaining contradiction measures in the framework of A-IFSs and to study what continuity properties these measures satisfy. Furthermore, we show the geometrical interpretations motivating the measures

Crisp sets as classes of discontinuous fuzzy sets

AbstractThis paper aims to show how, by using a threshold-based approach, a path from imprecise information to a crisp ‘decision’ can be developed. It deals with the problem of the logical transformation of a fuzzy set into a crisp set. Such threshold arises from the ideas of contradiction and separation, and allows us to prove that crisp sets can be structurally considered as classes of discontinuous fuzzy sets. It is also shown that continuous fuzzy sets are computationally indistinguishable from some kind of discontinuous fuzzy sets

Vague heuristics

Even when they are defined with precision, one can often read and hear judgments about the vagueness of heuristics in debates about heuristic reasoning. This opinion is not just frequent but also quite reasonable. In fact, during the 1990s, there was a certain controversy concerning this topic that confronted two of the leading groups in the field of heuristic reasoning research, each of whom held very different perspectives. In the present text, we will focus on two of the papers published in Psychological Review, wherein the arguments of each of these groups were presented:

The WID-EC test for the detection and risk prediction of endometrial cancer

The incidence of endometrial cancer is rising. Measures to identify women at risk and to detect endometrial cancer earlier are required to reduce the morbidity triggered by the aggressive treatment required for advanced endometrial cancer. We developed the WID-EC (Women's cancer risk IDentification-Endometrial Cancer) test, which is based on DNA methylation at 500 CpG sites, in a discovery set of cervical liquid-based cytology samples from 1,086 women with and without an endometrial cancer (217 cancer cases and 869 healthy controls) with a worse prognosis (grade 3 or ≥stage IB). We validated the WID-EC test in an independent external validation set of 64 endometrial cancer cases and 225 controls. We further validated the test in 150 healthy women (prospective set) who provided a cervical sample as part of the routine Swedish cervical screening programme, 54 of whom developed endometrial cancer within three years of sample collection. The WID-EC test identified women with endometrial cancer with a receiver operator characteristic area under the curve (AUC) of 0.92 (95% CI: 0.88-0.97) in the external set and of 0.82 (95% CI: 0.74-0.89) in the prospective validation set. Using an optimal cutoff, cancer cases were detected with a sensitivity of 86% and a specificity of 90% in the external validation set, and a sensitivity and specificity of 52% and 98% respectively in the prospective validation set. The WID-EC test can identify women with or at risk of endometrial cancer

Activating Generalized Fuzzy Implications from Galois Connections

This paper deals with the relation between fuzzy implications and Galois connections, trying to raise the awareness that the fuzzy implications are indispensable to generalise Formal Concept Analysis. The concrete goal of the paper is to make evident that Galois connections, which are at the heart of some of the generalizations of Formal Concept Analysis, can be interpreted as fuzzy incidents. Thus knowledge processing, discovery, exploration and visualization as well as data mining are new research areas for fuzzy implications as they are areas where Formal Concept Analysis has a niche.F.J. Valverde-Albacete—was partially supported by EU FP7 project LiMoSINe, (contract 288024). C. Peláez-Moreno—was partially supported by the Spanish Government-CICYT project 2011-268007/TEC.Publicad

Multi-argument fuzzy measures on lattices of fuzzy sets

In this paper, we axiomatically introduce fuzzy multi-measures on bounded lattices. In particular, we make a distinction between four different types of fuzzy set multi-measures on a universe X, considering both the usual or inverse real number ordering of this lattice and increasing or decreasing monotonicity with respect to the number of arguments. We provide results from which we can derive families of measures that hold for the applicable conditions in each case

Enhanced Botrytis cinerea resistance of Arabidopsis plants grown in compost may be explained by increased expression of defense-related genes, as revealed by microarray analysis

Composts are the products obtained after the aerobic degradation of different types of organic matter waste and can be used as substrates or substrate/soil amendments for plant cultivation. There is a small but increasing number of reports that suggest that foliar diseases may be reduced when using compost, rather than standard substrates, as growing medium. The purpose of this study was to examine the gene expression alteration produced by the compost to gain knowledge of the mechanisms involved in compost-induced systemic resistance. A compost from olive marc and olive tree leaves was able to induce resistance against Botrytis cinerea in Arabidopsis, unlike the standard substrate, perlite. Microarray analyses revealed that 178 genes were differently expressed, with a fold change cut-off of 1, of which 155 were up-regulated and 23 were down-regulated in compost-grown, as against perlite-grown plants. A functional enrichment study of up-regulated genes revealed that 38 Gene Ontology terms were significantly enriched. Response to stress, biotic stimulus, other organism, bacterium, fungus, chemical and abiotic stimulus, SA and ABA stimulus, oxidative stress, water, temperature and cold were significantly enriched, as were immune and defense responses, systemic acquired resistance, secondary metabolic process and oxireductase activity. Interestingly, PR1 expression, which was equally enhanced by growing the plants in compost and by B. cinerea inoculation, was further boosted in compost-grown pathogen-inoculated plants. Compost triggered a plant response that shares similarities with both systemic acquired resistance and ABA-dependent/independent abiotic stress responses