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PurposeThe purpose of this research paper is to develop an algorithm/methodology for the reduction of a fuzzy recognizer through an algebraic concept such as homomorphism.Design/methodology/approachThe approach of this research is to introduce the concepts, compatible with the purpose of this paper, and then to find a necessary and sufficient condition for the reduction of a fuzzy recognizer.FindingsA fuzzy Σ‐recognizer M with non‐empty fuzzy initial state and the behavior A is reduced if and only if it is isomorphic to MA.Research limitations/implicationsThe research proposes an algebraic method for the reduction of a fuzzy recognizer. The problem of finding dispensable fuzzy productions of a regular fuzzy grammar may be tackled by the use this algebraic method, as fuzzy recognizers and fuzzy regular grammars are equivalent.Originality/valueThe concepts and the methodology are original. The work is useful to the researchers in the field of fuzzy automata, fuzzy grammars and pattern recognition.

A 30-year-old woman underwent Tc-pertechnetate scintigraphy for evaluation of thyrotoxicosis. The scintigraphy revealed hypervascular thyroid gland with markedly increased trapping function in both the lobes suggesting diagnosis of Graves disease. Incidentally, a hypervascular and pertechnetate avid focus was seen along the lateral margin of the right parotid gland. Pertechnetate avidity and site of uptake suggested possibility of Warthin tumor. Clinical examination and ultrasonography revealed a well-defined lesion in the superficial lobe of the right parotid gland favoring diagnosis of benign lesion. Postsurgery specimen confirmed diagnosis of Warthin tumor.

In this paper we establish interrelations between fuzzy direct revelation axiom (FDRA), fuzzy transitive-closure coherence axiom (FTCCA), fuzzy consistent-closure coherence axiom (FCCCA) and fuzzy intermediate congruence axiom (FICA). We also establish their relationships with weak fuzzy congruence axiom (WFCA), strong fuzzy congruence axiom (SFCA) and weak axiom of fuzzy revealed preference (WAFRP). Condition for equivalence of fuzzy Arrow axiom (FAA) and weak fuzzy congruence axiom (WFCA) on arbitrary domain is also given.