Profile hidden Markov models (HMMs) based on classical HMMs have been widely applied for protein sequence identification. The formulation of the forward and backward variables in profile HMMs is made under statistical independence assumption of the probability theory. We propose a fuzzy profile HMM to overcome the limitations of that assumption and to achieve an improved alignment for protein s...

The paper discusses integration in possibility theory, both in an ordinal and in a numerical (behavioral) context. It is shown that in an ordinal context, the fuzzy integral has an important part in at least three areas: the extension of possibility measures to larger domains, the construction of product measures from marginals and the definition of conditional possibilities. In a numerical (be...

The purpose of this paper is to prove a Jensen type inequality for Choquet integrals with respect to a non-additive measure which was introduced by Choquet [1] and Sugeno [20]; Φ((C) ∫ fdμ) ≤ (C) ∫ Φ(f)dμ, where f is Choquet integrable, Φ : [0,∞) −→ [0,∞) is convex, Φ(α) ≤ α for all α ∈ [0,∞) and μf (α) ≤ μΦ(f)(α) for all α ∈ [0,∞). Furthermore, we give some examples assuring both satisfaction ...

In this paper, we generalize Ying’s model of linguistic quantifiers [M.S. Ying, Linguistic quantifiers modeled by Sugeno integrals, Artificial Intelligence, 170 (2006) 581-606] to intuitionistic linguistic quantifiers. An intuitionistic linguistic quantifier is represented by a family of intuitionistic fuzzy-valued fuzzy measures and the intuitionistic truth value (the degrees of satisfaction a...

We introduce a Choquet-Sugeno-like operator generalizing many operators for bounded nonnegative functions and monotone measures from the literature, e.g., Sugeno-like operator, Lovász Owen measure extensions, F-decomposition integral with respect to partition decomposition system, others. The new is based on concepts of dependence relation conditional aggregation operators, but it does not depe...

Keywords: Fuzzy measure Sugeno integral Choquet integral Stolarsky's inequality a b s t r a c t Recently Flores-Franulič, Román-Flores and Chalco-Cano proved the Stolarsky type inequality for Sugeno integral with respect to the Lebesgue measure k. The present paper is devoted to generalize this result by relaxing some of its requirements. Moreover, Stolar-sky inequality for Choquet integral is ...

The additivity property of the ``measure'', one of the most important concepts in mathematics, is often inflexible or too rigid to represent the many facets of human reasoning. In order to be able to express human subjectivity, recent researches proposed to replace this property by a weaker one, the ``monotonicity'' and called these non-additive monotonic measures ``fuzzy measures''. “Fuzzy int...

In this paper, we study fuzzy calculus in two main branches differential and integral.  Some rules for finding limit and $gH$-derivative of $gH$-difference, constant multiple of two fuzzy-valued functions are obtained and we also present fuzzy chain rule for calculating  $gH$-derivative of a composite function.  Two techniques namely,  Leibniz's rule and integration by parts are introduced for ...