Iranian journal of fuzzy systems
Volume:15 Issue: 7, Sep-Oct 2018

Several fuzzy connectives, including those proposed by Lotfi Zadeh, can be seen as linear extensions of the Boolean connectives from the scale $\{0,1\}$ into the scale $[0,1]$. We discuss these extensions, in particular, we focus on the dualities arising from the Boolean dualities. These dualities allow to transfer the results from some particular class of extended Boolean functions, e.g., from conjunctive functions, into some other distinguished classes, e.g., into fuzzy implications. We also stress the role of aggregation functions in fuzzy set theory. Then we continue with several recent advances and new directions in aggregation theory. In particular, we discuss some generalizations of monotonicity, additivity and maxitivity issues. Finally, some applications of aggregation functions are sketched.

Super- and sub-additive transformations of aggregation functions have been recently introduced by Greco, Mesiar, Rindone and \v{S}ipeky [The superadditive and the subadditive transformations of integrals and aggregation functions, {\it Fuzzy Sets and Systems} {\bf 291} (2016), 40--53]. In this article we give a survey of the recent development regarding the existence of aggregation functions with a preassigned super- and sub-additive transformation, and address approximation of these transformations. The underpinning feature of the presented results is dependence of global properties of super- and sub-additive transformations on local properties of aggregation functions.

In this paper, we provide theoretical justification for the application of higher degree fuzzy transform in time series analysis. Under the assumption that a time series can be additively decomposed into a trend-cycle, a seasonal component and a random noise, we demonstrate that the higher degree fuzzy transform technique can be used for the estimation of the trend-cycle, which is one of the basic tasks in time series analysis. We prove that  high frequencies appearing in the seasonal component can be  arbitrarily suppressed and that random noise, as a stationary process, can be successfully decreased  using the fuzzy transform of higher degree with a reasonable adjustment of parameters of a generalized uniform fuzzy partition.

In this study, we consider two different inequivalent formulations of the logistic difference equation $x_{n+1}= \beta x_n(1- x_n),\ \ n=0,1,..., $ where $x_n$ is a sequence of fuzzy numbers and $\beta$ is a positive fuzzy number. The major contribution of this paper is to study the existence, uniqueness and global behavior of the solutions for two corresponding equations, using the concept of Hukuhara difference for fuzzy numbers. Finally, some examples are given to illustrate our results.

In this paper, we use the generalized differentiability concept to study the fuzzy transport equation. We consider transport equation in the homogeneous and non-homogeneous cases with fuzzy initial condition. We also present the solution when speed parameter is a fuzzy number. Our method is based on the construction of the solutions by employing Zadeh's extension principle.

In this note, we define the concepts of admissible relation and admissible partition for an arbitrary BL-general fuzzy automaton. In particular, a connection between the admissible partition and the quotient BL-general fuzzy automaton is presented. It is shown that if we use the maximal admissible partition, then we obtain a quotient BL-general fuzzy automaton and this quotient is minimal. Finally, we present some examples to clarify the notions and results of this paper.

In this paper, we introduce the notion of co-annihilator of a subset in a triangle algebra. It is shown that the co-annihilator of a subset is an interval valued residuated lattice (IVRL)-filter. Also, a special set of a triangle algebra is defined and the relationship between this set and co-annihilator of a subset in triangle algebra is considered. Finally, co-annihilators preserving congruence relation, or $CP$-congruence are defined and some results of them are given.

In this paper, at first we define the concepts of response function and accessible states of a complete residuated lattice-valued (for simplicity we write $\mathcal{L}$-valued) tree automaton with a threshold $c.$ Then, related to these concepts, we prove some lemmas and theorems that are applied in considering some decision problems such as finiteness-value and emptiness-value of recognizable tree languages. Moreover, we propose a reduction algorithm for $\mathcal{L}$-valued tree automata with a threshold $c.$ The goal of reducing an $ \mathcal{L}$-valued tree automaton is to obtain an $\mathcal{L}$-valued tree automaton with reduced number of states %that all of its states are accessible all of which are accessible, in addition it recognizes the same language as the first one given. We compare our algorithm with some other algorithms in the literature. Finally, utilizing the obtained results, we consider some fundamental decision problems for $\mathcal{L}$-valued tree automata including the membership-value, the emptiness-value, the finiteness-value, the intersection-value and the equivalence-value problems.

In this paper, we deal with games with fuzzy payoffs. We proved that players who are playing a zero-sum game with fuzzy payoffs against Nature are able to increase their joint payoff, and hence their individual payoffs by cooperating. It is shown that, a cooperative game with the fuzzy characteristic function can be constructed via the optimal game values of the zero-sum games with fuzzy payoffs against Nature at which players' combine their strategies and act like a single player. It is also proven that, the fuzzy characteristic function that is constructed in this way satisfies the superadditivity condition. Thus we considered a transition from two-person zero-sum games with fuzzy payoffs to cooperative games with fuzzy payoffs. The fair allocation of the maximum payoff (game value) of this cooperative game among players is done using the Shapley vector.

The Bosphorus (Istanbul Strait) that connects the continents of Europe and Asia is too complex due to geographical conditions and have a continuously increasing maritime traffic. The length of the Bosphorus which connect the Black Sea and the  Marmara Sea is 29.9 km. The number of ships (Tanker, general Cargo and bulk carrier) passing through the Istanbul strait was recorded as 42553 in 2016 and these transit ships cause more than half of the amount total ship emissions in the Bosphorus. The aim of this study is to estimate the PM amounts emitted from transit vessels passing through the Bosphorus by using fuzzy inference system in MATLAB. Total emissions from ships are expressed by surfaces allowing the analysis of the data according to the gross tonnage and the types of ships.